BU 423 Searchable PDF 1-200
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CH1
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Aone-yearforwardcontractisanagree-
mentwhere
A. One side has the right to buy an asset for a certain price in one year's time.
B. One side has the obligation to buy an asset for a certain price in one year's time.
C. One side has the obligation to buy an asset for a certain price at some
time during the next year.
D. One side has the obligation to buy an asset for the maret price in one
year's time.
B. One side has the obligation to buy an asset for a certain price in one year's time.
Which of the following is true
A. $hen a CBO' call option onIBM is ex-
ercised" IBM issues more stoc
B. An American option can be exercised at any time during its life
C. An call option will always be exercised at maturity if the underlying
asset price is greater than the strie price
D. A put option will always be exercised at maturity if the strie price is
greater than the underlying asset price.
A. $hen a CBOE call option onIBM is exercised" IBM issues more stoc
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Which of the following is true
A. Both forward and futures contracts are traded on exchanges.
B. Forward contracts are traded on ex-
changes, but futures contracts are not.
C. Futures contracts are traded on ex-
changes, but forward contracts are not.
D. Neither futures contracts nor forward contracts are traded on
exchanges.
C. Futures contracts are traded on ex-
changes, but forward contracts are not.
Which of the following is NOT true
A. Futures contracts nearly always last longer than forward contracts
B. Futures contracts are standardized; forward contracts are not.
C. Delivery or final cash settlement usu-
ally takes place with forward
contracts; the same is not true of futures contracts.
D. Forward contracts usually have one specified delivery date; futures
contract often have a range of delivery dates.
A. Futures contracts nearly always last longer than forward contracts
In the corn futures contract a number of different types of corn can be delivered (with price adjustments specified by the exchange) and there are a number of different delivery locations. Which of the following is true
A. This flexibility tends increase the fu-
tures price.
B. This flexibility tends decrease the fu-
tures price.
C. This flexibility may increase and may decrease the futures price.
D. This flexibility has no effect on the futures price
B. This flexibility tends decrease the fu-
tures price.
The party with the short position choos-
es between the alternatives. The alterna-
tives therefore make the futures contract more attractive to the party with the short position. The lower the futures price the less attractive it is to the party with the short position. The benefit of the alter-
natives available to the party with the short position is therefore compensated for by the futures price being lower than it would otherwise be.
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A company enters into a short futures contract to sell 50,000 units of a com-
modity for 70 cents per unit. The initial margin is $4,000 and the maintenance margin is $3,000. What is the futures price per unit above which there will be a margin call?
A. 78 cents
B. 76 cents
C. 74 cents
D. 72 cents
D. 72 cents
There will be a margin call when more than $1000 has been lost from the mar-
gin account so that the balance in the account is below the maintenance mar-
gin level. Because the company is short, each one cent rise in the price leads to a loss or 0.01×50,000 or $500. A greater than 2 cent rise in the futures price will therefore lead to a margin call. The fu-
ture price is currently 70 cents. When the price rises above 72 cents there will be a margin call.
A company enters into a long futures contract to buy 1,000 units of a com-
modity for $60 per unit. The initial margin is $6,000 and the maintenance margin is $4,000. What futures price will allow $2,000 to be withdrawn from the margin account?
A. $58 B. $62 C. $64 D. $66
B. $62 Amounts in the margin account in excess of the initial margin can be withdrawn. Each $1 increase in the futures price leads to a gain of $1000. When the fu-
tures price increases by $2 the gain will be $2000 and this can be withdrawn. The futures price is currently $60. The answer is therefore $62.
One futures contract is traded where both the long and short parties are clos-
ing out existing positions. What is the resultant change in the open interest?
A. No change
B. Decrease by one
C. Decrease by two
D. Increase by one
B. Decrease by one
Who initiates delivery in a corn futures contract
A. The party with the long position
B. The party with the short position
C. Either party
D. The exchange
B. The party with the short position
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You sell one December futures contracts when the futures price is $1,010 per unit. Each contract is on 100 units and the initial margin per contract that you pro-
vide is $2,000. The maintenance margin per contract is $1,500. During the next day the futures price rises to $1,012 per unit. What is the balance of your margin account at the end of the day?
A. $1,800
B. $3,300
C. $2,200
D. $3,700
B. $3,300
The price has increased by $2. Because you have a short position you lose 2×100 or $200. The balance in the margin ac-
count therefore goes down from $3,500 to $3,300.
A hedger takes a long position in a fu-
tures contract on a commodity on No-
vember 1, 2012 to hedge an exposure on March 1, 2013. The initial futures price is $60. On December 31, 2012 the fu-
tures price is $61. On March 1, 2013 it is $64. The contract is closed out on March 1, 2013. What gain is recognized in the accounting year January 1 to December 31, 2013? Each contract is on 1000 units of the commodity.
A. $0
B. $1,000
C. $3,000
D. $4,000
D. $4,000
Hedge accounting is used. The whole of the gain or loss on the futures is therefore recognized in 2013. None is recognized in 2012. In this case the
gain is $4 per unit or $4,000 in total.
A speculator takes a long position in a futures contract on a commodity on No-
vember 1, 2012 to hedge an exposure on March 1, 2013. The initial futures price is $60. On December 31, 2012 the fu-
tures price is $61. On March 1, 2013 it is $64. The contract is closed out on March 1, 2013. What gain is recognized in the C. $3,000
In this case there is no hedge account-
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accounting year January 1 to December 31, 2013? Each contract is on 1000 units of the commodity.
A. $0
B. $1,000
C. $3,000
D. $4,000
ing. Gains or losses are accounted for as they are accrued. The price per unit increases by $3 in 2013. The total gain in 2013 is therefore $3,000.
.The frequency with which futures mar-
gin accounts are adjusted for gains and losses is
A. Daily
B. Weekly C. Monthly D. Quarterly
a
Margin accounts have the effect of
A. Reducing the risk of one party regret-
ting the deal and backing out B. Ensuring funds are available to pay traders when they make a profit C. Reducing systemic risk due to col-
lapse of futures markets
D. All of the above
D. All of the above
Initial margin requirements dramatically reduce the risk that a party will walk away from a futures contract. As a result they reduce the risk that the exchange clear-
ing house will not have enough funds to pays profits to traders. Furthermore, if traders are less likely to suffer losses because of counterparty defaults there is less systemic risk.
Which entity in the United States takes primary responsibility for regulating fu-
tures market?
A. Federal Reserve Board
B. Commodities Futures Trading Com-
mission (CFTC) C. Security and Exchange Commission (SEC)
D. US Treasury
B. Commodities Futures Trading Com-
mission (CFTC)
For a futures contract trading in April 2012, the open interest for a June 2012 contract, when compared to the open in-
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terest for Sept 2012 contracts, is usually
A. Higher
B. Lower
C. The same
D. Equally likely to be higher or lower
A. higher
The contracts which are close to maturity tend to have the highest open interest. However, during the maturity month itself the open interest declines.
Clearing houses are
A. Never used in futures markets and sometimes used in OTC markets
B. Used in OTC markets, but not in fu-
tures markets
C. Always used in futures markets and sometimes used in OTC
markets
D. Always used in both futures markets and OTC markets
C. Always used in futures markets and sometimes used in OTC
A haircut of 20% means that
A. A bond with a market value of $100 is considered to be worth $80 when used to satisfy a collateral request
B. A bond with a face value of $100 is considered to be worth $80 when used to satisfy a collateral request
C. A bond with a market value of $100 is considered to be worth $83.3
when used to satisfy a collateral request
D. A bond with a face value of $100 is considered to be worth $83.3
when used to satisfy a collateral request
A. A bond with a market value of $100 is considered to be worth $80 when used to satisfy a collateral request
A haircut is the amount the market price of asset is reduced by for the purposes of determining its value for collateral pur-
poses
With bilateral clearing, the number of agreements between four dealers, who trade with each other, is
A. 12 B. 1 C. 6 D. 2
C. 6
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.Which of the following best describes central clearing parties A. Help market participants to value de-
rivative transactions B. Must be used for all OTC derivative transactions
C. Are used for futures transactions
D. Perform a similar function to exchange clearing houses
D. Perform a similar function to exchange clearing houses
.Which of the following are cash settled A. All futures contracts
B. All option contracts
C. Futures on commodities D. Futures on stock indices
D. Futures on stock indices
A limit order
A. Is an order to trade up to a certain number of futures contracts at a
certain price
B. Is an order that can be executed at a specified price or one more
favorable to the investor
C. Is an order that must be executed within a specified period of time
D. None of the above
B. Is an order that can be executed at a specified price or one more
favorable to the investor
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1. The basis is defined as spot minus futures. A trader is hedging the sale of an asset with a short futures position. The basis increases unexpectedly. Which of the following is true? A. The hedger's position improves. B. The hedger's position worsens. C. The hedger's position sometimes worsens and sometimes improves. D. The hedger's position stays the same.
A. The hedger's position improves. The price received by the trader is the futures price plus the basis. It follows that the trader's position improves when the basis increases.
2. Futures contracts trade with every month as a delivery month. A company is hedging the purchase of the underlying asset on June 15. Which futures contract should it use? A. The June contract B. The July contract C. The May contract D. The August contract
B. The July contract As a general rule the futures maturity month should be as close as possible to but after the month when the asset will be purchased. In this case the asset will be purchased in June and so the best contract is the July contract.
3. On March 1 a commodity's spot price is $60 and its August futures price is $59. On July 1 the spot price is $64 and the August futures price is $63.50. A com-
pany entered into futures contracts on March 1 to hedge its purchase of the commodity on July 1. It closed out its position on July 1. What is the effective price (after taking account of hedging) paid by the company? A. $59.50
B. $60.50
C. $61.50
D. $63.50
A. $59.50
The user of the commodity takes a long futures position. The gain on the futures is 63.5059 or $4.50. The effective paid realized is therefore 644.50 or $59.50. This can also be calculated as the March 1 futures price (=59) plus the basis on July 1 (=0.50).
4. On March 1 the price of a commodity is $1,000 and the December futures price is $1,015. On November 1 the price is $980 and the December futures price is $981. A producer of the commodity 1 / 7
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entered into a December futures con-
tracts on March 1 to hedge the sale of the commodity on November 1. It closed out its position on November 1. What is the effective price (after taking account of hedging) received by the company for the commodity? A. $1,016
B. $1,001
C. $981
D. $1,014
D. $1,014
The producer of the commodity takes a short futures position. The gain on the futures is 1015981 or $34. The effec-
tive price realized is therefore 980+34 or $1014. This can also be calculated as the March 1 futures price (=1015) plus the November 1 basis (=1).
5. Suppose that the standard deviation of monthly changes in the price of com-
modity A is $2. The standard deviation of monthly changes in a futures price for a contract on commodity B (which is similar to commodity A) is $3. The cor-
relation between the futures price and the commodity price is 0.9. What hedge ratio should be used when hedging a one month exposure to the price of commod-
ity A? A. 0.60
B. 0.67
C. 1.45
D. 0.90
A. 0.60
The optimal hedge ratio is 0.9×(2/3) or 0.6.
6. A company has a $36 million portfolio with a beta of 1.2. The futures price for a contract on an index is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to reduce beta to 0.9?
A. Long 192 contracts B. Short 192 contracts
C. Long 48 contracts
D. Short 48 contracts
D. Short 48 contracts
To reduce the beta by 0.3 we need to short 0.3×36,000,000/(900×250) or 48 contracts.
7. A company has a $36 million portfolio with a beta of 1.2. The futures price for 2 / 7
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a contract on an index is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to increase beta to 1.8?
A. Long 192 contracts B. Short 192 contracts
C. Long 96 contracts
D. Short 96 contracts
C. Long 96 contracts
To increase beta by 0.6 we need to go long 0.6×36,000,000/(900×250) or 96 contracts
8. Which of the following is true? A. The optimal hedge ratio is the slope of the best fit line when the spot price (on the y-axis) is regressed against the futures price (on the x-axis). B. The optimal hedge ratio is the slope of the best fit line when the futures price (on the y-axis) is regressed against the spot price (on the x-axis). C. The optimal hedge ratio is the slope of the best fit line when the change in the spot price (on the y-axis) is regressed against the change in the futures price (on the x-axis).
D. The optimal hedge ratio is the slope of the best fit line when the change in the futures price (on the y-axis) is regressed against the change in the spot price (on the x-axis).
C. The optimal hedge ratio is the slope of the best fit line when the change in the spot price (on the y-axis) is regressed against the change in the futures price (on the x-axis).
The optimal hedge ratio reflects the ratio of movements in the spot price to move-
ments in the futures price.
9. Which of the following describes tailing the hedge?
A. A strategy where the hedge position is increased at the end of the life of the hedge
B. A strategy where the hedge position is increased at the end of the life of the futures contract
C. A more exact calculation of the hedge ratio when forward contracts are used for D. None of the above Tailing the hedge is a calculation appro-
priate when futures are used for hedging. It corrects for daily settlement
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hedging
D. None of the above
10. A company due to pay a certain amount of a foreign currency in the future decides to hedge with futures contracts. Which of the following best describes the advantage of hedging?
A. It leads to a better exchange rate be-
ing paid
B. It leads to a more predictable ex-
change rate being paid
C. It caps the exchange rate that will be paid
D. It provides a floor for the exchange rate that will be paid
B. It leads to a more predictable ex-
change rate being paid
Hedging is designed to reduce risk not increase expected profit. Options can be used to create a cap or floor on the price. Futures attempt to lock in the price
11. Which of the following best describes the capital asset pricing model?
A. Determines the amount of capital that is needed in particular situations
B. Is used to determine the price of fu-
tures contracts
C. Relates the return on an asset to the return on a stock index
D. Is used to determine the volatility of a stock index
C. Relates the return on an asset to the return on a stock index
CAPM relates the return on an asset to its beta. The parameter beta measures the sensitivity of the return on the asset to the return on the market. The latter is usually assumed to be the return on a stock index such as the S&P 500.
12. Which of the following best describes "stack and roll"?
A. Creates long-term hedges from short term futures contracts
B. Can avoid losses on futures contracts by entering into further futures contracts
C. Involves buying a futures contract with one maturity and selling a futures con-
tract with a different maturity
D. Involves two different exposures si-
multaneously
A. Creates long-term hedges from short term futures contracts
Stack and roll is a procedure where short maturity futures contracts are entered into. When they are close to maturity they are replaced by more short maturity fu-
tures contracts and so on. The result is the creation of a long term hedge from short-term futures contracts.
B. Dissimilarity between the underlying asset of the futures contract and the 4 / 7
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13. Which of the following increases ba-
sis risk? A. A large difference between the futures prices when the hedge is put in place and when it is closed out
B. Dissimilarity between the underlying asset of the futures contract and the hedger's exposure
C. A reduction in the time between the date when the futures contract is closed and its delivery month
D. None of the above
hedger's exposure
Basis is the difference between spot and futures at the time the hedge is closed out. This increases as the time between the date when the futures contract is put in place and the delivery month increas-
es. (C is not therefore correct). It also increases as the asset underlying the futures contract becomes more different from the asset being hedged. (B is there-
fore correct.)
14. Which of the following is a reason for hedging a portfolio with an index futures?
A. The investor believes the stocks in the portfolio will perform better than the market but is uncertain about the future performance of the market
B. The investor believes the stocks in the portfolio will perform better than the market and the market is expected to do well C. The portfolio is not well diversified and so its return is uncertain
D. All of the above
A. The investor believes the stocks in the portfolio will perform better than the market but is uncertain about the future performance of the market
Index futures can be used to remove the impact of the performance of the overall market on the portfolio. If the market is expected to do well hedging against the performance of the market is not appro-
priate. Hedging cannot correct for a poor-
ly diversified portfolio.
15. Which of the following does NOT de-
scribe beta?
A. A measure of the sensitivity of the return on an asset to the return on an index B. The slope of the best fit line when the return on an asset is regressed against the return on the market
C. The hedge ratio necessary to remove market risk from a portfolio
D. Measures correlation between futures prices and spot prices for a commodity
D. Measures correlation between futures prices and spot prices for a commodity
A, B, and C all describe beta but beta has nothing to do with the correlation between futures and spot prices for a commodity
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16. Which of the following is true?
A. Hedging can always be done more easily by a company's shareholders than by the company itself
B. If all companies in an industry hedge, a company in the industry can some-
times reduce its risk by choosing not to hedge C. If all companies in an industry do not hedge, a company in the industry can reduce its risk by hedging
D. If all companies in an industry do not hedge, a company is liable increase its risk by hedging
D. If all companies in an industry do not hedge, a company is liable increase its risk by hedging If all companies in a industry hedge, the price of the end product tends to reflect movements in relevant market variables. Attempting to hedge those movements can therefore increase risk.
Which of the following is necessary for tailing a hedge? A. Comparing the size in units of the position being hedged with the size in units of the futures contract
B. Comparing the value of the position being hedged with the value of one fu-
tures contract C. Comparing the futures price of the asset being hedged to its forward price D. None of the above
B. Comparing the value of the position being hedged with the value of one fu-
tures contract When tailing a hedge the optimal hedge ratio is applied to the ratio of the value of the position being hedged to the value of one futures contract.
19. A silver mining company has used futures markets to hedge the price it will receive for everything it will produce over the next 5 years. Which of the following is true?
A. It is liable to experience liquidity prob-
lems if the price of silver falls dramatical-
ly
B. It is liable to experience liquidity prob-
lems if the price of silver rises dramati-
cally
C. It is liable to experience liquidity prob-
lems if the price of silver rises dramati-
B. It is liable to experience liquidity prob-
lems if the price of silver rises dramati-
cally
The mining company shorts futures. It gains on the futures when the price de-
creases and loses when the price in-
creases. It may get margin calls which lead to liquidity problems when the price rises even though the silver in the ground is worth more.
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cally or falls dramatically
D. The operation of futures markets pro-
tects it from liquidity problems
Which of the following is true?
A. Gold producers should always hedge the price they will receive for their pro-
duction of gold over the next three years
B. Gold producers should always hedge the price they will receive for their pro-
duction of gold over the next one year
C. The hedging strategies of a gold producer should depend on whether it shareholders want exposure to the price of gold
D. Gold producers can hedge by buying gold in the forward market
C. The hedging strategies of a gold producer should depend on whether it shareholders want exposure to the price of gold
Some shareholders buy gold stocks to gain exposure to the price of gold. They do not want the company they invest in to hedge. In practice gold mining compa-
nies make their hedging strategies clear to shareholders.
20. A company will buy 1000 units of a certain commodity in one year. It decides to hedge 80% of its exposure using fu-
tures contracts. The spot price and the futures price are currently $100 and $90, respectively. The spot price and the fu-
tures price in one year turn out to be $112 and $110, respectively. What is the average price paid for the commodity?
A. $92
B. $96
C. $102
D. $106
B. $96
On the 80% (hedged) part of the com-
modity purchase the price paid will 112(11090) or $92. On the other 20% the price paid will be the spot price of $112. The weighted average of the two prices is 0.8×92+0.2×112 or $96.
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1.
The compounding frequency for an interest rate defines
A. The frequency with which inter-
est is paid
B. A unit of measurement for the interest rate
C. The relationship between the an-
nual interest rate and the monthly
interest rate
D. None of the above
B. A unit of measurement for the inter-
est rate
2.
An interest rate is 6% per annum with annual compounding. What is the equivalent rate with continu-
ous compounding?
A. 5.79% B. 6.21% C. 5.83% D. 6.18%
Answer: C
The equivalent rate with continuous compounding is ln(1.06) = 0.0583 or 5.83%.
3.
An interest rate is 5% per an-
num with continuous compound-
ing. What is the equivalent rate with semiannual compounding?
A. 5.06% B. 5.03% C. 4.97% D. 4.94%
A.
The equivalent rate with semiannual compounding is 2×(e0.05/21) = 0.0506 or 5.06%.
4.
An interest rate is 12% per an-
num with semiannual compound-
ing. What is the equivalent rate with quarterly compounding?
A. 11.83% B. 11.66% C. 11.77% D. 11.92%
A. 11.83%
The equivalent rate per quarter is 1.06-
1 2.956% . The annualized rate with quarterly compounding is four times this or 11.83%.
5.
The two-year zero rate is 6% and the three year zero rate is 6.5%. What is the forward rate for the D:
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third year? All rates are continu-
ously compounded.
A. 6.75% B. 7.0% C. 7.25% D. 7.5%
The forward rate for the third year is (3×0.0652×0.06)/(32) = 0.075 or 7.5%.
6.
The six-month zero rate is 8% per annum with semiannual com-
pounding. The price of a one-year bond that provides a coupon of 6% per annum semiannually is 97. What is the one-year continuously compounded zero rate?
A. 8.02%
B. 8.52%
C. 9.02%
D. 9.52%
C.
If the rate is R we must have
R = ln(1/0.9137) = 0.0902 or 9.02%.
7.
The yield curve is flat at 6% per annum. What is the value of an FRA where the holder receives interest at the rate of 8% per annum for a six-month period on a principal of $1,000 starting in two years? All rates are compounded semiannu-
ally.
A. $9.12 B. $9.02 C. $8.88 D. $8.63
D.
The value of the FRA is the value of re-
ceiving an extra 0.5×(0.080.06)×1000 = $10 in 2.5 years. This is 10/(1.035) = $8.63.
8.
Under liquidity preference theory, which of the following is always true?
A. The forward rate is higher than the spot rate when both have the same
maturity.
B. Forward rates are unbiased pre-
dictors of expected future spot D. Forward rates are higher than ex-
pected future spot rates.
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rates.
C. The spot rate for a certain matu-
rity is higher than the par yield for that
maturity.
D. Forward rates are higher than expected future spot rates.
9.
The zero curve is upward sloping. Define X as the 1-year par yield, Y as the 1- year zero rate and Z as the forward rate for the period between 1 and 1.5 year. Which of the following is true?
A. XislessthanYwhichislessthanZ
B. YislessthanXwhichislessthanZ
C. X is less than Z which is less than Y
D. Z is less than Y which is less than X
Answer: A
When the zero curve is upward sloping, the one-year zero rate is higher than the one-year par yield and the forward rate corresponding to the period be-
tween 1.0 and 1.5 years is higher than the one-year zero rate. The correct an-
swer is therefore A.
10.
Which of the following is true of the fed funds rate
A. It is the same as the Treasury rate
B. It is an overnight interbank rate
C. It is a rate for which collateral is posted
D. It is a type of repo rate
B. It is an overnight interbank rate
11.
The modified duration of a bond portfolio worth $1 million is 5 years. By approximately how much does the value of the portfolio change if all yields increase by 5 basis points?
B. Decrease of $2,500
When yields increase bond prices decrease. The proportional decrease is the modified duration times the yield increase. In this case, it is 3 / 7
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A. Increase of $2,500 B. Decrease of $2,500
C. Increase of $25,000 D. Decrease of $25,000
5×0.0005=0.0025. The decrease is therefore 0.0025×1,000,000 or $2,500.
12.
A company invests $1,000 in a five-year zero-coupon bond and $4,000 in a ten-year zero-coupon bond. What is the duration of the portfolio?
A. 6 years
B. 7 years
C. 8 years D. 9 years
D. 9 years
The duration of the first bond is 5 years and the duration of the second bond is 10 years. The duration of the portfolio is a weighted average with weights cor-
responding to the amounts invested in the bonds. It is 0.2×5+0.8×10=9 years.
13.
Which of the following is true of LIBOR
A. The LIBOR rate is free of credit risk
B. A LIBOR rate is lower than the Treasury rate when the two have the
same maturity
C. It is a rate used when borrowing and lending takes place between
banks
D. It is subject to favorable tax treatment in the U.S.
C. It is a rate used when borrowing and lending takes place between banks
14.
Which of following describes for-
ward rates?
A. Interest rates implied by current zero rates for future periods of time
B. Interest rate earned on an in-
vestment that starts today and last for n-years in the future without A. Interest rates implied by current zero rates for future periods of time
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coupons
C. The coupon rate that causes a bond price to equal its par (or prin-
cipal)value
D. A single discount rate that gives the value of a bond equal to its mar-
ket price when applied to all cash flows
15.
Which of the following is NOT a theory of the term structure A. Expectations theory
B. Market segmentation theory C. Liquidity preference theory D. Maturity preference theory
D. Maturity preference theory
16.
A repo rate is
A.An uncollateralized rate
B.A rate where the credit risk is relative high
C.The rate implicit in a transac-
tion where securities are sold and bought
back later at a higher price D.None of the above
C.The rate implicit in a transaction where securities are sold and bought back later at a higher price
17.
Bootstrapping involves
A.Calculating the yield on a bond
B.Working from short maturity in-
struments to longer maturity in-
struments
determining zero rates at each step
C.Working from long maturity in-
struments to shorter maturity in-
struments
determining zero rates at each B. Working from short maturity instru-
ments to longer maturity instruments
determining zero rates at each step
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step D.The calculation of par yields
18.
The zero curve is downward slop-
ing. Define X as the 1-year par yield, Y as the 1-year zero rate and Z as the forward rate for the period between 1 and 1.5 year. Which of the following is true?
A. XislessthanYwhichislessthanZ
B. YislessthanXwhichislessthanZ
C. X is less than Z which is less than Y
D. Z is less than Y which is less than X
D. Z is less than Y which is less than X
19.
.Which of the following is true?
A. When interest rates in the econ-
omy increase, all bond prices in-
crease
B. As its coupon increases, a bond's price decreases
C. Longer maturity bonds are al-
ways worth more that shorter ma-
turity
bonds when the coupon rates are the same
D. None of the above
D. None of the above
When interest rates increase the im-
pact of discounting is to make future cash flows worth less. Bond prices therefore decline. A is therefore wrong. As coupons increase a bond becomes more valuable because higher cash flows will be received. B is therefore wrong. When the coupon is higher than prevailing interest rates, longer maturi-
ty bonds are worth more than shorter maturity bonds. When it is less than prevailing interest rates, longer matu-
rity bonds are worth less than shorter maturity bonds. C is therefore not true. The correct answer is therefore D
20.
The six month and one-year rates are 3% and 4% per annum with semiannual compounding. Which A.
The six month rate is 1.5% per six 6 / 7
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of the following is closest to the one-year par yield expressed with semiannual compounding?
A. 3.99% B. 3.98% C. 3.97% D. 3.96%
months. The one year rate is 2% per six months. The one year par yield is the coupon that leads to a bond being worth par. A is the correct answer because (3.99/2)/1.015+(100+3.99/2)/1.022 = 100. The formula in the text can also be used to give the par yield as [(100-100/1.022)×2]/(1/1.015+1.022)=3.99.
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1. Which of the following is a consump-
tion asset?
A. The S&P 500 index
B. The Canadian dollar
C. Copper D. IBM stock
C. Copper A, B, and D are investment assets (held by at least some investors purely for in-
vestment purposes). C is a consumption asset.
2. An investor shorts 100 shares when the share price is $50 and closes out the position six months later when the share price is $43. The shares pay a dividend of $3 per share during the six months. How much does the investor gain? A. $1,000
B. $400
C. $700
D. $300
B. $400
The investor gains $7 per share because he or she sells at $50 and buys at $43. However, the investor has to pay the $3 per share dividend. The net profit is therefore 73 or $4 per share. 100 shares are involved. The total gain is therefore $400.
3. The spot price of an investment as-
set that provides no income is $30 and the risk-free rate for all maturities (with continuous compounding) is 10%. What is the three-year forward price? A. $40.50
B. $22.22
C. $33.00
D. $33.16
A. $40.50
The 3-year forward price is the spot price grossed up for 3 years at the risk-free rate. It is 30e0.1×3 =$40.50.
4. The spot price of an investment as-
set is $30 and the risk-free rate for all maturities is 10% with continuous com-
pounding. The asset provides an income of $2 at the end of the first year and at the end of the second year. What is the three-year forward price?
A. $19.67
B. $35.84
C. $45.15
D. $40.50
B. $35.84
The present value of the income is 2e-0.1×1+2e-0.1×2= $3.447. The three year forward price is obtained by sub-
tracting the present value of the income from the current stock price and then grossing up the result for three years at the risk-free rate. It is (303.447)e0.1×3 = $35.84.
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5. An exchange rate is 0.7000 and the six-month domestic and foreign risk-free interest rates are 5% and 7% (both ex-
pressed with continuous compounding). What is the six-month forward rate?
A. 0.7070
B. 0.7177
C. 0.7249
D. 0.6930
D. 0.6930
The six-month forward rate is 0.7000e^(0.050.07)×0.5=0.6930.
6. Which of the following is true? A. The convenience yield is always posi-
tive or zero. B. The convenience yield is always posi-
tive for an investment asset. C. The convenience yield is always neg-
ative for a consumption asset. D. The convenience yield measures the average return earned by holding futures contracts.
A. The convenience yield is always posi-
tive or zero. The convenience yield measures the benefit of owning an asset rather than having a forward/futures contract on an asset. For an investment asset it is al-
ways zero. For a consumption asset it is greater than or equal to zero.
7. A short forward contract that was ne-
gotiated some time ago will expire in three months and has a delivery price of $40. The current forward price for three-month forward contract is $42. The three month risk-free interest rate (with continuous compounding) is 8%. What is the value of the short forward contract?
A. +$2.00
B. $2.00
C. +$1.96
D. $1.96
D. $1.96
The contract gives one the obligation to sell for $40 when a forward price negoti-
ated today would give one the obligation to sell for $42. The value of the contract is the present value of $2 or 2e-0.08×0.25 = $1.96.
8. The spot price of an asset is positively correlated with the market. Which of the following would you expect to be true? A. The forward price equals the expected future spot price. B. The forward price is greater than the expected future spot price. C. The forward price is less than the ex-
pected future spot price. When the spot price is positively corre-
lated with the market the forward price is less than the expected future spot price. This is because the spot price is expect-
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C. The forward price is less than the ex-
pected future spot price. D. The forward price is sometimes greater and sometimes less than the ex-
pected future spot price.
ed to provide a return greater than the risk-free rate and the forward price is the spot price grossed up at the risk-free rate.
9. Which of the following describes the way the futures price of a foreign curren-
cy is quoted by the CME group?
A. The number of U.S. dollars per unit of the foreign currency
B. The number of the foreign currency per U.S. dollar
C. Some futures prices are always quot-
ed as the number of U.S. dollars per unit of the foreign currency and some are always quoted the other way round
D. There are no quotation conventions for futures prices
A. The number of U.S. dollars per unit of the foreign currency
The futures price is quoted as the num-
ber of US dollars per unit of the for-
eign currency. Spot exchange rates and forward exchange rates are sometimes quoted this way and sometimes quoted the other way round.
10. Which of the following describes the way the forward price of a foreign curren-
cy is quoted?
A. The number of U.S. dollars per unit of the foreign currency
B. The number of the foreign currency per U.S. dollar
C. Some forward prices are quoted as the number of U.S. dollars per unit of the foreign currency and some are quoted the other way round
D. There are no quotation conventions for forward prices
C. Some forward prices are quoted as the number of U.S. dollars per unit of the foreign currency and some are quoted the other way round
The futures price is quoted as the num-
ber of US dollars per unit of the for-
eign currency. Spot exchange rates and forward exchange rates are sometimes quoted this way and sometimes quoted the other way round.
11. Which of the following is NOT a rea-
son why a short position in a stock is closed out?
A. The investor with the short position chooses to close out the position
B. The lender of the shares issues in-
structions to close out the position
B. The lender of the shares issues in-
structions to close out the position
A, C, and D are all reasons why the short position might be closed out. B is not. The 3 / 7
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C. The broker is no longer able to borrow shares from other clients
D. The investor does not maintain mar-
gins required on his/her margin account
lender of shares cannot issue instruc-
tions to close out the short position.
12. Which of the following is NOT true?
A. Gold and silver are investment assets
B. Investment assets are held by signifi-
cant numbers of investors for investment purposes
C. Investment assets are never held for consumption
D. The forward price of an investment as-
set can be obtained from the spot price, interest rates, and the income paid on the asset
C. Investment assets are never held for consumption
Investment assets are sometimes held for consumption. Silver is an example. To be an investment asset, an asset has to be held for investment by at least some traders
13. What should a trader do when the one-year forward price of an asset is too low? Assume that the asset provides no income.
A. The trader should borrow the price of the asset, buy one unit of the asset and enter into a short forward contract to sell the asset in one year.
B. The trader should borrow the price of the asset, buy one unit of the asset and enter into a long forward contract to buy the asset in one year.
C. The trader should short the asset, in-
vest the proceeds of the short sale at the risk-free rate, enter into a short forward contract to sell the asset in one year D. The trader should short the asset, in-
vest the proceeds of the short sale at the risk-free rate, enter into a long forward contract to buy the asset in one year
D. The trader should short the asset, in-
vest the proceeds of the short sale at the risk-free rate, enter into a long forward contract to buy the asset in one year If the forward price is too low relative to the spot price the trader should short the asset in the spot market and buy it in the forward market.
14. Which of the following is NOT true about forward and futures contracts?
A. Forward contracts are more liquid than 4 / 7
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futures contracts
B. The futures contracts are traded on exchanges while forward contracts are traded in the over-the-counter market
C. In theory forward prices and futures prices are equal when there is no uncer-
tainty about future interest rates D. Taxes and transaction costs can lead to forward and futures prices being dif-
ferent
A. Forward contracts are more liquid than futures contracts
Futures contracts are more liquid than forward contracts. To unwind a futures position it is simply necessary to take an offsetting position. The statements in B, C, and D are correct
15. As the convenience yield increases, which of the following is true?
A. The one-year futures price as a per-
centage of the spot price increases
B. The one-year futures price as a per-
centage of the spot price decreases
C. The one-year futures price as a per-
centage of the spot price stays the same
D. Any of the above can happen
B. The one-year futures price as a per-
centage of the spot price decreases
As the convenience yield increases, the futures price declines relative to the spot price. This is because the convenience of owning the asset (as opposed to having a futures contract) becomes more impor-
tant.
16. As inventories of a commodity de-
cline, which of the following is true? A. The one-year futures price as a per-
centage of the spot price increases
B. The one-year futures price as a per-
centage of the spot price decreases
C. The one-year futures price as a per-
centage of the spot price stays the same
D. Any of the above can happen
B. The one-year futures price as a per-
centage of the spot price decreases
When inventories decline, the conve-
nience yield increases and the futures price as a percentage of the spot price declines.
17. Which of the following describes a known dividend yield on a stock?
A. The size of the dividend payments each year is known
B. Dividends per year as a percentage of today's stock price are known
C. Dividends per year as a percentage of the stock price at the time when divi-
dends are paid are known C. Dividends per year as a percentage of the stock price at the time when divi-
dends are paid are known The dividend yield is the dividend per year as a percent of the stock price at the time when the dividend is paid.
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D. Dividends will yield a certain return to a person buying the stock today
18. Which of the following is an argument used by Keynes and Hicks?
A. If hedgers hold long positions and speculators holds short positions, the fu-
tures price will tend to be higher than the expected future spot price
B. If hedgers hold long positions and speculators holds short positions, the fu-
tures price will tend to be lower than the expected future spot price
C. If hedgers hold long positions and speculators holds short positions, the fu-
tures price will tend to be lower than today's spot price
D. If hedgers hold long positions and speculators holds short positions, the fu-
tures price will tend to be higher than today's spot price
A. If hedgers hold long positions and speculators holds short positions, the fu-
tures price will tend to be higher than the expected future spot price
Keynes and Hicks argued that hedgers will be prepared to accept negative re-
turns on average because of the benefits of hedging whereas speculators require positive returns on average. This leads to A.
19. Which of the following describes con-
tango? A. The futures price is below the expect-
ed future spot price
B. The futures price is below today's spot price
C. The futures price is a declining func-
tion of the time to maturity
D. The futures price is above the expect-
ed future spot price
D. The futures price is above the expect-
ed future spot price Contango is defined as the futures price being above the expected future spot price. It is also sometimes used to de-
scribe the situation where the futures price is above the spot price.
20. Which of the following is true for a consumption commodity?
A. There is no limit to how high or low the futures price can be, except that the futures price cannot be negative
C. There is an upper limit to the futures price but no lower limit, except that the futures price cannot be negative
If the futures price of a consumption com-
modity becomes too high an arbitrageur will buy the commodity and sell futures to lock in a profit. An arbitrageur can-
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B. There is a lower limit to the futures price but no upper limit
C. There is an upper limit to the futures price but no lower limit, except that the futures price cannot be negative
D. The futures price can be determined with reasonable accuracy from the spot price and interest rates
not follow the opposite strategy of buying futures and selling or shorting the as-
set when the futures price is low. This is because consumption assets cannot be shorted . Furthermore, people who hold the asset in general do so because they need the asset for their business. They are not prepared to swap their position in the asset for a similar position in a futures. Consequently, there is an upper limit but no lower limit to the futures price.
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Which of the following is a use of a cur-
rency swap?
A. To exchange an investment in one cur-
rency for an investment in
another currency
B. To exchange borrowing in one curren-
cy for borrowings in another
currency
C. To take advantage situations where the tax rates in two countries are
different
D. All of the above
D. All of the above
A company can invest funds for five years at LIBOR minus 30 basis points. The five-year swap rate is 3%. What fixed rate of interest can the company earn by using the swap?
A. 2.4% B. 2.7% C. 3.0% D. 3.3%
B. 2.7% When the company invests at LIBOR mi-
nus 0.3% and then enters into a swap where it pays LIBOR and receives 3% it earns 2.7% per annum. Note that it is the bid rate that will apply to the swap.
Which of the following is true?
A. Principals are not usually exchanged in a currency swap
B. The principal amounts usually flow in the opposite direction to interest pay-
ments at the beginning of a currency swap and in the same direction as inter-
est payments at the end of the swap.
C. The principal amounts usually flow in the same direction as interest payments at the beginning of a currency swap and in the opposite
direction to interest payments at the end of the swap.
D. Principals are not usually specified in a currency swap
B. The principal amounts usually flow in the opposite direction to interest pay-
ments at the beginning of a currency swap and in the same direction as inter-
est payments at the end of the swap.
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Company X and Company Y have been offered the following rates
Fixed Rate Floating Rate
Co. X: 3.5% 3-month LIBOR plus 10bp
Co Y: 4.5% 3-month LIBOR plus 30 bp
Suppose that Company X borrows fixed and company Y borrows floating. If they enter into a swap with each other where the apparent benefits are shared equally, what is company X's effective borrowing rate?
A. 3-month LIBOR30bp B. 3.1%
C. 3-month LIBOR10bp D. 3.3%
A. 3-month LIBOR30bp The interest rate differential between the fixed rates is 100 basis points. The inter-
est rate differential between the floating rates is 20 basis points. The difference between the interest rates differentials is 100 - 20 = 80 basis points. This is the total apparent gain from the swap to the two sides. Since the benefits are shared equally company X should be able to borrow at 40 bp less than it is currently offered in the floating rate market, i.e., at LIBOR minus 30 bp.
Which of the following describes the five-year swap rate?
A. The fixed rate of interest which a swap market maker is prepared to pay in ex-
change for LIBOR on a 5-year swap
B. The fixed rate of interest which a swap market maker is prepared to
receive in exchange for LIBOR on a 5-year swap
C. The average of A and B
D. The higher of A and B
C. The average of A and B
The reference entity in a credit default swap is A. The buyer of protection
B. The seller of protection
C. The company or country whose de-
fault is being insured against
D. None of the above
C. The company or country whose de-
fault is being insured against
Which of the following describes an inter-
est rate swap?
A. The exchange of a fixed rate bond for 2 / 8
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a floating rate bond
B. A portfolio of forward rate agreements
C. An agreement to exchange interest at a fixed rate for interest at a
floating rate
D. All of the above
D. All of the above
Which of the following is true for an inter-
est rate swap?
A. A swap is usually worth close to zero when it is first negotiated
B. Each forward rate agreement underly-
ing a swap is worth close to zero
when the swap is first entered into
C. Comparative advantage is a valid rea-
son for entering into the swap
D. None of the above
A. A swap is usually worth close to zero when it is first negotiated
Which of the following is true for the party paying fixed in a newly negotiated inter-
est rate swap when the yield curve is upward sloping?
A. The early forward contracts underlying the swap have a positive value and the later ones have a negative value
B. The early forward contracts underlying the swap have a negative value and the later ones have a positive value
C. The swap is designed so that all for-
ward rates have zero value
D. Sometimes A is true and sometimes B is true
B. The early forward contracts underlying the swap have a negative value and the later ones have a positive value
A bank enters into a 3-year swap with company X where it pays LIBOR and re-
ceives 3.00%. It enters into an offsetting swap with company Y where is receives LIBOR and pays 2.95%. Which of the following is true:
C. If company X defaults, the swap with company Y continues
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A. If company X defaults, the swap with company Y is null and void
B. If company X defaults, the bank will be able to replace company X at
no cost
C. If company X defaults, the swap with company Y continues
D. The bank's bid-offer spread is 0.5 ba-
sis points
The bank`s bid-offer spread is 5 basis points not 0.5 basis points. The bank has quite separate transactions with X and Y. If one defaults, it still has to honor the swap with the other.
When LIBOR is used as the discount rate:
A. The value of a swap is worth zero immediately after a payment date
B. The value of a swap is worth zero immediately before a payment date
C. The value of the floating rate bond un-
derlying a swap is worth par immediately after a payment date
D. The value of the floating rate bond un-
derlying a swap is worth par immediately before a payment date
C. The value of the floating rate bond un-
derlying a swap is worth par immediately after a payment date
A company enters into an interest rate swap where it is paying fixed and receiv-
ing LIBOR. When interest rates increase, which of the following is true?
A. The value of the swap to the company increases
B. The value of the swap to the company decreases
C. The value of the swap can either in-
crease or decrease
D. The value of the swap does not change providing the swap rate
remains the same
A. The value of the swap to the company increases
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A floating for floating currency swap is equivalent to
A. Two interest rate swaps, one in each currency
B. A fixed-for-fixed currency swap and one interest rate swap
C. A fixed-for-fixed currency swap and two interest rate swaps, one in
each currency
D. None of the above
C. A fixed-for-fixed currency swap and two interest rate swaps, one in each cur-
rency
A floating-for-floating currency swap where the currency paid is X and the cur-
rency received is Y is equivalent to (a) a fixed-for-fixed currency swap where, say, 5% in currency X is paid and say, say, 4% in currency Y is received, (b) a regular interest rate swap where 5% in currency X is received and floating in currency X is paid and (c) a regular interest rate swap where 4% in currency Y is paid and floating in currency Y is received.
A floating-for-fixed currency swap is equivalent to
A. Two interest rate swaps, one in each currency
B. A fixed-for-fixed currency swap and one interest rate swap
C. A fixed-for-fixed currency swap and two interest rate swaps, one in
each currency
D. None of the above
B. A fixed-for-fixed currency swap and one interest rate swap
A floating-for-fixed currency swap where the floating rate is paid in currency X and the fixed rate is received in currency Y is equivalent to (a) a fixed-for-fixed curren-
cy swap where, say, 5% in currency X is paid and the fixed rate in currency Y is received, (b) a regular interest rate swap where 5% in currency X is received and floating in currency X is paid.
An interest rate swap has three years of remaining life. Payments are ex-
changed annually. Interest at 3% is paid and 12-month LIBOR is received. A exchange of payments has just taken place. The one-year, two-year and three- year LIBOR/swap zero rates are 2%, 3% and 4%. All rates an annually compound-
ed. What is the value of the swap as a percentage of the principal when LIBOR discounting is used.
B. 2.66 Suppose the principal 100. The val-
ue of the floating rate bond underly-
ing the swap is 100. The value of the fixed rate bond is 3/1.02+3/(1.03)2+103/ (1.04)3=97.34. The value of the swap is 5 / 8
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A. 0.00 B. 2.66 C. 2.06 D. 1.06
therefore 10097.34 = 2.66 or 2.66% of the principal
.A semi-annual pay interest rate swap where the fixed rate is 5.00% (with semi-annual compounding) has a re-
maining life of nine months. The six- month LIBOR rate observed three months ago was 4.85% with semi-annu-
al compounding. Today's three and nine month LIBOR rates are 5.3% and 5.8% (continuously compounded) respective-
ly. From this it can be calculated that the forward LIBOR rate for the peri-
od between three- and nine-months is 6.14% with semi-annual compounding. If the swap has a principal value of $15,000,000, what is the value of the swap to the party receiving a fixed rate of interest?
A. $74,250 B. $70,760 C. $11,250 D. $103,790
B. $70,760 C. $11,250 D. $103,790
The forward rates for the floating payment at time 9 months is 6.14%. The swap can be valued assuming that the fixed payments are 2.5% of principal at 3 months and 9 months and that the floating payments are 2.425% and 3.07% of the principal at 3 months and 9 months. The value of the swap to the party receiving fixed is therefore 1,000,000(0.025-0.02425)e-0.053×0.25+1,0
= - $70,760
Which of the following describes the way a LIBOR-in-arrears swap differs from a plain vanilla interest rate swap?
A. Interest is paid at the beginning of the accrual period in a LIBOR-in- arrears swap
B. Interest is paid at the end of the accru-
al period in a LIBOR-in-arrears swap
C. No floating interest is paid until the end of the life of the swap in a LIBOR-in-ar-
A. Interest is paid at the beginning of the accrual period in a LIBOR-in- arrears swap
6 / 8
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CH7
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rears swap, but fixed payments are made throughout the life of the swap
D. Neither floating nor fixed payments are made until the end of the life of the swap
In a fixed-for-fixed currency swap, 3% on a US dollar principal of $150 million is received and 4% on a British pound prin-
cipal of 100 million pounds is paid. The current exchange rate is 1.55 dollar per pound. Interest rates in both countries for all maturities are currently 5% (contin-
uously compounded). Payments are ex-
changed every year. The swap has 2.5 years left in its life. What is the value of the swap?
A. $7.15
B. $8.15
C. $9.15
D. $10.15
C. $9.15
The value of the British pound bond un-
derlying the swap is in millions of pounds
4e-0.05×0.5+4e-0.05×1.5+104e-0.05×2.5 = 99.39
The value of the U.S. dollar bond is in millions of dollars
4.5e-0.05×0.5+4.5e-0.05×1.5+154.5e-0.05×
= 144.91
The value of the swap is 144.91 - 99.39×1.55 = -9.15
Which of the following is a typical bid-of-
fer spread on the swap rate for a plain vanilla interest rate swap?
A. 3 basis points B. 8 basis points C. 13 basis points D. 18 basis points
A. 3 basis points
3 basis points is a typical spread be-
tween the bid and the offer on a plain vanilla interest rate swap.
Which of the following describes the five-year swap rate?
A. The rate on a five-year loan to a AA-rated company
B. The rate on a five-year loan to an A-rated company
C. The rate that can be earned over five years from a series of short-term
C. The rate that can be earned over five years from a series of short-term
loans to AA-rated companies
7 / 8
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loans to AA-rated companies
D. The rate that can be earned over five years from a series of short-term
loans to A-rated companies
8 / 8
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All main topics / Finance & Investment / Derivatives
Derivatives (239 Cards)
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1.A one-year forward contract is an agreement where
A.One side has the right to buy an asset for a certain price in
one year’s time.
B.One side has the obligation to buy an asset for a certain
price in one year’s time.
C.One side has the obligation to buy an asset for a certain
price at some time during the next year.
D.One side has the obligation to buy an asset for the market
price in one year’s time.
Answer: B
A one-year forward contract is an obligation to buy or sell in one
year’s time for a predetermined price. By contrast, an option is the
right to buy or sell.
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2.Which of the following is NOT true A.When a CBOE call option on IBM is exercised, IBM issues
more stock
B.An American option can be exercised at any time during its
life
C.An call option will always be exercised at maturity if the
underlying asset price is greater than the strike price
D.A put option will always be exercised at maturity if the strike
price is greater than the underlying asset price.
Answer: A
When an IBM call option is exercised the option seller must buy
shares in the market to sell to the option buyer. IBM is not involved
in any way. Answers B, C, and D are true.
Flashcard set info:
Author: CoboCards-User
Main topic: Finance & Investment
Topic: Derivatives
Published: 27.10.2015
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A one-year call option on a stock with a strike price of $30
costs $3; a one-year put option on the stock with a strike price
of $30 costs $4. Suppose that a trader buys two call options
and one put option. The breakeven stock price above which the
trader makes a profit is
A.$35
B.$40
C.$30
D.$36
Answer: A
When the stock price is $35, the two call options provide a payoff of
2×(35−30) or $10. The put option provides no payoff. The total cost
of the options is 2×3+ 4 or $10. The stock price in A, $35, is
therefore the breakeven stock price above which the position is
profitable because it is the price for which the cost of the options
equals the payoff.
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4.A one-year call option on a stock with a strike price of $30
costs $3; a one-year put option on the stock with a strike price
of $30 costs $4. Suppose that a trader buys two call options
and one put option. The breakeven stock price below which the
trader makes a profit is
A.$25
B.$28
C.$26
D.$20
Answer: D
When the stock price is $20 the two call options provide no payoff.
The put option provides a payoff of 30−20 or $10. The total cost of
the options is 2×3+ 4 or $10. The stock price in D, $20, is therefore
the breakeven stock price below which the position is profitable
because it is the price for which the cost of the options equals the
payoff.
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Which of the following is approximately true when size is
measured in terms of the underlying principal amounts or
value of the underlying assets
A.The exchange-traded market is twice as big as the over-the-
counter market.
B.The over-the-counter market is twice as big as the exchange-
traded market.
C.The exchange-traded market is ten times as big as the over-
the-counter market.
D.The over-the-counter market is ten times as big as the
exchange-traded market.
Answer: D
The OTC market is about $600 trillion whereas the exchange-traded
market is about $60 trillion.
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Which of the following best describes the term “spot price”
A.The price for immediate delivery
B.The price for delivery at a future time
C.The price of an asset that has been damaged
D.The price of renting an asset
Answer: A
The spot price is the price for immediate delivery. The futures or
forward price is the price for delivery in the future
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Which of the following is true about a long forward contract
A.The contract becomes more valuable as the price of the
asset declines
B.The contract becomes more valuable as the price of the
asset rises
C.The contract is worth zero if the price of the asset declines
after the contract has been entered into
D.The contract is worth zero if the price of the asset rises after
the contract has been entered into
Answer: B
A long forward contract is an agreement to buy the asset at a
predetermined price. The contract becomes more attractive as the
market price of the asset rises. The contract is only worth zero when
the predetermined price in the forward contract equals the current
forward price (as it usually does at the beginning of the contract).
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An investor sells a futures contract an asset when the futures
price is $1,500. Each contract is on 100 units of the asset. The
contract is closed out when the futures price is $1,540. Which
of the following is true
A.The investor has made a gain of $4,000
B.The investor has made a loss of $4,000
C.The investor has made a gain of $2,000
D.The investor has made a loss of $2,000
Answer: B
An investor who buys (has a long position) has a gain when a
futures price increases. An investor who sells (has a short position)
has a loss when a futures price increases.
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Which of the following describes European options?
A.Sold in Europe
B.Priced in Euros
C.Exercisable only at maturity
D.Calls (there are no European puts)
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Answer: C
European options can be exercised only at maturity. This is in
contrast to American options which can be exercised at any time.
The term “European” has nothing to do with geographical location,
currencies, or whether the option is a call or a put.
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Which of the following is NOT true
A.A call option gives the holder the right to buy an asset by a
certain date for a certain price
B.A put option gives the holder the right to sell an asset by a
certain date for a certain price
C.The holder of a call or put option must exercise the right to
sell or buy an asset
D.The holder of a forward contract is obligated to buy or sell an
asset
Answer: C
The holder of a call or put option has the right to exercise the option
but is not required to do so. A, B, and C are correct
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Which of the following is NOT true about call and put options:
A.An American option can be exercised at any time during its
life
B. A European option can only be exercised only on the
maturity date
C.Investors must pay an upfront price (the option premium) for
an option contract
D.The price of a call option increases as the strike price
increases
Answer: D
A call option is the option to buy for the strike price. As the strike
price increases this option becomes less attractive and is therefore
less valuable. A, B, and C are true.
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The price of a stock on July 1 is $57. A trader buys 100 call
options on the stock with a strike price of $60 when the option
price is $2. The options are exercised when the stock price is
$65. The trader’s net profit is
A. $700
B.$500
C. $300
D.$600
Answer: C
The payoff from the options is 100×(65-60) or $500. The cost of the
options is 2×100 or $200. The net profit is therefore 500−200 or
$300.
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The price of a stock on February 1 is $124. A trader sells 200
put options on the stock with a strike price of $120 when the
option price is $5. The options are exercised when the stock
price is $110. The trader’s net profit or loss is
A. Gain of $1,000
B.Loss of $2,000
C.Loss of $2,800
D.Loss of $1,000
Answer: D
The payoff that must be made on the options is 200×(120−110) or
$2000. The amount received for the options is 5×200 or $1000. The
net loss is therefore 2000−1000 or $1000.
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The price of a stock on February 1 is $84. A trader buys 200 put
options on the stock with a strike price of $90 when the option
price is $10. The options are exercised when the stock price is
$85. The trader’s net profit or loss is
A.Loss of $1,000
B.Loss of $2,000
C.Gain of $200
D.Gain of $1000
Answer: A
The payoff is 90−85 or $5 per option. For 200 options the payoff is
therefore 5×200 or $1000. However the options cost 10×200 or
$2000. There is therefore a net loss of $1000.
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The price of a stock on February 1 is $48. A trader sells 200 put
options on the stock with a strike price of $40 when the option
price is $2. The options are exercised when the stock price is
$39. The trader’s net profit or loss is
A. Loss of $800
B.Loss of $200
C. Gain of $200
D.Loss of $900
Answer: C
The payoff is 40−39 or $1 per option. For 200 options the payoff is
therefore 1×200 or $200. However the premium received by the
trader is 2×200 or $400. The trader therefore has a net gain of
$200.
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16
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16.A speculator can choose between buying 100 shares of a
stock for $40 per share and buying 1000 European call options
on the stock with a strike price of $45 for $4 per option. For
second alternative to give a better outcome at the option
maturity, the stock price must be above
A.$45
B.$46
C.$55
D.$50
Answer: D
When the stock price is $50 the first alternative leads to a position in
the stock worth 100×50 or $5000. The second alternative leads to a
payoff from the options of 1000×(50−45) or $5000. Both alternatives
cost $4000. It follows that the alternatives are equally profitable
when the stock price is $50. For stock prices above $50 the option
alternative is more profitable.
17
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A company knows it will have to pay a certain amount of a
foreign currency to one of its suppliers in the future. Which of
the following is true
A.A forward contract can be used to lock in the exchange rate
B.A forward contract will always give a better outcome than an
option
C.An option will always give a better outcome than a forward
contract
D.An option can be used to lock in the exchange rate
Answer: A
A forward contract ensures that the effective exchange rate will
equal the current forward exchange rate. An option provides
insurance that the exchange rate will not be worse than a certain
level, but requires an upfront premium. Options sometimes give a
better outcome and sometimes give a worse outcome than
forwards.
18
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A short forward contract on an asset plus a long position in a
European call option on the asset with a strike price equal to
the forward price is equivalent to
A. A short position in a call option
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B.A short position in a put option
C. A long position in a put option
D.None of the above
Answer: C
Suppose that ST is the final asset price and K is the strike
price/forward price. A short forward contract leads to a payoff of
K−ST. A long position in a European call option leads to a payoff of
max(ST−K, 0). When added together we see that the total position
leads to a payoff of max(0, K−ST), which is the payoff from a long
position in a put option. C can also be seen to be true by plotting the
payoffs as a function of the final stock price. 19
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A trader has a portfolio worth $5 million that mirrors the
performance of a stock index. The stock index is currently
1,250. Futures contracts trade on the index with one contract
being on 250 times the index. To remove market risk from the
portfolio the trader should
A. Buy 16 contracts
B.Sell 16 contracts
C.Buy 20 contracts
D.Sell 20 contracts
Answer: B
One futures contract protects a portfolio worth 1250×250. The
number of contract required is therefore 5,000,000/(1250×250)=16. To remove market risk we need to gain on the contracts when the
market declines. A short futures position is therefore required.
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Which of the following best describes a central clearing party
A.It is a trader that works for an exchange
B.It stands between two parties in the over-the-counter market
C.It is a trader that works for a bank
D.It helps facilitate futures trades
Answer: B
A central clearing party (CCP) is a clearing house that stands
between two parties in the over-the-counter market. It serves the
same purpose as an exchange clearing house.
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21
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Which of the following is true
A.Both forward and futures contracts are traded on exchanges.
B. Forward contracts are traded on exchanges, but futures
contracts are not.
C.Futures contracts are traded on exchanges, but forward
contracts are not.
D.Neither futures contracts nor forward contracts are traded on
exchanges.
Answer: C
Futures contracts trade only on exchanges. Forward contracts trade
only in the over-the-counter market.
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Which of the following is NOT true
A.Futures contracts nearly always last longer than forward
contracts
B.Futures contracts are standardized; forward contracts are
not.
C.Delivery or final cash settlement usually takes place with
forward contracts; the same is not true of futures contracts.
D.Forward contracts usually have one specified delivery date;
futures contract often have a range of delivery dates.
Answer: A
Forward contracts often last longer than futures contracts. B, C, and
D are true
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23
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In the corn futures contract a number of different types of corn
can be delivered (with price adjustments specified by the
exchange) and there are a number of different delivery
locations. Which of the following is true
A. This flexibility tends increase the futures price.
B.This flexibility tends decrease the futures price.
C.This flexibility may increase and may decrease the futures
price.
D.This flexibility has no effect on the futures price
Answer: B
The party with the short position chooses between the alternatives.
The alternatives therefore make the futures contract more attractive
to the party with the short position. The lower the futures price the
less attractive it is to the party with the short position. The benefit of
the alternatives available to the party with the short position is
therefore compensated for by the futures price being lower than it
would otherwise be.
24
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A company enters into a short futures contract to sell 50,000
units of a commodity for 70 cents per unit. The initial margin is
$4,000 and the maintenance margin is $3,000. What is the
futures price per unit above which there will be a margin call?
A.78 cents
B.76 cents
C.74 cents
D.72 cents Answer: D
There will be a margin call when more than $1000 has been lost
from the margin account so that the balance in the account is below
the maintenance margin level. Because the company is short, each
one cent rise in the price leads to a loss or 0.01×50,000 or $500. A
greater than 2 cent rise in the futures price will therefore lead to a
margin call. The future price is currently 70 cents. When the price
rises above 72 cents there will be a margin call.
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25
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A company enters into a long futures contract to buy 1,000
units of a commodity for $60 per unit. The initial margin is
$6,000 and the maintenance margin is $4,000. What futures
price will allow $2,000 to be withdrawn from the margin
account? A. $58
B. $62
C. $64
D. $66
Answer: B
Amounts in the margin account in excess of the initial margin can be
withdrawn. Each $1 increase in the futures price leads to a gain of
$1000. When the futures price increases by $2 the gain will be
$2000 and this can be withdrawn. The futures price is currently $60.
The answer is therefore $62.
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One futures contract is traded where both the long and short
parties are closing out existing positions. What is the resultant
change in the open interest?
A. No change
B.Decrease by one
C.Decrease by two
D.Increase by one
Answer: B
The open interest goes down by one. There is one less long position
and one less short position.
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Who initiates delivery in a corn futures contract
A.The party with the long position
B.The party with the short position
C.Either party
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D.The exchange
Answer: B
The party with the short position initiates delivery by sending a
“Notice of Intention to Deliver” to the exchange. The exchange has a
procedure for choosing a party with a long position to take delivery.
28
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You sell one December futures contracts when the futures
price is $1,010 per unit. Each contract is on 100 units and the
initial margin per contract that you provide is $2,000. The
maintenance margin per contract is $1,500. During the next day
the futures price rises to $1,012 per unit. What is the balance of
your margin account at the end of the day? A.$1,800
B.$3,300
C.$2,200
D.$3,700
Answer: B
The price has increased by $2. Because you have a short position
you lose 2×100 or $200. The balance in the margin account
therefore goes down from $3,500 to $3,300.
29
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A hedger takes a long position in a futures contract on a
commodity on November 1, 2012 to hedge an exposure on
March 1, 2013. The initial futures price is $60. On December 31,
2012 the futures price is $61. On March 1, 2013 it is $64. The
contract is closed out on March 1, 2013. What gain is
recognized in the accounting year January 1 to December 31,
2013? Each contract is on 1000 units of the commodity.
A. $0
B.$1,000
C.$3,000
D.$4,000
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Answer: D
Hedge accounting is used. The whole of the gain or loss on the
futures is therefore recognized in 2013. None is recognized in 2012.
In this case the gain is $4 per unit or $4,000 in total.
30
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A speculator takes a long position in a futures contract on a
commodity on November 1, 2012 to hedge an exposure on
March 1, 2013. The initial futures price is $60. On December 31,
2012 the futures price is $61. On March 1, 2013 it is $64. The
contract is closed out on March 1, 2013. What gain is
recognized in the accounting year January 1 to December 31,
2013? Each contract is on 1000 units of the commodity.
A. $0
B. $1,000
C.$3,000
D.$4,000
Answer: C
In this case there is no hedge accounting. Gains or losses are
accounted for as they are accrued. The price per unit increases by
$3 in 2013. The total gain in 2013 is therefore $3,000.
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The frequency with which futures margin accounts are
adjusted for gains and losses is
A.Daily
B.Weekly
C.Monthly
D.Quarterly
Answer: A
In futures contracts margin accounts are adjusted for gains or
losses daily.
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32
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Margin accounts have the effect of
A.Reducing the risk of one party regretting the deal and
backing out
B. Ensuring funds are available to pay traders when they make
a profit
C.Reducing systemic risk due to collapse of futures markets
D.All of the above
Answer: D
Initial margin requirements dramatically reduce the risk that a party
will walk away from a futures contract. As a result they reduce the
risk that the exchange clearing house will not have enough funds to
pays profits to traders. Furthermore, if traders are less likely to
suffer losses because of counterparty defaults there is less systemic
risk.
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Which entity in the United States takes primary responsibility
for regulating futures market?
A.Federal Reserve Board
B.Commodities Futures Trading Commission (CFTC)
C.Security and Exchange Commission (SEC)
D.US Treasury
Answer: B
The CFTC has primary responsibility for regulating futures markets
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34
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For a futures contract trading in April 2012, the open interest
for a June 2012 contract, when compared to the open interest
for Sept 2012 contracts, is usually
A.Higher
B.Lower
C.The same
D.Equally likely to be higher or lower
Answer: A
The contracts which are close to maturity tend to have the highest
open interest. However, during the maturity month itself the open
interest declines.
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15.Clearing houses are
A.Never used in futures markets and sometimes used in OTC
markets
B.Used in OTC markets, but not in futures markets
C.Always used in futures markets and sometimes used in OTC
markets
D.Always used in both futures markets and OTC markets
Answer: C
Clearing houses are always used by exchanges trading futures.
Increasingly, OTC products are cleared through CCPs, which are a
type of clearing house.
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A haircut of 20% means that
A.A bond with a market value of $100 is considered to be worth
$80 when used to satisfy a collateral request
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B. A bond with a face value of $100 is considered to be worth
$80 when used to satisfy a collateral request
C.A bond with a market value of $100 is considered to be worth
$83.3 when used to satisfy a collateral request
D.A bond with a face value of $100 is considered to be worth
$83.3 when used to satisfy a collateral request
Answer: A
A haircut is the amount the market price of asset is reduced by for
the purposes of determining its value for collateral purposes. A is
therefore correct.
37
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With bilateral clearing, the number of agreements between four
dealers, who trade with each other, is
A.12
B.1
C.6
D.2
Answer: C
Suppose the dealers are W, X, Y , and Z. The agreements are
between W and X, W and Y, W and Z, X and Y, X and Z, and Y and
Z. There are therefore a total of 6 agreements.
38
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Which of the following best describes central clearing parties
A.Help market participants to value derivative transactions
B.Must be used for all OTC derivative transactions
C.Are used for futures transactions
D.Perform a similar function to exchange clearing houses
Answer: D
CCPs do for the OTC market what exchange clearing houses do for
the exchange-traded market. The correct answer is therefore D.
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CCPs must be used for most standard OTC derivatives
transactions, but not for all derivatives transactions.
39
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Which of the following are cash settled
A.All futures contracts
B.All option contracts
C.Futures on commodities
D.Futures on stock indices
Answer: D
Futures on stock indices are usually cash settled. The rest are
settled by delivery of the underlying assets
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A limit order
A.Is an order to trade up to a certain number of futures
contracts at a certain price
B. Is an order that can be executed at a specified price or one
more favorable to the investor
C.Is an order that must be executed within a specified period of
time
D.None of the above
Answer: B
In a limit order a trader specifies the worst price (from the trader’s
perspective) at which the trade can be carried out.
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The compounding frequency for an interest rate defines
A.The frequency with which interest is paid
B. A unit of measurement for the interest rate
C.The relationship between the annual interest rate and the
monthly interest rate
D.None of the above
Answer: B
The compounding frequency is a unit of measurement. The
frequency with which interest is paid may be different from the
compounding frequency used for quoting the rate.
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An interest rate is 6% per annum with annual compounding.
What is the equivalent rate with continuous compounding?
A.5.79%
B.6.21%
C.5.83%
D.6.18%
Answer: C
The equivalent rate with continuous compounding is ln(1.06) =
0.0583 or 5.83%.
Rc= mln(1+ Rm/m)
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An interest rate is 5% per annum with continuous
compounding. What is the equivalent rate with semiannual
compounding?
A.5.06%
B.5.03%
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C.4.97%
D.4.94%
Answer: A
The equivalent rate with semiannual compounding is 2×(e0.05/2−1)
= 0.0506 or 5.06%.
m(eRc/m -1) =Rm
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An interest rate is 12% per annum with semiannual
compounding. What is the equivalent rate with quarterly
compounding?
A. 11.83%
B.11.66%
C.11.77%
D.11.92%
Answer: A
The equivalent rate per quarter is 1.06^0.5 -1=2.956% . The
annualized rate with quarterly compounding is four times this or
11.83%.
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The two-year zero rate is 6% and the three year zero rate is
6.5%. What is the forward rate for the third year? All rates are
continuously compounded.
A.6.75%
B.7.0%
C.7.25%
D.7.5%
Answer: D
The forward rate for the third year is (3×0.065−2×0.06)/(3−2) =
0.075 or 7.5%
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The six-month zero rate is 8% per annum with semiannual
compounding. The price of a one-year bond that provides a
coupon of 6% per annum semiannually is 97. What is the one-
year continuously compounded zero rate?
A.8.02%
B.8.52%
C.9.02%
D.9.52%
Answer: C
If the rate is R we must have
97= 3/1.04+103e^-R*1
or
e^-R= (97-3/1.04)/103 =0.9137
so that R = ln(1/0.9137) = 0.0902 or 9.02%.
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The yield curve is flat at 6% per annum. What is the value of an
FRA where the holder receives interest at the rate of 8% per
annum for a six-month period on a principal of $1,000 starting
in two years? All rates are compounded semiannually.
A.$9.12
B.$9.02
C.$8.88
D.$8.63
Answer: D
The value of the FRA is the value of receiving an extra
0.5×(0.08−0.06)×1000 = $10 in 2.5 years. This is 10/(1.035) = $8.63
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Under liquidity preference theory, which of the following is
always true? A.The forward rate is higher than the spot rate when both have
the same maturity.
B.Forward rates are unbiased predictors of expected future
spot rates.
C.The spot rate for a certain maturity is higher than the par
yield for that maturity.
D.Forward rates are higher than expected future spot rates.
Answer: D
Liquidity preference theory argues that individuals like their
borrowings to have a long maturity and their deposits to have a
short maturity. To induce people to lend for long periods forward
rates are raised relative to what expected future short rates would
predict.
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The zero curve is upward sloping. Define X as the 1-year par
yield, Y as the 1-year zero rate and Z as the forward rate for the
period between 1 and 1.5 year. Which of the following is true?
A.X is less than Y which is less than Z
B.Y is less than X which is less than Z
C.X is less than Z which is less than Y D.Z is less than Y which is less than X
E.X is less than Y which is less than Z
F.Y is less than X which is less than Z
G.X is less than Z which is less than Y H.Z is less than Y which is less than X
Answer: A
When the zero curve is upward sloping, the one-year zero rate is
higher than the one-year par yield and the forward rate
corresponding to the period between 1.0 and 1.5 years is higher
than the one-year zero rate. The correct answer is therefore A.
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10.Which of the following is true of the fed funds rate
A.It is the same as the Treasury rate
B.It is an overnight interbank rate
C.It is a rate for which collateral is posted
D.It is a type of repo rate
Answer: B
At the end of each day some banks have surplus reserves on
deposit with the Federal Reserve others have deficits. They use
overnight borrowing and lending at what is termed the fed funds rate
to rectify this.
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The modified duration of a bond portfolio worth $1 million is 5
years. By approximately how much does the value of the
portfolio change if all yields increase by 5 basis points?
A.Increase of $2,500
B.Decrease of $2,500
C.Increase of $25,000
D.Decrease of $25,000
Answer: B
When yields increase bond prices decrease. The proportional
decrease is the modified duration times the yield increase. In this
case, it is 5×0.0005=0.0025. The decrease is therefore
0.0025×1,000,000 or $2,500.
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A company invests $1,000 in a five-year zero-coupon bond and
$4,000 in a ten-year zero-coupon bond. What is the duration of
the portfolio?
A. 6 years
B. 7 years
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C. 8 years
D. 9 years
Answer: D
The duration of the first bond is 5 years and the duration of the
second bond is 10 years. The duration of the portfolio is a weighted
average with weights corresponding to the amounts invested in the
bonds. It is 0.2×5+0.8×10=9 years.
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Which of the following is true of LIBOR
A.The LIBOR rate is free of credit risk
B.A LIBOR rate is lower than the Treasury rate when the two
have the same maturity
C.It is a rate used when borrowing and lending takes place
between banks
D.It is subject to favorable tax treatment in the U.S.
Answer: C
LIBOR is a rate used for interbank transactions.
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Which of following describes forward rates?
A.Interest rates implied by current zero rates for future periods
of time
B.Interest rate earned on an investment that starts today and
last for n-years in the future without coupons
C.The coupon rate that causes a bond price to equal its par (or
principal) value
D.A single discount rate that gives the value of a bond equal to
its market price when applied to all cash flows
Answer: A
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The forward rate is the interest rate implied by the current term
structure for future periods of time. For example, earning the zero
rate for one year and the forward rate for the period between one
and two years gives the same result as earning the zero rate for two
years.
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Which of the following is NOT a theory of the term structure
A.Expectations theory
B.Market segmentation theory
C.Liquidity preference theory
D.Maturity preference theory
Answer: C
Maturity preference theory is not a theory of the term structure. The
other three are.
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A repo rate is
A.An uncollateralized rate
B.A rate where the credit risk is relative high
C.The rate implicit in a transaction where securities are sold
and bought back later at a higher price
D.None of the above
Answer: C
A repo transaction is one where a company agrees to sell securities
today and buy them back at a future time. It is a form of
collateralized borrowing. The credit risk is very low.
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Bootstrapping involves
A.Calculating the yield on a bond
B.Working from short maturity instruments to longer maturity
instruments determining zero rates at each step
C.Working from long maturity instruments to shorter maturity
instruments determining zero rates at each step
D.The calculation of par yields
Answer: B
Bootstrapping is a way of constructing the zero coupon yield curve
from coupon-bearing bonds. It involves working from the shortest
maturity bond to progressively longer maturity bonds making sure
that the calculated zero coupon yield curve is consistent with the
market prices of the instruments.
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The zero curve is downward sloping. Define X as the 1-year par
yield, Y as the 1-year zero rate and Z as the forward rate for the
period between 1 and 1.5 year. Which of the following is true?
A.X is less than Y which is less than Z
B.Y is less than X which is less than Z
C.X is less than Z which is less than Y D.Z is less than Y which is less than X
Answer: D
The forward rate accentuates trends in the zero curve. The par yield
shows the same trends but in a less pronounced way.
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Which of the following is true?
A.When interest rates in the economy increase, all bond prices
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increase
B. As its coupon increases, a bond’s price decreases
C.Longer maturity bonds are always worth more that shorter
maturity bonds when the coupon rates are the same
D.None of the above
Answer: D
When interest rates increase the impact of discounting is to make
future cash flows worth less. Bond prices therefore decline. A is
therefore wrong. As coupons increase a bond becomes more
valuable because higher cash flows will be received. B is therefore
wrong. When the coupon is higher than prevailing interest rates,
longer maturity bonds are worth more than shorter maturity bonds.
When it is less than prevailing interest rates, longer maturity bonds
are worth less than shorter maturity bonds. C is therefore not true.
The correct answer is therefore D.
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The six month and one-year rates are 3% and 4% per annum
with semiannual compounding. Which of the following is
closest to the one-year par yield expressed with semiannual
compounding?
A.3.99%
B.3.98%
C.3.97%
D.3.96%
Answer: A
The six month rate is 1.5% per six months. The one year rate is 2%
per six months. The one year par yield is the coupon that leads to a
bond being worth par. A is the correct answer because (3.99/2)/1.015+(100+3.99/2)/1.022 = 100. The formula in the text
can also be used to give the par yield as [(100-
100/1.022)×2]/(1/1.015+1.022)=3.99.
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Which of the following is a consumption asset?
A.The S&P 500 index
B.The Canadian dollar
C.Copper
D.IBM stock
Answer: C
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A, B, and D are investment assets (held by at least some investors
purely for investment purposes). C is a consumption asset.
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An investor shorts 100 shares when the share price is $50 and
closes out the position six months later when the share price is
$43. The shares pay a dividend of $3 per share during the six
months. How much does the investor gain? A. $1,000
B. $400
C. $700
D. $300
Answer: B
The investor gains $7 per share because he or she sells at $50 and
buys at $43. However, the investor has to pay the $3 per share
dividend. The net profit is therefore 7−3 or $4 per share. 100 shares
are involved. The total gain is therefore $400.
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The spot price of an investment asset that provides no income
is $30 and the risk-free rate for all maturities (with continuous
compounding) is 10%. What is the three-year forward price? A. $40.50
B. $22.22
C. $33.00
D.$33.16
Answer: A
The 3-year forward price is the spot price grossed up for 3 years at
the risk-free rate. It is 30e0.1×3 =$40.50.
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The spot price of an investment asset is $30 and the risk-free
rate for all maturities is 10% with continuous compounding.
The asset provides an income of $2 at the end of the first year
and at the end of the second year. What is the three-year
forward price?
A. $19.67
B. $35.84
C. $45.15
D. $40.50
Answer: B
The present value of the income is 2e-0.1×1+2e-0.1×2= $3.447.
The three year forward price is obtained by subtracting the present
value of the income from the current stock price and then grossing
up the result for three years at the risk-free rate. It is
(30−3.447)e0.1×3 = $35.84.
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An exchange rate is 0.7000 and the six-month domestic and
foreign risk-free interest rates are 5% and 7% (both expressed
with continuous compounding). What is the six-month forward
rate?
A. 0.7070
B.0.7177
C.0.7249
D.0.6930
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Answer: D
The six-month forward rate is 0.7000e−(0.05−0.07)×0.5=0.6930.
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Which of the following is true? A.The convenience yield is always positive or zero.
B.The convenience yield is always positive for an investment
asset.
C.The convenience yield is always negative for a consumption
asset.
D.The convenience yield measures the average return earned
by holding futures contracts.
Answer: A
The convenience yield measures the benefit of owning an asset
rather than having a forward/futures contract on an asset. For an
investment asset it is always zero. For a consumption asset it is
greater than or equal to zero.
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A short forward contract that was negotiated some time ago
will expire in three months and has a delivery price of $40. The
current forward price for three-month forward contract is $42.
The three month risk-free interest rate (with continuous
compounding) is 8%. What is the value of the short forward
contract?
A. +$2.00
B. −$2.00
C. +$1.96
D. −$1.96
Answer: D
The contract gives one the obligation to sell for $40 when a forward
price negotiated today would give one the obligation to sell for $42.
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The value of the contract is the present value of −$2 or −2e-
0.08×0.25 = −$1.96.
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The spot price of an asset is positively correlated with the
market. Which of the following would you expect to be true?
A.The forward price equals the expected future spot price.
B.The forward price is greater than the expected future spot
price.
C.The forward price is less than the expected future spot price.
D.The forward price is sometimes greater and sometimes less
than the expected future spot price.
Answer: C
When the spot price is positively correlated with the market the
forward price is less than the expected future spot price. This is
because the spot price is expected to provide a return greater than
the risk-free rate and the forward price is the spot price grossed up
at the risk-free rate.
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Which of the following describes the way the futures price of a
foreign currency is quoted by the CME group?
A.The number of U.S. dollars per unit of the foreign currency
B.The number of the foreign currency per U.S. dollar
C.Some futures prices are always quoted as the number of U.S.
dollars per unit of the foreign currency and some are always
quoted the other way round
D.There are no quotation conventions for futures prices
Answer: A
The futures price is quoted as the number of US dollars per unit of
the foreign currency. Spot exchange rates and forward exchange
rates are sometimes quoted this way and sometimes quoted the
other way round.
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Which of the following describes the way the forward price of a
foreign currency is quoted?
A.The number of U.S. dollars per unit of the foreign currency
B.The number of the foreign currency per U.S. dollar
C.Some forward prices are quoted as the number of U.S.
dollars per unit of the foreign currency and some are quoted
the other way round
D.There are no quotation conventions for forward prices
Answer: C
The futures price is quoted as the number of US dollars per unit of
the foreign currency. Spot exchange rates and forward exchange
rates are sometimes quoted this way and sometimes quoted the
other way round.
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Which of the following is NOT a reason why a short position in
a stock is closed out?
A.The investor with the short position chooses to close out the
position
B.The lender of the shares issues instructions to close out the
position
C.The broker is no longer able to borrow shares from other
clients
D.The investor does not maintain margins required on his/her
margin account
Answer: B
A, C, and D are all reasons why the short position might be closed
out. B is not. The lender of shares cannot issue instructions to close
out the short position.
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72
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Which of the following is NOT true?
A.Gold and silver are investment assets
B.Investment assets are held by significant numbers of
investors for investment purposes
C.Investment assets are never held for consumption
D.The forward price of an investment asset can be obtained
from the spot price, interest rates, and the income paid on the
asset
Answer: C
Investment assets are sometimes held for consumption. Silver is an
example. To be an investment asset, an asset has to be held for
investment by at least some traders
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What should a trader do when the one-year forward price of an
asset is too low? Assume that the asset provides no income.
A.The trader should borrow the price of the asset, buy one unit
of the asset and enter into a short forward contract to sell the
asset in one year.
B.The trader should borrow the price of the asset, buy one unit
of the asset and enter into a long forward contract to buy the
asset in one year.
C.The trader should short the asset, invest the proceeds of the
short sale at the risk-free rate, enter into a short forward
contract to sell the asset in one year D.The trader should short the asset, invest the proceeds of the
short sale at the risk-free rate, enter into a long forward
contract to buy the asset in one year
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Answer: D
If the forward price is too low relative to the spot price the trader
should short the asset in the spot market and buy it in the forward
market.
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Which of the following is NOT true about forward and futures
contracts?
A.Forward contracts are more liquid than futures contracts
B.The futures contracts are traded on exchanges while forward
contracts are traded in the over-the-counter market
C.In theory forward prices and futures prices are equal when
there is no uncertainty about future interest rates
D.Taxes and transaction costs can lead to forward and futures
prices being different
Answer: A
Futures contracts are more liquid than forward contracts. To unwind
a futures position it is simply necessary to take an offsetting
position. The statements in B, C, and D are correct
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As the convenience yield increases, which of the following is
true?
A.The one-year futures price as a percentage of the spot price
increases
B.The one-year futures price as a percentage of the spot price
decreases
C.The one-year futures price as a percentage of the spot price
stays the same
D.Any of the above can happen
Answer: B
As the convenience yield increases, the futures price declines
relative to the spot price. This is because the convenience of owning
the asset (as opposed to having a futures contract) becomes more
important.
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As inventories of a commodity decline, which of the following
is true?
A.The one-year futures price as a percentage of the spot price
increases
B.The one-year futures price as a percentage of the spot price
decreases
C.The one-year futures price as a percentage of the spot price
stays the same
D.Any of the above can happen
Answer: B
When inventories decline, the convenience yield increases and the
futures price as a percentage of the spot price declines.
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Which of the following describes a known dividend yield on a
stock?
A.The size of the dividend payments each year is known
B.Dividends per year as a percentage of today’s stock price are
known
C.Dividends per year as a percentage of the stock price at the
time when dividends are paid are known D.Dividends will yield a certain return to a person buying the
stock today
Answer: C
The dividend yield is the dividend per year as a percent of the stock
price at the time when the dividend is paid.
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Which of the following is an argument used by Keynes and
Hicks?
A.If hedgers hold long positions and speculators holds short
positions, the futures price will tend to be higher than the
expected future spot price
B.If hedgers hold long positions and speculators holds short
positions, the futures price will tend to be lower than the
expected future spot price
C.If hedgers hold long positions and speculators holds short
positions, the futures price will tend to be lower than today’s
spot price
D.If hedgers hold long positions and speculators holds short
positions, the futures price will tend to be higher than today’s
spot price
Answer: A
Keynes and Hicks argued that hedgers will be prepared to accept
negative returns on average because of the benefits of hedging
whereas speculators require positive returns on average. This leads
to A.
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19.Which of the following describes contango?
A.The futures price is below the expected future spot price
B.The futures price is below today’s spot price
C.The futures price is a declining function of the time to
maturity
D.The futures price is above the expected future spot price
Answer: D
Contango is defined as the futures price being above the expected
future spot price. It is also sometimes used to describe the situation
where the futures price is above the spot price.
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Which of the following is true for a consumption commodity?
A.There is no limit to how high or low the futures price can be,
except that the futures price cannot be negative
B.There is a lower limit to the futures price but no upper limit
C.There is an upper limit to the futures price but no lower limit,
except that the futures price cannot be negative
D.The futures price can be determined with reasonable
accuracy from the spot price and interest rates
Answer: C
If the futures price of a consumption commodity becomes too high
an arbitrageur will buy the commodity and sell futures to lock in a
profit. An arbitrageur cannot follow the opposite strategy of buying
futures and selling or shorting the asset when the futures price is
low. This is because consumption assets cannot be shorted .
Furthermore, people who hold the asset in general do so because
they need the asset for their business. They are not prepared to
swap their position in the asset for a similar position in a futures.
Consequently, there is an upper limit but no lower limit to the futures
price.
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A company can invest funds for five years at LIBOR minus 30
basis points. The five-year swap rate is 3%. What fixed rate of
interest can the company earn by using the swap? A.2.4%
B.2.7%
C.3.0%
D.3.3%
Answer: B
When the company invests at LIBOR minus 0.3% and then enters
into a swap where it pays LIBOR and receives 3% it earns 2.7% per
annum. Note that it is the bid rate that will apply to the swap.
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Which of the following is true?
A.Principals are not usually exchanged in a currency swap
B.The principal amounts usually flow in the opposite direction
to interest payments at the beginning of a currency swap and
in the same direction as interest payments at the end of the
swap.
C.The principal amounts usually flow in the same direction as
interest payments at the beginning of a currency swap and in
the opposite direction to interest payments at the end of the
swap.
D.Principals are not usually specified in a currency swap
Answer: B
The correct answer is B. There are two principals in a currency
swap, one for each currency. They flow in the opposite direction to
the corresponding interest payments at the beginning of the life of
the swap and in the same direction as the corresponding interest
payments at the end of the life of the swap.
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Company X and Company Y have been offered the following
rates
Fixed Rate Floating Rate
Company X3.5% 3-month LIBOR plus 10bp
Company Y4.5% 3-month LIBOR plus 30 bp
Suppose that Company X borrows fixed and company Y
borrows floating. If they enter into a swap with each other
where the apparent benefits are shared equally, what is
company X’s effective borrowing rate?
A.3-month LIBOR−30bp
B.3.1%
C.3-month LIBOR−10bp
D.3.3%
Answer: A
The interest rate differential between the fixed rates is 100 basis
points. The interest rate differential between the floating rates is 20
basis points. The difference between the interest rates differentials
is 100 – 20 = 80 basis points. This is the total apparent gain from
the swap to the two sides. Since the benefits are shared equally
company X should be able to borrow at 40 bp less than it is
currently offered in the floating rate market, i.e., at LIBOR minus 30
bp.
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84
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Which of the following describes the five-year swap rate?
A.The fixed rate of interest which a swap market maker is
prepared to pay in exchange for LIBOR on a 5-year swap
B.The fixed rate of interest which a swap market maker is
prepared to receive in exchange for LIBOR on a 5-year swap
C.The average of A and B
D.The higher of A and B
Answer: C
The swap rate is the average of the bid swap rate (i.e. A) and the
offer swap rate (i.e. B)
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Which of the following is a use of a currency swap?
A.To exchange an investment in one currency for an
investment in another currency
B.To exchange borrowing in one currency for borrowings in
another currency
C.To take advantage situations where the tax rates in two
countries are different
D.All of the above
Answer: D
A currency swap can be used for any of A, B, and C.
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The reference entity in a credit default swap is
A.The buyer of protection
B.The seller of protection
C.The company or country whose default is being insured
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against
D.None of the above
Answer: C
In a credit default swap the buyer of protection pays a CDS spread
to the seller of protection and the protection seller has to make a
payoff if there is a default by the reference entity.
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Which of the following describes an interest rate swap?
A.The exchange of a fixed rate bond for a floating rate bond
B.A portfolio of forward rate agreements
C.An agreement to exchange interest at a fixed rate for interest
at a floating rate
D.All of the above
Answer: D
The answer is D because all of A, B, and C are true for an interest
rate swap.
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Which of the following is true for an interest rate swap?
A.A swap is usually worth close to zero when it is first
negotiated
B. Each forward rate agreement underlying a swap is worth
close to zero when the swap is first entered into
C.Comparative advantage is a valid reason for entering into the
swap
D.None of the above
Answer: A
A swap is worth close to zero at the beginning of its life. (It may not
be worth exactly zero because of the impact of the market maker’s
bid-offer spread.) It is not true that each of the forward contracts
underlying the swap are worth zero. (The sum of the value of the
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forward contracts is zero, but this does not mean that each one is
worth zero.) The remaining floating payments on a swap are worth
the notional principal immediately after a swap payment date, but
this is not necessarily true for the remaining fixed payments.
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Which of the following is true for the party paying fixed in a
newly negotiated interest rate swap when the yield curve is
upward sloping?
A.The early forward contracts underlying the swap have a
positive value and the later ones have a negative value
B.The early forward contracts underlying the swap have a
negative value and the later ones have a positive value
C.The swap is designed so that all forward rates have zero
value
D.Sometimes A is true and sometimes B is true
Answer: B
The forward contracts are contracts where fixed is paid and floating
is received. They can be valued assuming that forward rates are
realized. Forward rates increase with maturity. This means that the
value of the forward contracts increase with maturity. The total
value of the forward contracts is zero. This means that the value of
the early contracts is negative and the value of the later contracts is
positive.
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A bank enters into a 3-year swap with company X where it pays
LIBOR and receives 3.00%. It enters into an offsetting swap
with company Y where is receives LIBOR and pays 2.95%.
Which of the following is true:
A.If company X defaults, the swap with company Y is null and
void
B.If company X defaults, the bank will be able to replace
company X at no cost
C.If company X defaults, the swap with company Y continues
D.The bank’s bid-offer spread is 0.5 basis points
Answer: C
The bank`s bid-offer spread is 5 basis points not 0.5 basis points.
The bank has quite separate transactions with X and Y. If one
defaults, it still has to honor the swap with the other.
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91
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When LIBOR is used as the discount rate:
A.The value of a swap is worth zero immediately after a
payment date
B. The value of a swap is worth zero immediately before a
payment date
C.The value of the floating rate bond underlying a swap is
worth par immediately after a payment date
D.The value of the floating rate bond underlying a swap is
worth par immediately before a payment date
Answer: C
The value of the floating rate bond underlying an interest rate swap
is worth par immediately after a swap payment date. This result is
used when the swap is valued as the difference between two
bonds. 92
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A company enters into an interest rate swap where it is paying
fixed and receiving LIBOR. When interest rates increase, which
of the following is true?
A.The value of the swap to the company increases
B.The value of the swap to the company decreases
C.The value of the swap can either increase or decrease
D.The value of the swap does not change providing the swap
rate remains the same
Answer: A
It is receiving the floating rate. When interest rates increase the
floating rate can be expected to be higher and so the swap
becomes more valuable. The answer is therefore A.
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93
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A floating for floating currency swap is equivalent to
A.Two interest rate swaps, one in each currency
B.A fixed-for-fixed currency swap and one interest rate swap
C.A fixed-for-fixed currency swap and two interest rate swaps,
one in each currency
D.None of the above
Answer: C
A floating-for-floating currency swap where the currency paid is X
and the currency received is Y is equivalent to (a) a fixed-for-fixed
currency swap where, say, 5% in currency X is paid and say, say,
4% in currency Y is received, (b) a regular interest rate swap where
5% in currency X is received and floating in currency X is paid and
(c) a regular interest rate swap where 4% in currency Y is paid and
floating in currency Y is received.
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A floating-for-fixed currency swap is equivalent to
A.Two interest rate swaps, one in each currency
B.A fixed-for-fixed currency swap and one interest rate swap
C.A fixed-for-fixed currency swap and two interest rate swaps,
one in each currency
D.None of the above
Answer: B
A floating-for-fixed currency swap where the floating rate is paid in
currency X and the fixed rate is received in currency Y is equivalent
to (a) a fixed-for-fixed currency swap where, say, 5% in currency X
is paid and the fixed rate in currency Y is received, (b) a regular
interest rate swap where 5% in currency X is received and floating
in currency X is paid.
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An interest rate swap has three years of remaining life.
Payments are exchanged annually. Interest at 3% is paid and
12-month LIBOR is received. A exchange of payments has just
taken place. The one-year, two-year and three-year LIBOR/swap
zero rates are 2%, 3% and 4%. All rates an annually
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compounded. What is the value of the swap as a percentage of
the principal when LIBOR discounting is used.
A. 0.00
B.2.66
C. 2.06
D.1.06
Answer: B
Suppose the principal 100. The value of the floating rate bond
underlying the swap is 100. The value of the fixed rate bond is
3/1.02+3/(1.03)2+103/(1.04)3=97.34. The value of the swap is
therefore 100−97.34 = 2.66 or 2.66% of the principal
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A semi-annual pay interest rate swap where the fixed rate is
5.00% (with semi-annual compounding) has a remaining life of
nine months. The six-month LIBOR rate observed three
months ago was 4.85% with semi-annual compounding.
Today’s three and nine month LIBOR rates are 5.3% and 5.8%
(continuously compounded) respectively. From this it can be
calculated that the forward LIBOR rate for the period between
three- and nine-months is 6.14% with semi-annual
compounding. If the swap has a principal value of $15,000,000,
what is the value of the swap to the party receiving a fixed rate
of interest?
A.$74,250
B.−$70,760
C.−$11,250
D.$103,790
Answer: B
The forward rates for the floating payment at time 9 months is
6.14%. The swap can be valued assuming that the fixed payments
are 2.5% of principal at 3 months and 9 months and that the floating
payments are 2.425% and 3.07% of the principal at 3 months and 9
months. The value of the swap to the party receiving fixed is
therefore
1,000,000(0.025-0.02425)e-0.053×0.25+1,000,000(0.025-0.0307)e-
0.058×0.75 = –$70,760
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Which of the following describes the way a LIBOR-in-arrears
swap differs from a plain vanilla interest rate swap?
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A.Interest is paid at the beginning of the accrual period in a
LIBOR-in-arrears swap
B.Interest is paid at the end of the accrual period in a LIBOR-in-
arrears swap
C.No floating interest is paid until the end of the life of the
swap in a LIBOR-in-arrears swap, but fixed payments are made
throughout the life of the swap
D.Neither floating nor fixed payments are made until the end of
the life of the swap
Answer: A
In a LIBOR-in-arrears swap interest is observed for an accrual
period and paid at the beginning of that accrual period (not at the
end of the accrual period which is normal)
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In a fixed-for-fixed currency swap, 3% on a US dollar principal
of $150 million is received and 4% on a British pound principal
of 100 million pounds is paid. The current exchange rate is 1.55
dollar per pound. Interest rates in both countries for all
maturities are currently 5% (continuously compounded).
Payments are exchanged every year. The swap has 2.5 years
left in its life. What is the value of the swap?
A. −$7.15
B.−$8.15
C.−$9.15
D.−$10.15
Answer: C
The value of the British pound bond underlying the swap is in
millions of pounds
4e-0.05×0.5+4e-0.05×1.5+104e-0.05×2.5 = 99.39
The value of the U.S. dollar bond is in millions of dollars
4.5e-0.05×0.5+4.5e-0.05×1.5+154.5e-0.05×2.5 = 144.91
The value of the swap is 144.91 – 99.39×1.55 = –9.15
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19.Which of the following is a typical bid-offer spread on the
swap rate for a plain vanilla interest rate swap?
A.3 basis points
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B.8 basis points
C.13 basis points
D.18 basis points
Answer: A
3 basis points is a typical spread between the bid and the offer on a
plain vanilla interest rate swap.
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Which of the following describes the five-year swap rate?
A.The rate on a five-year loan to a AA-rated company
B.The rate on a five-year loan to an A-rated company
C.The rate that can be earned over five years from a series of
short-term loans to AA-rated companies
D.The rate that can be earned over five years from a series of
short-term loans to A-rated companies Answer: C
By considering the effect of making a series of LIBOR loans to AA-
rated companies and entering into a swap we see that the swap rate
corresponds to the risk in a series of short-term loans.
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The basis is defined as spot minus futures. A trader is hedging
the sale of an asset with a short futures position. The basis
increases unexpectedly. Which of the following is true?
A. The hedger’s position improves.
B.The hedger’s position worsens.
C.The hedger’s position sometimes worsens and sometimes
improves.
D.The hedger’s position stays the same.
Answer: A
The price received by the trader is the futures price plus the basis. It
follows that the trader’s position improves when the basis increases.
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102
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Futures contracts trade with every month as a delivery month.
A company is hedging the purchase of the underlying asset on
June 15. Which futures contract should it use?
A.The June contract
B.The July contract
C.The May contract
D.The August contract
Answer: B
As a general rule the futures maturity month should be as close as
possible to but after the month when the asset will be purchased. In
this case the asset will be purchased in June and so the best
contract is the July contract.
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On March 1 a commodity’s spot price is $60 and its August
futures price is $59. On July 1 the spot price is $64 and the
August futures price is $63.50. A company entered into futures
contracts on March 1 to hedge its purchase of the commodity
on July 1. It closed out its position on July 1. What is the
effective price (after taking account of hedging) paid by the
company?
A.$59.50
B.$60.50
C.$61.50
D.$63.50
Answer: A
The user of the commodity takes a long futures position. The gain
on the futures is 63.50−59 or $4.50. The effective paid realized is
therefore 64−4.50 or $59.50. This can also be calculated as the
March 1 futures price (=59) plus the basis on July 1 (=0.50).
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104
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On March 1 the price of a commodity is $1,000 and the
December futures price is $1,015. On November 1 the price is
$980 and the December futures price is $981. A producer of the
commodity entered into a December futures contracts on
March 1 to hedge the sale of the commodity on November 1. It
closed out its position on November 1. What is the effective
price (after taking account of hedging) received by the
company for the commodity? A. $1,016
B. $1,001
C.$981
D.$1,014
Answer: D
The producer of the commodity takes a short futures position. The
gain on the futures is 1015−981 or $34. The effective price realized
is therefore 980+34 or $1014. This can also be calculated as the
March 1 futures price (=1015) plus the November 1 basis (=−1).
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5.Suppose that the standard deviation of monthly changes in
the price of commodity A is $2. The standard deviation of
monthly changes in a futures price for a contract on
commodity B (which is similar to commodity A) is $3. The
correlation between the futures price and the commodity price
is 0.9. What hedge ratio should be used when hedging a one
month exposure to the price of commodity A? A. 0.60
B. 0.67
C. 1.45
D.0.90
Answer: A
The optimal hedge ratio is 0.9×(2/3) or 0.6.
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106
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A company has a $36 million portfolio with a beta of 1.2. The
futures price for a contract on an index is 900. Futures
contracts on $250 times the index can be traded. What trade is
necessary to reduce beta to 0.9?
A.Long 192 contracts
B.Short 192 contracts
C.Long 48 contracts
D.Short 48 contracts
Answer: D
To reduce the beta by 0.3 we need to short
0.3×36,000,000/(900×250) or 48 contracts.
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A company has a $36 million portfolio with a beta of 1.2. The
futures price for a contract on an index is 900. Futures
contracts on $250 times the index can be traded. What trade is
necessary to increase beta to 1.8?
A.Long 192 contracts
B.Short 192 contracts
C.Long 96 contracts
D.Short 96 contracts
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Answer: C
To increase beta by 0.6 we need to go long 0.6×36,000,000/(900×250) or 96 contracts
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Which of the following is true? A.The optimal hedge ratio is the slope of the best fit line when
the spot price (on the y-axis) is regressed against the futures
price (on the x-axis).
B.The optimal hedge ratio is the slope of the best fit line when
the futures price (on the y-axis) is regressed against the spot
price (on the x-axis).
C.The optimal hedge ratio is the slope of the best fit line when
the change in the spot price (on the y-axis) is regressed
against the change in the futures price (on the x-axis).
D.The optimal hedge ratio is the slope of the best fit line when
the change in the futures price (on the y-axis) is regressed
against the change in the spot price (on the x-axis).
Answer: C
The optimal hedge ratio reflects the ratio of movements in the spot
price to movements in the futures price.
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Which of the following describes tailing the hedge?
A.A strategy where the hedge position is increased at the end
of the life of the hedge
B.A strategy where the hedge position is increased at the end
of the life of the futures contract
C.A more exact calculation of the hedge ratio when forward
contracts are used for hedging
D.None of the above Answer: D
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Tailing the hedge is a calculation appropriate when futures are used
for hedging. It corrects for daily settlement
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A company due to pay a certain amount of a foreign currency
in the future decides to hedge with futures contracts. Which of
the following best describes the advantage of hedging?
A.It leads to a better exchange rate being paid
B.It leads to a more predictable exchange rate being paid
C.It caps the exchange rate that will be paid
D.It provides a floor for the exchange rate that will be paid
Answer: B
Hedging is designed to reduce risk not increase expected profit.
Options can be used to create a cap or floor on the price. Futures
attempt to lock in the price
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11.Which of the following best describes the capital asset
pricing model?
A.Determines the amount of capital that is needed in particular
situations
B.Is used to determine the price of futures contracts
C.Relates the return on an asset to the return on a stock index
D.Is used to determine the volatility of a stock index
Answer: C
CAPM relates the return on an asset to its beta. The parameter
beta measures the sensitivity of the return on the asset to the return
on the market. The latter is usually assumed to be the return on a
stock index such as the S&P 500.
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112
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Which of the following best describes “stack and roll”?
A.Creates long-term hedges from short term futures contracts
B.Can avoid losses on futures contracts by entering into
further futures contracts
C.Involves buying a futures contract with one maturity and
selling a futures contract with a different maturity
D.Involves two different exposures simultaneously
Answer: A
Stack and roll is a procedure where short maturity futures contracts
are entered into. When they are close to maturity they are replaced
by more short maturity futures contracts and so on. The result is the
creation of a long term hedge from short-term futures contracts.
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Which of the following increases basis risk?
A.A large difference between the futures prices when the hedge
is put in place and when it is closed out
B.Dissimilarity between the underlying asset of the futures
contract and the hedger’s exposure
C.A reduction in the time between the date when the futures
contract is closed and its delivery month
D.None of the above
Answer: B
Basis is the difference between futures and spot at the time the
hedge is closed out. This increases as the time between the date
when the futures contract is put in place and the delivery month
increases. (C is not therefore correct). It also increases as the asset
underlying the futures contract becomes more different from the
asset being hedged. (B is therefore correct.)
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114
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Which of the following is a reason for hedging a portfolio with
an index futures?
A.The investor believes the stocks in the portfolio will perform
better than the market but is uncertain about the future
performance of the market
B.The investor believes the stocks in the portfolio will perform
better than the market and the market is expected to do well
C.The portfolio is not well diversified and so its return is
uncertain
D.All of the above
Answer: A
Index futures can be used to remove the impact of the performance
of the overall market on the portfolio. If the market is expected to do
well hedging against the performance of the market is not
appropriate. Hedging cannot correct for a poorly diversified portfolio.
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Which of the following does NOT describe beta?
A.A measure of the sensitivity of the return on an asset to the
return on an index
B.The slope of the best fit line when the return on an asset is
regressed against the return on the market
C.The hedge ratio necessary to remove market risk from a
portfolio
D.Measures correlation between futures prices and spot prices
for a commodity
Answer: D
A, B, and C all describe beta but beta has nothing to do with the
correlation between futures and spot prices for a commodity
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Which of the following is true?
A.Hedging can always be done more easily by a company’s
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shareholders than by the company itself
B.If all companies in an industry hedge, a company in the
industry can sometimes reduce its risk by choosing not to
hedge C.If all companies in an industry do not hedge, a company in
the industry can reduce its risk by hedging
D.If all companies in an industry do not hedge, a company is
liable increase its risk by hedging
Answer: D
If all companies in a industry hedge, the prices of the end product
tends to reflect movements in relevant market variables. Attempting
to hedge those movements can therefore increase risk.
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Which of the following is necessary for tailing a hedge?
A.Comparing the size in units of the position being hedged
with the size in units of the futures contract
B.Comparing the value of the position being hedged with the
value of one futures contract
C.Comparing the futures price of the asset being hedged to its
forward price
D.None of the above
Answer: B
When tailing a hedge the optimal hedge ratio is applied to the ratio
of the value of the position being hedged to the value of one futures
contract.
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Which of the following is true?
A.Gold producers should always hedge the price they will
receive for their production of gold over the next three years
B.Gold producers should always hedge the price they will
receive for their production of gold over the next one year
C.The hedging strategies of a gold producer should depend on
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whether it shareholders want exposure to the price of gold
D.Gold producers can hedge by buying gold in the forward
market
Answer: C
Some shareholders buy gold stocks to gain exposure to the price of
gold. They do not want the company they invest in to hedge. In
practice gold mining companies make their hedging strategies clear
to shareholders.
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A silver mining company has used futures markets to hedge
the price it will receive for everything it will produce over the
next 5 years. Which of the following is true?
A.It is liable to experience liquidity problems if the price of
silver falls dramatically
B.It is liable to experience liquidity problems if the price of
silver rises dramatically
C.It is liable to experience liquidity problems if the price of
silver rises dramatically or falls dramatically
D.The operation of futures markets protects it from liquidity
problems
Answer: B
The mining company shorts futures. It gains on the futures when the
price decreases and loses when the price increases. It may get
margin calls which lead to liquidity problems when the price rises
even though the silver in the ground is worth more.
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A company will buy 1000 units of a certain commodity in one
year. It decides to hedge 80% of its exposure using futures
contracts. The spot price and the futures price are currently
$100 and $90, respectively. If the spot price and the futures
price in one year turn out to be $112 and $110, respectively.
What is the average price paid for the commodity?
A.$92
B.$96
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C.$102
D.$106
Answer: B
On the 80% (hedged) part of the commodity purchase the price paid
will 112−(110−90) or $92. On the other 20% the price paid will be
the spot price of $112. The weighted average of the two prices is
0.8×92+0.2×112 or $96. 121
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Which of following is applicable to corporate bonds in the
United States?
A.Actual/360
B.Actual/Actual
C.30/360
D.Actual/365
Answer: C
Corporate bonds in the U.S are usually quoted with a 30/360 day
count. This means that there are assumed to be 30 days per month
and 360 days per year when the length of an accrual period is
calculated.
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It is May 1. The quoted price of a bond with an Actual/Actual (in
period) day count and 12% per annum coupon (paid
semiannually) in the United States is 105. It has a face value of
100 and pays coupons on April 1 and October 1. What is the
cash price?
A.106.00
B. 106.02
C.105.98
D. 106.04
Answer: C
The cash price is the quoted price plus accrued interest. There are
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30 actual days between April 1 and May 1 and 183 actual days
between April 1 and October 1. In this case the quoted price is 105
and the accrued interest is 0.06×100×30/183=0.98. The answer is
therefore 105.98.
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It is May 1. The quoted price of a bond with a 30/360 day count
and 12% per annum coupon in the United States is 105. It has a
face value of 100 and pays coupons on April 1 and October 1.
What is the cash price?
A. 106.00
B. 106.02
C.105.98
D. 106.04
Answer: A
The cash price is the quoted price plus accrued interest. There are
30 assumed days between April 1 and May 1 and 180 assumed
days between April 1 and October 1. In this case the quoted price is
105 and the accrued interest is 0.06×100×30/180 = 1.00. The
answer is therefore 106.00.
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The most recent settlement bond futures price is 103.5. Which
of the following four bonds is cheapest to deliver?
A.Quoted bond price = 110; conversion factor = 1.0400.
B.Quoted bond price = 160; conversion factor = 1.5200.
C.Quoted bond price = 131; conversion factor = 1.2500.
D.Quoted bond price = 143; conversion factor = 1.3500.
Answer: C
The cost of delivering a bond is the quoted bond price minus the
most recent settlement price times the conversion factor. This is
2.36, 2.68, 1.625, and 3.275 for bonds in A, B, C, and D,
respectively. The bond in C is therefore cheapest to deliver.
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Which of the following is NOT an option open to the party with
a short position in the Treasury bond futures contract?
A.The ability to deliver any of a number of different bonds
B.The wild card play
C.The fact that delivery can be made any time during the
delivery month
D.The interest rate used in the calculation of the conversion
factor
Answer: D
A, B, and C describe options that the party with the short position
has. D does not
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A trader enters into a long position in one Eurodollar futures
contract. How much does the trader gain when the futures
price quote increases by 6 basis points?
A. $6
B. $150
C.$60
D. $600
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Answer: B
The trader gains $25 for each basis point. The gain is therefore
25×6 or $150.
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The bonds that can be delivered in a Treasury bond futures
contract are
A.Assets that provide no income
B.Assets that provide a known cash income
C.Assets that provide a known yield
D.None of the above
Answer: B
A bond is an asset that provides a known cash income (the
coupons)
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An ultra T-bond futures contract is one where
A.Bonds with maturities less than 3 years can be delivered
B.Bonds with maturities less than 10 years can be delivered
C.Bonds with maturities greater than 15 years can be delivered
D.Bonds with maturities greater than 25 year can be delivered
Answer: D
In the ultra T-bond futures contract bonds with maturities over 25
years can be delivered.
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A portfolio is worth $24,000,000. The futures price for a
Treasury note futures contract is 110 and each contract is for
the delivery of bonds with a face value of $100,000. On the
delivery date the duration of the bond that is expected to be
cheapest to deliver is 6 years and the duration of the portfolio
will be 5.5 years. How many contracts are necessary for
hedging the portfolio? A.100
B.200
C.300
D.400
Answer: B
The contract price is 110,000. The number of contracts is
(24,000,000×5.5)/(110,000×6.0)=200
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Which of the following is true?
A.The futures rates calculated from a Eurodollar futures quote
are always less than the corresponding forward rate
B.The futures rates calculated from a Eurodollar futures quote
are always greater than the corresponding forward rate
C.The futures rates calculated from a Eurodollar futures quote
should equal the corresponding forward rate
D.The futures rates calculated from a Eurodollar futures quote
are sometimes greater than and sometimes less than the
corresponding forward rate
Answer: B
The futures rate must be reduced by what is known as a convexity
adjustment to get the forward rate.
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How much is a basis point?
A.1.0%
B.0.1%
C.0.01%
D.0.001%
Answer: C
A basis point is 0.01%.
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Which of the following day count conventions applies to a US
Treasury bond?
A.Actual/360
B.Actual/Actual (in period)
C.30/360
D.Actual/365
Answer: B
Actual/Actual (in period) is used for US Treasury bonds. This means
that the interest earned during a period that lies between two
coupon payment dates is calculated by dividing the actual number
of days in the period by the number of days between the coupon
payments and multiplying the result by the next coupon payment
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What is the quoted discount rate on a money market
instrument?
A.The interest rate earned as a percentage of the final face
value of a bond
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B.The interest rate earned as a percentage of the initial price of
a bond
C.The interest rate earned as a percentage of the average price
of a bond
D.The risk-free rate used to calculate the present value of
future cash flows from a bond
Answer: A
The quoted discount rate is the interest earned as a percentage of
the final face value
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Which of the following is closest to the duration of a 2-year
bond that pays a coupon of 8% per annum semiannually? The
yield on the bond is 10% per annum with continuous
compounding.
A.1.82
B.1.85
C.1.88
D.1.92
Answer: C
The duration of the bond is the weighted average of the times when
cash flows are received with weights proportional to the present
values of the cash flows.
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Which of the following is NOT true about duration?
A.It equals the years-to-maturity for a zero coupon bond
B.It equals the weighted average of payment times for a bond,
where weights are proportional to the present value of
payments
C.Equals the weighted average of individual bond durations for
a portfolio, where weights are proportional to the present value
of bond prices
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D.The prices of two bonds with the same duration change by
the same percentage amount when interest rate moves up by
100 basis points
Answer: D
D is only approximately true. A, B, and C are exactly true.
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16.The conversion factor for a bond is approximately
The price it would have if all cash flows were discounted at 6%
per annum
B.The price it would have if it paid coupons at 6% per annum
C.The price it would have if all cash flows were discounted at
8% per annum
D.The price it would have if it paid coupons at 8% per annum
Answer: A
The calculation of the conversion factor involves discounting the
cash flows on the bond at 6%.
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The time-to-maturity of a Eurodollars futures contract is 4
years and the time-to-maturity of the rate underlying the
futures contract is 4.25 years. The standard deviation of the
change in the short term interest rate, ± = 0.011. What does the
model in the text estimate as the difference between the futures
and the forward interest rate?
A. 0.105%
B. 0.103%
C. 0.098%
D. 0.093%
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Answer: B
With the notation in the text, the futures rate exceeds the forward
rate by 0.5±2T1T2. In this case ±=0.011, T1=4 and T2=4.25 so the
difference between the forward and futures price is
0.5×0.011×4×4.25=0.00103.
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A trader uses 3-month Eurodollar futures to lock in a rate on $5
million for six months. How many contracts are required?
A.5
B.10
C.15
D.20
Answer: B
Each contract locks in the rate on $1 million dollars for three
months. A six month instrument is approximately twice as sensitive
to rate movements as a three month instrument because it has
twice the duration. 2×5 = 10 contracts are therefore required
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In the U.S. what is the longest maturity for 3-month Eurodollar
futures contracts?
A: 2 years
B: 5 years
C: 10 years
D: 20 years
Answer: C
Eurodollar futures have maturities out to 10 years.
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Duration matching immunizes a portfolio against
A.Any parallel shift in the yield curve
B.All shifts in the yield curve
C.Changes in the steepness of the yield curve
D.Small parallel shifts in the yield curve
Answer: D
Duration matching only protects against small parallel shifts. It does
not provide protection against large parallel shifts and non-parallel
shifts.
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Which of the following describes a call option?
A.The right to buy an asset for a certain price
B.The obligation to buy an asset for a certain price
C.The right to sell an asset for a certain price
D.The obligation to sell an asset for a certain price
Answer: A
A call option is the right, but not the obligation to buy.
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2.Which of the following is true?
A.A long call is the same as a short put
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B.A short call is the same as a long put
C.A call on a stock plus a stock the same as a put
D.None of the above
Answer: D
None of the statements are true. Long calls, short calls, long puts,
and short puts all have different payoffs as indicated by Figure 10.5.
A put on a stock plus the stock provides a payoff that is similar to a
call, as explained in Chapters 11 and 12. But a call on a stock plus a
stock does not provide a similar payoff to a put.
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3.An investor has exchange-traded put options to sell 100
shares for $20. There is a 2 for 1 stock split. Which of the
following is the position of the investor after the stock split?
A.Put options to sell 100 shares for $20
B.Put options to sell 100 shares for $10
C.Put options to sell 200 shares for $10
D.Put options to sell 200 shares for $20
Answer: C
When there is a stock split the number of shares increases and the
strike price decreases. In this case, because it is a 2 for 1 stock
split, the number of shares doubles and the strike price halves.
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4.An investor has exchange-traded put options to sell 100
shares for $20. There is 25% stock dividend. Which of the
following is the position of the investor after the stock
dividend?
A.Put options to sell 100 shares for $20
B.Put options to sell 75 shares for $25
C.Put options to sell 125 shares for $15
D.Put options to sell 125 shares for $16
Answer: D
The stock dividend is equivalent to a 5 for 4 stock split. The number
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of shares goes up by 25% and the strike price is reduced to 4/5 of
its previous value.
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5.An investor has exchange-traded put options to sell 100
shares for $20. There is a $1 cash dividend. Which of the
following is then the position of the investor?
A.The investor has put options to sell 100 shares for $20
B.The investor has put options to sell 100 shares for $19
C.The investor has put options to sell 105 shares for $19
D.The investor has put options to sell 105 shares for $19.05
Answer: A
Cash dividends unless they are unusually large have no effect
on the terms of an option.
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6.Which of the following describes a short position in an
option?
A.A position in an option lasting less than one month
B.A position in an option lasting less than three months
C.A position in an option lasting less than six months
D.A position where an option has been sold
Answer: D
A short position is a position where the option has been sold (the
opposite to a long position).
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7.Which of the following describes a difference between a
warrant and an exchange-traded stock option?
A.In a warrant issue, someone has guaranteed the performance
of the option seller in the event that the option is exercised
B.The number of warrants is fixed whereas the number of
exchange-traded options in existence depends on trading
C.Exchange-traded stock options have a strike price
D.Warrants cannot be traded after they have been purchased
Answer: B
A warrant is a fixed number of options issued by a company. They
often trade on an exchange after they have been issued.
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1.Which of the following describes LEAPS?
A.Options which are partly American and partly European
B.Options where the strike price changes through time
C.Exchange-traded stock options with longer lives than regular
exchange-traded stock options
D.Options on the average stock price during a period of time
Answer: C
LEAPS are long-term equity anticipation securities. They are
exchange-traded options with relatively long maturities.
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8.Which of the following is an example of an option class?
A.All calls on a certain stock
B.All calls with a particular strike price on a certain stock
C.All calls with a particular time to maturity on a certain stock
D.All calls with a particular time to maturity and strike price on
a certain stock
Answer: A
An option class is all calls on a certain stock or all puts on a certain
stock.
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9.Which of the following is an example of an option series?
A.All calls on a certain stock
B.All calls with a particular strike price on a certain stock
C.All calls with a particular time to maturity on a certain stock
D.All calls with a particular time to maturity and strike price on
a certain stock
Answer: D
All options on a certain stock of a certain type (calls or put) with a
certain strike price and time to maturity are referred to as an option
series
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10.Which of the following must post margin?
A.The seller of an option
B.The buyer of an option
C.The seller and the buyer of an option
D.Neither the seller nor the buyer of an option
Answer: A
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The seller of the option must post margin as a guarantee that the
payoff on the option (if there is one) will be made. The buyer of the
option usually pays for the option upfront and so no margin is
required.
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11.Which of the following describes a long position in an
option?
A.A position where there is more than one year to maturity
B.A position where there is more than five years to maturity
C.A position where an option has been purchased
D.A position that has been held for a long time
Answer: C
A long position is a position where an option has been purchased. It
can be contrasted with a short position which is a position where an
option has been sold.
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12.Which of the following is NOT traded by the CBOE?
A.Weeklys
B.Monthlys
C.Binary options
D.DOOM options
Answer: B
Monthlys are not a CBOE product. The others are.
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13.When a six-month option is purchased
A.The price must be paid in full
B.Up to 25% of the option price can be borrowed using a
margin account
C.Up to 50% of the option price can be borrowed using a
margin account
D.Up to 75% of the option price can be borrowed using a
margin account
Answer: A
Only options lasting more than 9 months can be bought on
margin.
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14.Which of the following are true for CBOE stock options?
A.There are no margin requirements
B.The initial margin and maintenance margin are determined by
formulas and are equal
C.The initial margin and maintenance margin are determined by
formulas and are different
D.The maintenance margin is usually about 75% of the initial
margin
Answer: B
Margin accounts for options must be brought up to the
initial/maintenance margin level every day.
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15.The price of a stock is $67. A trader sells 5 put option
contracts on the stock with a strike price of $70 when the
option price is $4. The options are exercised when the stock
price is $69. What is the trader’s net profit or loss?
A.Loss of $1,500
B.Loss of $500
C.Gain of $1,500
D.Loss of $1,000
Answer: C
The option payoff is 70−69 = $1. The amount received for the option
is $4. The gain is $3 per option. In total 5×100 = 500 options are
sold. The total gain is therefore $3 × 500 = $1,500.
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16.A trader buys a call and sells a put with the same strike
price and maturity date. What is the position equivalent to?
A.A long forward
B.A short forward
C.Buying the asset
D.None of the above
Answer: A
From adding up the two payoffs we see that A is true:
max(ST−K,0)−max(K−ST,0)= ST−K
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17.The price of a stock is $64. A trader buys 1 put option
contract on the stock with a strike price of $60 when the option
price is $10. When does the trader make a profit?
A.When the stock price is below $60
B.When the stock price is below $64
C.When the stock price is below $54
D.When the stock price is below $50
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Answer: D
The payoff must be more than the $10 paid for the option. The stock
price must therefore be below $50.
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18.Consider a put option and a call option with the same strike
price and time to maturity. Which of the following is true?
A.It is possible for both options to be in the money
B.It is possible for both options to be out of the money
C.One of the options must be in the money
D.One of the options must be either in the money or at the
money
Answer: D
If the stock price is greater than the strike price the call is in the
money and the put is out of the money. If the stock price is less than
the strike price the call is out of the money and the put is in the
money. If the stock price is equal to the strike price both options are
at the money.
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19.In which of the following cases is an asset NOT considered
constructively sold?
A.The owner shorts the asset
B.The owner buys an in-the-money put option on the asset C.The owner shorts a forward contract on the asset
D.The owner shorts a futures contract on the stock
Answer: B
Profits on the asset have to be recognized in A, C, and D. The
holder of the asset cannot defer recognition of profits with the trades
indicated. In the case of B the asset is not considered constructively
sold. Buying a deep-in-the-money put option is a way of almost
certainly locking in a profit on an asset without triggering an
immediate tax liability.
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1.When the stock price increases with all else remaining the
same, which of the following is true?
A.Both calls and puts increase in value
B.Both calls and puts decrease in value
C.Calls increase in value while puts decrease in value
D.Puts increase in value while calls decrease in value
Answer: C
Stock price increases cause the values of calls to increase and the
values of puts to decline.
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2.When the strike price increases with all else remaining the
same, which of the following is true? A.Both calls and puts increase in value
B.Both calls and puts decrease in value
C.Calls increase in value while puts decrease in value
D.Puts increase in value while calls decrease in value
Answer: D
Strike price increases cause the values of puts to increase and the
values of calls to decline.
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3.When volatility increases with all else remaining the same,
which of the following is true? A.Both calls and puts increase in value
B.Both calls and puts decrease in value
C.Calls increase in value while puts decrease in value
D.Puts increase in value while calls decrease in value
Answer: A
Volatility increases the likelihood of a high payoff from either a call
or a put option. The payoff can never be negative. It follows that as
volatility increases the value of all options increase.
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4.When dividends increase with all else remaining the same,
which of the following is true? A.Both calls and puts increase in value
B.Both calls and puts decrease in value
C.Calls increase in value while puts decrease in value
D.Puts increase in value while calls decrease in value
Answer: D
Dividends during the life of an option reduce the final stock price. As
a result dividend increases cause puts to increase in value and calls
to decrease in value.
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5.When interest rates increase with all else remaining the
same, which of the following is true? A.Both calls and puts increase in value
B.Both calls and puts decrease in value
C.Calls increase in value while puts decrease in value
D.Puts increase in value while calls decrease in value
Answer: C
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Calls increase and puts decrease in value. As explained in the text
an increase in interest rates causes the growth rate of the stock
price to increase and the discount rate to increase. An increase in
interest rates therefore reduces the value of puts because puts are
hurt by both a discount rate increase and a growth rate increase.
For calls it turns out that the growth rate increase is more important
than the discount rate increase so that their values increase when
interest rates increase. (Note that we are assuming all else equal
and so the asset price does not change.)
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6.When the time to maturity increases with all else remaining
the same, which of the following is true? A.European options always increase in value
B.The value of European options either stays the same or
increases
C.There is no effect on European option values
D.European options are liable to increase or decrease in value
Answer: D
When the time to maturity increases from X to Y, European options
usually increase in value. But they can decrease in value if a big
dividend expected between X and Y.
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7.The price of a stock, which pays no dividends, is $30 and the
strike price of a one year European call option on the stock is
$25. The risk-free rate is 4% (continuously compounded).
Which of the following is a lower bound for the option such
that there are arbitrage opportunities if the price is below the
lower bound and no arbitrage opportunities if it is above the
lower bound?
A.$5.00
B.$5.98
C.$4.98
D.$3.98
Answer: B
The lower bound in S0 − Ke-rT. In this case it is 30 – 25e-0.04×1 =
$5.98.
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8.A stock price (which pays no dividends) is $50 and the strike
price of a two year European put option is $54. The risk-free
rate is 3% (continuously compounded). Which of the following
is a lower bound for the option such that there are arbitrage
opportunities if the price is below the lower bound and no
arbitrage opportunities if it is above the lower bound?
A.$4.00
B.$3.86
C.$2.86
D.$0.86
Answer: D
The lower bound in Ke-rT −S0 In this case it is 54e−0.03×2 – 50=
$0.86.
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9.Which of the following is NOT true? (Present values are
calculated from the end of the life of the option to the
beginning.)
A.An American put option is always worth less than the present
value of the strike price
B.A European put option is always worth less than the present
value of the strike price
C.A European call option is always worth less than the stock
price
D.An American call option is always worth less than the stock
price
Answer: A
If it is optimal to exercise an American option today and the stock
price is very low the option will be worth more than the present
value of the strike price
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10.Which of the following best describes the intrinsic value of
an option?
A.The value it would have if the owner had to exercise it
immediately or not at all
B.The Black-Scholes-Merton price of the option
C.The lower bound for the option’s price
D.The amount paid for the option
Answer: A
The intrinsic value of an option is the value it would have if it were
about the expire which is the same as the value in A.
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11.Which of the following describes a situation where an
American put option on a stock becomes more likely to be
exercised early?
A.Expected dividends increase
B.Interest rates decrease
C.The stock price volatility decreases
D.All of the above
Answer: C
As the volatility of the option decreases the time value declines and
the option becomes more likely to be exercised early. In the case of
A and B, time value increases and the option is less likely to be
exercised early.
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12.Which of the following is true?
A.An American call option on a stock should never be
exercised early
B.An American call option on a stock should never be
exercised early when no dividends are expected
C.There is always some chance that an American call option on
a stock will be exercised early
D.There is always some chance that an American call option on
a stock will be exercised early when no dividends are expected
Answer: B
An American call option should never be exercised early when the
underlying stock does not pay dividends. There are two reasons.
First, it is best to delay paying the strike price. Second the insurance
provided by the option (that the stock price will fall below the strike
price) is lost.
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13.Which of the following is the put-call parity result for a non-
dividend-paying stock?
A.The European put price plus the European call price must
equal the stock price plus the present value of the strike price
B.The European put price plus the present value of the strike
price must equal the European call price plus the stock price
C.The European put price plus the stock price must equal the
European call price plus the strike price
D.The European put price plus the stock price must equal the
European call price plus the present value of the strike price
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Answer: D
The put-call parity result is c+Ke-rT=p+S0.
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14.Which of the following is true when dividends are expected?
A.Put-call parity does not hold
B.The basic put-call parity formula can be adjusted by
subtracting the present value of expected dividends from the
stock price
C.The basic put-call parity formula can be adjusted by adding
the present value of expected dividends to the stock price
D.The basic put-call parity formula can be adjusted by
subtracting the dividend yield from the interest rate
Answer: B
Put call parity still holds for European options providing the present
value of the dividends is subtracted from the stock price.
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15.The price of a European call option on a non-dividend-
paying stock with a strike price of $50 is $6. The stock price is
$51, the continuously compounded risk-free rate (all maturities)
is 6% and the time to maturity is one year. What is the price of a
one-year European put option on the stock with a strike price
of $50? A.$9.91
B.$7.00
C.$6.00
D.$2.09
Answer: D
Put-call parity is c+Ke-rT=p+S0. In this case K=50, S0=51, r=0.06,
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T=1, and c=6. It follows that
p=6+50e-0.06×1−51 = 2.09.
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16.The price of a European call option on a stock with a strike
price of $50 is $6. The stock price is $51, the continuously
compounded risk-free rate (all maturities) is 6% and the time to
maturity is one year. A dividend of $1 is expected in six
months. What is the price of a one-year European put option on
the stock with a strike price of $50? A.$8.97
B.$6.97
C.$3.06
D.$1.12
Answer: C
Put-call parity is c+Ke-rT=p+S0. In this case K=50, S0=51, r=0.06,
T=1, and c=6. The present value of the dividend is 1×e−0.06×0.5 =
0.97. It follows that
p=6+50e-0.06×1−(51-0.97) = 3.06
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17. A European call and a European put on a stock have the
same strike price and time to maturity. At 10:00am on a certain
day, the price of the call is $3 and the price of the put is $4. At
10:01am news reaches the market that has no effect on the
stock price or interest rates, but increases volatilities. As a
result the price of the call changes to $4.50. Which of the
following is correct?
A.The put price increases to $6.00
B.The put price decreases to $2.00
C.The put price increases to $5.50
D.It is possible that there is no effect on the put price
Answer: C
The price of the call has increased by $1.50. From put-call parity the
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price of the put must increase by the same amount. Hence the put
price will become 4.00 +1.50 = $5.50.
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18.Interest rates are zero. A European call with a strike price of
$50 and a maturity of one year is worth $6. A European put with
a strike price of $50 and a maturity of one year is worth $7. The
current stock price is $49. Which of the following is true?
A.The call price is high relative to the put price
B.The put price is high relative to the call price
C.Both the call and put must be mispriced
D.None of the above
Answer: D
In this case because interest rates are zero c+K=p+S0. The left side
of this equation is 50+6=56. The right side is 49+7=56. There is no
mispricing.
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19.Which of the following is true for American options?
A.Put-call parity provides an upper and lower bound for the
difference between call and put prices
B.Put call parity provides an upper bound but no lower bound
for the difference between call and put prices
C.Put call parity provides an lower bound but no upper bound
for the difference between call and put prices
D.There are no put-call parity results Answer: A
Put call parity provides both an upper and lower bound for the
difference between call and put prices. See equation (11.11).
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20.Which of the following can be used to create a long position
in a European put option on a stock?
A.Buy a call option on the stock and buy the stock
B.Buy a call on the stock and short the stock
C.Sell a call option on the stock and buy the stock
D.Sell a call option on the stock and sell the stock
Answer: B
As payoff diagrams show a call on a stock combined with a short
position in the stock gives a payoff similar to a put option.
Alternatively we can use put-call parity, which shows that a call
minus the stock equals the put minus the present value of the strike
price.
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Which of the following creates a bull spread?
A.Buy a low strike price call and sell a high strike price call
B.Buy a high strike price call and sell a low strike price call
C.Buy a low strike price call and sell a high strike price put
D.Buy a low strike price put and sell a high strike price call
Answer: A
A bull spread is created by buying a low strike call and selling a high
strike call. Alternatively, it can be created by buying a low strike put
and selling a high strike put.
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2.Which of the following creates a bear spread?
A.Buy a low strike price call and sell a high strike price call
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B.Buy a high strike price call and sell a low strike price call
C.Buy a low strike price call and sell a high strike price put
D.Buy a low strike price put and sell a high strike price call
Answer: B
A bear spread is created by buying a high strike call and selling a
low strike call. Alternatively, it can be created by buying a high strike
put and selling a low strike put
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3.Which of the following creates a bull spread?
A.Buy a low strike price put and sell a high strike price put
B.Buy a high strike price put and sell a low strike price put
C.Buy a high strike price call and sell a low strike price put
D.Buy a high strike price put and sell a low strike price call
Answer: A
A bull spread is created by buying a low strike call and selling a high
strike call. Alternatively, it can be created by buying a low strike put
and selling a high strike put.
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4. Which of the following creates a bear spread?
A.Buy a low strike price put and sell a high strike price put
B.Buy a high strike price put and sell a low strike price put
C.Buy a high strike price call and sell a low strike price put
D.Buy a high strike price put and sell a low strike price call
Answer: B
A bear spread is created by buying a high strike call and selling a
low strike call. Alternatively, it can be created by buying a high strike
put and selling a low strike put.
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5.What is the number of different option series used in creating
a butterfly spread?
A.1
B.2
C.3
D.4
Answer: C
Three different options all with the same maturity are involved in
creating a butterfly spread. The strike prices are usually equally
spaced. The creator buys the low strike option, buys the high strike
option, and sells two of the intermediate strike option
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1.A stock price is currently $23. A reverse (i.e short) butterfly
spread is created from options with strike prices of $20, $25,
and $30. Which of the following is true?
A.The gain when the stock price is greater that $30 is less than
the gain when the stock price is less than $20
B.The gain when the stock price is greater that $30 is greater
than the gain when the stock price is less than $20
C.The gain when the stock price is greater that $30 is the same
as the gain when the stock price is less than $20
D.It is incorrect to assume that there is always a gain when the
stock price is greater than $30 or less than $20 Answer: C
The gain from a very high stock price or a very low stock price is the
same. Suppose calls are used. In the case of a very low stock price
none are exercised and the gain is c1+c3−2c2 from the option
premium. In the case of a very high stock price all options are
exercised. The net payoff is zero and the gain is the same.
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7.Which of the following is correct?
A.A calendar spread can be created by buying a call and selling
a put when the strike prices are the same and the times to
maturity are different
B.A calendar spread can be created by buying a put and selling
a call when the strike prices are the same and the times to
maturity are different
C.A calendar spread can be created by buying a call and selling
a call when the strike prices are different and the times to
maturity are different
D.A calendar spread can be created by buying a call and selling
a call when the strike prices are the same and the times to
maturity are different
Answer: D
A calendar spread is created by buying an option with one maturity
and selling an option with another maturity when the strike prices
are the same and the option types (calls or puts) are the same.
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8.What is a description of the trading strategy where an
investor sells a 3-month call option and buys a one-year call
option, where both options have a strike price of $100 and the
underlying stock price is $75?
A.Neutral Calendar Spread
B.Bullish Calendar Spread
C.Bearish Calendar Spread
D.None of the above
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Answer: B
This is a bullish calendar spread because a big increase in the stock
price between three months and one year is necessary for the
trading strategy to be profitable.
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9.Which of the following is correct?
A.A diagonal spread can be created by buying a call and selling
a put when the strike prices are the same and the times to
maturity are different
B.A diagonal spread can be created by buying a put and selling
a call when the strike prices are the same and the times to
maturity are different
C.A diagonal spread can be created by buying a call and selling
a call when the strike prices are different and the times to
maturity are different
D.A diagonal spread can be created by buying a call and selling
a call when the strike prices are the same and the times to
maturity are different
Answer: C
Both the strike prices and times to maturity are different in a
diagonal spread.
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10.Which of the following is true of a box spread?
A.It is a package consisting of a bull spread and a bear spread
B.It involves two call options and two put options
C.It has a known value at maturity D.All of the above
Answer: D
A, B, and C are all true.
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11.How can a straddle be created?
A.Buy one call and one put with the same strike price and same
expiration date
B.Buy one call and one put with different strike prices and
same expiration date
C.Buy one call and two puts with the same strike price and
expiration date
D.Buy two calls and one put with the same strike price and
expiration date
Answer: A
A straddle consists of one call and one put where the strike price
and time to maturity are the same. It has a V-shaped payoff.
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12.How can a strip trading strategy be created?
A.Buy one call and one put with the same strike price and same
expiration date
B.Buy one call and one put with different strike prices and
same expiration date
C.Buy one call and two puts with the same strike price and
expiration date
D.Buy two calls and one put with the same strike price and
expiration date
Answer: C
A strip consists of one call and two puts with the same strike price
and time to maturity.
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13.How can a strap trading strategy be created?
A.Buy one call and one put with the same strike price and same
expiration date
B.Buy one call and one put with different strike prices and
same expiration date
C.Buy one call and two puts with the same strike price and
expiration date
D.Buy two calls and one put with the same strike price and
expiration date
Answer: D
A strap consists of two calls and one put with the same strike price
and time to maturity.
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14.How can a strangle trading strategy be created?
A.Buy one call and one put with the same strike price and same
expiration date
B.Buy one call and one put with different strike prices and
same expiration date
C.Buy one call and two puts with the same strike price and
expiration date
D.Buy two calls and one put with the same strike price and
expiration date
Answer: B
A straddle consists of one call and one put where the times to
maturity are the same but the call strike price is greater than the put
strike price.
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15.Which of the following describes a protective put?
A.A long put option on a stock plus a long position in the
stock
B.A long put option on a stock plus a short position in the
stock
C.A short put option on a stock plus a short call option on the
stock
D.A short put option on a stock plus a long position in the
stock
Answer: A
A protective put consists of a long put plus the stock. The holder of
the put owns the stock that might become deliverable.
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16.Which of the following describes a covered call?
A.A long call option on a stock plus a long position in the
stock
B.A long call option on a stock plus a short put option on the
stock
C.A short call option on a stock plus a short position in the
stock
D.A short call option on a stock plus a long position in the
stock
Answer: D
A covered call consists of a short call plus a long position in the
stock. The if the call is exercised the owner of the position has the
stock ready to deliver if the other side exercises the call.
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17.When the interest rate is 5% per annum with continuous
compounding, which of the following creates a principal
protected note worth $1000?
A.A one-year zero-coupon bond plus a one-year call option
worth about $59
B.A one-year zero-coupon bond plus a one-year call option
worth about $49
C.A one-year zero-coupon bond plus a one-year call option
worth about $39
D.A one-year zero-coupon bond plus a one-year call option
worth about $29
Answer: B
A one-year zero-coupon bond is worth 1000e-0.05×1 or about $951.
This leaves 1000−951 = $49 for buying the option.
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18.A trader creates a long butterfly spread from options with
strike prices $60, $65, and $70 by trading a total of 400 options.
The options are worth $11, $14, and $18. What is the maximum
net gain (after the cost of the options is taken into account)?
A.$100
B.$200
C.$300
D.$400
Answer: D
The butterfly spread involves buying 100 options with strike prices
$60 and $70 and selling 200 options with strike price $65. The
maximum gain is when the stock price equals the middle strike
price, $65. The payoffs from the options are then, $500, 0, and 0,
respectively. The total payoff is $500. The cost of setting up the
butterfly spread is 11×100+18×100−14×200 = $100. The gain is
500−100 or $400.
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19.A trader creates a long butterfly spread from options with
strike prices $60, $65, and $70 by trading a total of 400 options.
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The options are worth $11, $14, and $18. What is the maximum
net loss (after the cost of the options is taken into account)?
A.$100
B.$200
C.$300
D.$400
Answer: A
The butterfly spread involves buying 100 options with strike prices
$60 and $70 and selling 200 options with strike price $65. The
maximum loss is when the stock price is less than $60 or greater
than $70. The total payoff is then zero. The cost of setting up the
butterfly spread is 11×100+18×100−14×200 = $100. The loss is
therefore $100.
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20.Six-month call options with strike prices of $35 and $40 cost
$6 and $4, respectively. What is the maximum gain when a bull
spread is created by trading a total of 200 options?
A.$100
B.$200
C.$300
D.$400
Answer: C
The bull spread involves buying 100 calls with strike $35 and selling
100 calls with strike price $40. The cost is 6×100−4×100=$200. The
maximum payoff (when the stock price is greater than or equal to
$40 is $500. The maximum gain is therefore 500 −200 = $300.
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1.The current price of a non-dividend-paying stock is $30. Over
the next six months it is expected to rise to $36 or fall to $26.
Assume the risk-free rate is zero. An investor sells call options
with a strike price of $32. Which of the following hedges the
position?
A.Buy 0.6 shares for each call option sold
B.Buy 0.4 shares for each call option sold
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C.Short 0.6 shares for each call option sold
D.Short 0.6 shares for each call option sold
Answer: B
The value of the option will be either $4 or zero. If ± is the position
in the stock we require 36±−4=26±
so that ±=0.4. it follows that 0.4 shares should be purchased for
each option sold.
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2.The current price of a non-dividend-paying stock is $30. Over
the next six months it is expected to rise to $36 or fall to $26.
Assume the risk-free rate is zero. What is the risk-neutral
probability of that the stock price will be $36?
A.0.6
B.0.5
C.0.4
D.0.3
Answer: C
The formula for the risk-neutral probability of an up movement is
In this case u=36/30 or 1.2 and d=26/30 =0.8667. Also r=0 and
T=0.5. The formula gives
p=(1-0.8667/(1.2-0.8667) =0.4.
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3.The current price of a non-dividend-paying stock is $30. Over
the next six months it is expected to rise to $36 or fall to $26.
Assume the risk-free rate is zero. An investor sells call options
with a strike price of $32. What is the value of each call option?
A.$1.6
B.$2.0
C.$2.4
D.$3.0
Answer: A
The formula for the risk-neutral probability of an up movement is
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In this case u=36/30 or 1.2 and d=26/30 =0.8667. Also r=0 and
T=0.5. The formula gives
p=(1-0.8667/(1.2-0.8667) =0.4.
The payoff from the call option is $4 if there is an up movement and
$0 if there is a down movement. The value of the option is therefore
0.4×4 +0.6×0 = $1.6. (We do not do any discounting because the
interest rate is zero.)
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4.The current price of a non-dividend-paying stock is $40. Over
the next year it is expected to rise to $42 or fall to $37. An
investor buys put options with a strike price of $41. Which of
the following is necessary to hedge the position?
A.Buy 0.2 shares for each option purchased
B.Sell 0.2 shares for each option purchased
C.Buy 0.8 shares for each option purchased
D.Sell 0.8 shares for each option purchased
Answer: C
The payoff from the put option is zero if there is an up movement
and 4 if there is a down movement. Suppose that the investor buys
one put option and buys ± shares. If there is an up movement the
value of the portfolio is ±×42. If there is a down movement it is
worth ±×37+4. These are equal when 37±+4=42± or ±=0.8. The
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5.The current price of a non-dividend-paying stock is $40. Over
the next year it is expected to rise to $42 or fall to $37. An
investor buys put options with a strike price of $41. What is the
value of each option? The risk-free interest rate is 2% per
annum with continuous compounding.
A.$3.93
B.$2.93
C.$1.93
D.$0.93
Answer: D
The formula for the risk-neutral probability of an up movement is
In this case r=0.02, T= 1, u=42/40=1.05 and d=37/40=0.925 so that
p=0.76 and the value of the option is (0.76×0+0.24×4)e-
0.02×1=0.93
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6.Which of the following describes how American options can
be valued using a binomial tree?
A.Check whether early exercise is optimal at all nodes where
the option is in-the-money
B.Check whether early exercise is optimal at the final nodes
C.Check whether early exercise is optimal at the penultimate
nodes and the final nodes
D.None of the above
Answer: A
For an American option we must check whether exercising is better
than not exercising at each node where the option is in the money. (It is clearly not worth exercising when the option is out of the
money)
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7.In a binomial tree created to value an option on a stock, the
expected return on stock is
A.Zero
B.The return required by the market
C.The risk-free rate
D.It is impossible to know without more information
Answer: C
The expected return on the stock on the tree is the risk-free rate.
This is an application of risk-neutral valuation.
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8.In a binomial tree created to value an option on a stock, what
is the expected return on the option?
A.Zero
B.The return required by the market
C.The risk-free rate
D.It is impossible to know without more information
Answer: C
The expected return on the option on the tree is the risk-free rate.
This is an application of risk-neutral valuation. The expected return
on all assets in a risk-neutral world is the risk-free rate.
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9.A stock is expected to return 10% when the risk-free rate is
4%. What is the correct discount rate to use for the expected
payoff on an option in the real world?
A.4%
B.10%
C.More than 10%
D.It could be more or less than 10%
Answer: D
The correct answer is D. There is no easy way of determining the
correct discount rate for an option’s expected payoff in the real
world. For a call option the correct discount rate in the real world is
often quite high and for a put option it is often quite low (even
negative). The example in the text illustrates this
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10.Which of the following is true for a call option on a stock
worth $50
A.As a stock’s expected return increases the price of the option
increases
B.As a stock’s expected return increases the price of the option
decreases
C.As a stock’s expected return increases the price of the option
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might increase or decrease
D.As a stock’s expected return increases the price of the option
on the stock stays the same
Answer: D
The option price when expressed in terms of the underlying stock
price is independent of the return on the stock. To put this another
way, everything relevant about the expected return is incorporated
in the stock price.
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11.Which of the following are NOT true
A.Risk-neutral valuation and no-arbitrage arguments give the
same option prices
B.Risk-neutral valuation involves assuming that the expected
return is the risk-free rate and then discounting expected
payoffs at the risk-free rate
C.A hedge set up to value an option does not need to be
changed
D.All of the above
Answer: C The hedge set up to value an option needs to be changed as time
passes. A and B are true.
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12.The current price of a non-dividend paying stock is $30. Use
a two-step tree to value a European call option on the stock
with a strike price of $32 that expires in 6 months. Each step is
3 months, the risk free rate is 8% per annum with continuous
compounding. What is the option price when u = 1.1 and d =
0.9.
A.$1.29
B.$1.49
C.$1.69
D.$1.89
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Answer: B
The probability of an up movement is
The tree is
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13.The current price of a non-dividend paying stock is $30. Use
a two-step tree to value a European put option on the stock
with a strike price of $32 that expires in 6 months with u = 1.1
and d = 0.9. Each step is 3 months, the risk free rate is 8%.
A.$2.24
B.$2.44
C.$2.64
D.$2.84
Answer: A
The probability of an up movement is
The tree is
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14.Which of the following is NOT true in a risk-neutral world?
A.The expected return on a call option is independent of its
strike price
B.Investors expect higher returns to compensate for higher
risk
C.The expected return on a stock is the risk-free rate
D.The discount rate used for the expected payoff on an option
is the risk-free rate
Answer: B
In a risk-neutral world investors require an expected return equal to
the risk-free rate and the discount rate that should be used for all
expected payoffs is the risk-free rate.
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15.If the volatility of a non-dividend paying stock is 20% per
annum and a risk-free rate is 5% per annum, which of the
following is closest to the Cox, Ross, Rubinstein parameter u
for a tree with a three-month time step?
A.1.05
B.1.07
C.1.09
D.1.11
Answer: D
The formula for u is
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16.If the volatility of a non-dividend-paying stock is 20% per
annum and a risk-free rate is 5% per annum, which of the
following is closest to the Cox, Ross, Rubinstein parameter p
for a tree with a three-month time step?
A.0.50
B.0.54
C.0.58
D.0.62
The formula for p is
=0.538
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17.The current price of a non-dividend paying stock is $50. Use
a two-step tree to value an American put option on the stock
with a strike price of $48 that expires in 12 months. Each step
is 6 months, the risk free rate is 5% per annum, and the
volatility is 20%. Which of the following is the option price?
A.$1.95
B.$2.00
C.$2.05
D.$2.10
Answer: B
In this case
The tree is
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18.Which of the following describes delta?
A.The ratio of the option price to the stock price
B.The ratio of the stock price to the option price
C.The ratio of a change in the option price to the
corresponding change in the stock price
D.The ratio of a change in the stock price to the corresponding
change in the option price
Answer: C
Delta is ±f/±S where ±S is a small change in the stock price (with
nothing else changing) and ±f is the corresponding change in the
option price.
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When moving from valuing an option on a non-dividend paying
stock to an option on a currency which of the following is true?
A.The risk-free rate is replaced by the excess of the domestic
risk-free rate over the foreign risk-free rate in all calculations
B.The formula for u changes
C.The risk-free rate is replaced by the excess of the domestic
risk-free rate over the foreign risk-free rate for discounting
D.The risk-free rate is replaced by the excess of the domestic
risk-free rate over the foreign risk-free rate when p is
calculated Answer: D The formula for u does not change. The discount rate does not
change. The formula for p becomes
showing that D is correct.
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20.A tree is constructed to value an option on an index which is
currently worth 100 and has a volatility of 25%. The index
provides a dividend yield of 2%. Another tree is constructed to
value an option on a non-dividend-paying stock which is
currently worth 100 and has a volatility of 25%. Which of the
following are true?
A.The parameters p and u are the same for both trees
B.The parameter p is the same for both trees but u is not
C.The parameter u is the same for both trees but p is not
D.None of the above
Answer: C
The formula for u is the same in the two cases so that the values of
the index on its tree are the same as the values of the stock on its
tree. However, in the formula for p, r is replaced by r−q.
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1.A variable x starts at 10 and follows the generalized Wiener
process
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dx = a dt + b dz
where time is measured in years. If a = 2 and b =3 what is the
expected value after 3 years?
A.12
B.14
C.16
D.18
Answer: C
The drift is 2 per year and so the expected increase over three
years is 2×3 = 6 and the expected value at the end of 3 years is
10+6 = 16.
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2.A variable x starts at 10 and follows the generalized Wiener
process
dx = a dt + b dz
where time is measured in years. If a = 3 and b =4 what is the
standard deviation of the value in 4 years?
A.4
B.8
C.12
D.16
Answer: B
The variance per year is 42 or 16. The variance over four years is
16×4 = 64. The standard deviation is .
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3.A variable x starts at 10 and follows the generalized Wiener
process
dx = a dt + b dz
If a = 3 and b =4 what is the standard deviation of the value in
three months?
A.1
B.2
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C.3
D.4
Answer: B
The variance per year is 42 or 16. The variance over three months
is 16×0.25 = 4. The standard deviation is .
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4.The variance of a Wiener process in time t is
A. t
B. t squared
C. the square root of t
D. t to the power of 4
Answer: A
The variance of a Wiener process is 1 per unit time or t in time t.
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5.The process followed by a variable X is
dX = mX dt+sX dz
What is the coefficient of dz in the process for the square of X.
A.sX
B.sX2
C.2sX2
D.msX
Answer: C
From Ito’s lemma, the coefficient of dz is where f = X2. Because ,
the coefficient of dz is 2sX2.
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6.The process followed by a variable X is
dX = mX dt+sX dz
What is the coefficient of dt in the process for the square of X.
A.2mX2+s2X2
B.2mX2
C.mX2+2s2X2
D.mX2+s2X2
Answer: A
From Ito’s lemma, the coefficient of dt is
where f = X2. Because and the coefficient of dt is 2mX2+s2X2
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7.Which of the following is true when the stock price follows
geometric Brownian motion
A.The future stock price has a normal distribution
B.The future stock price has a lognormal distribution
C.The future stock price has geometric distribution
D.The future stock price has a truncated normal distribution
Answer: B
Ito’s lemma show that the log of the stock price follows a
generalized Wiener process. This means that the log of the stock
price is normally distributed so that the stock price is lognormally
distributed.
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8.If a stock price follows a Markov process which of the
following could be true
A.Whenever the stock price has gone up for four successive
days it has a 70% chance of going up on the fifth day.
B.Whenever the stock price has gone up for four successive
days there is almost certain to be a correction on the fifth day.
C.The way the stock price moves on a day is unaffected by how
it moved on the previous four days.
D.Bad years for stock price returns are usually followed by
good years.
Answer: C
A Markov process is a particular type of stochastic process where
only the current value of a variable is relevant for predicting the
future. Stock prices are usually assumed to follow Markov
processes. This corresponds to a weak form market efficiency
assumption.
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9.A variable x starts at zero and follows the generalized Wiener
process
dx = a dt + b dz
where time is measured in years. During the first two years a=3
and b=4. During the following three years a=6 and b=3. What is
the expected value of the variable at the end of 5 years
A.16
B.20
C.24
D.30
Answer: C
During the first two years, the drift per year is 3 and so the total drift
is 3×2 or 6. During the next three years, the drift per year is 6 and
the total drift is 6×3 = 18. The total drift over the five years is 6+18
=24. Given that the variable starts at zero, its expected value at the
end of the five years is therefore 24.
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10.A variable x starts at zero and follows the generalized
Wiener process
dx = a dt + b dz
where time is measured in years. During the first two years a=3
and b=4. During the following three years a=6 and b=3. What
the standard deviation of the value of the variable at the end of
5 years
A.6.2
B.6.7
C.7.2
D.7.7
Answer: D
The variance per year for the first two years is 42 or 16. The
variance per year for the next three years is 32 or 9. The total
variance of the change over five years is 2×16+3×9= 59. The
standard deviation of the value of the variable at the end of the five
years is therefore 231
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11.If a variable x follows the process dx = b dz where dz is a
Wiener process, which of the following is the process followed
by y = exp(x).
A.dy = by dz
B.dy = 0.5b2y dt+by dz
C.dy = (y+0.5b2y) dt+by dz
D.dy = 0.5b2y dt+b dz
Answer: B
Ito’s lemma shows that the process followed by y is dy =
0.5b2exp(x) dt +bexp(x) dz. Substituting y = exp(x) we get the
answer in B.
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12.If the risk-free rate is r and price of a nondividend paying
stock grows at rate m±with volatility s, at what rate does a
forward price of the stock grow for a forward contract maturing
at a future time T.
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A.m
B.m−s2/2
C.m−r
D.r−s2/2
Answer: C
This is the application of Ito’s lemma in Section 14.6.
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13.When a stock price, S, follows geometric Brownian motion
with mean return m and volatility s what is the process follows
by X where X = ln S.
A.dX = m dt + s dz
B.dX = (m−r) dt + s dz
C.dX = (m±−s2) dt + s dz
D.dX = (m − s2/2) dt + s dz
Answer: D
This is the example in Section 14.7
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15.Which of the following defines an Ito process?
A.A process where the drift is non-constant and can be
stochastic
B.A process where the coefficient of dz is non-constant and
can be stochastic
C.A process where either the drift or the coefficient of dz or
both are non-constant and can be stochastic
D.A process where proportional changes follow a generalized
Wiener process
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Answer: C
In a generalized Wiener process the drift and coefficient of dz are
both constant. In an Ito process they are not both constant .
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16.A stock price is $20. It has an expected return of 12% and a
volatility of 25%. What is the standard deviation of the change
in the price in one day. (For this question assume that there
are 365 days in the year.)
A.$0.20
B.$0.23
C.$0.26
D.$0.29
Answer: C
The standard deviation of the change in one day is 236
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17. A stock price is $20. It has an expected return of 12% and a
volatility of 25%. What is the stock price that has a 2.5% chance
of being exceeded in one day? (For this question assume that
there are 365 days in the year.)
A.$20.41
B.$20.51
C.$20.61
D.$20.71
Answer: B
From the previous question the standard deviation of the change in
one day is $0.26. There is a 2.5% chance that the stock price will
increase by more than 1.96 standard deviations. The answer is
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therefore 20+1.96×0.26 = $20.51. The expected return in one day is
small and can be ignored.
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18.Which of the following is NOT a property of a Wiener
process?
A.The change during a short period of time dt has a variance dt
B.The changes in two different short periods of time are
independent
C.The mean change in any time period is zero
D.The standard deviation over two consecutive time periods is
the sum of the standard deviations over each of the periods
Answer D
Variances of Wiener processes are additive but standard deviations
are not.
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19. If e is a random sample from a standard normal distribution,
which of the following is the change in a Wiener process in
time dt .
A.e times the square root of dt
B.e times dt
C.dt times the square root of e
D.The square root of e times the square root of dt
Answer: A
The change is . This result is used when the process is simulated.
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20. For what value of the correlation between two Wiener
processes is the sum of the processes also a Wiener process?
A.0.5
B.−0.5
C.0
D.1
Answer: B
The variance of each process is 1 per unit time. The variance of the
sum is 1+1+2±±where ±±is the correlation. This is 1 when ±=−0.5.
Deutsch
English
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Derivatives Midterm Prep
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An investor sells a futures contract an asset when the futures price is $1,500. Each contract is on 100 units of the as-
set. The contract is closed out when the futures price is $1,540. Which of the fol-
lowing is true
The investor has made a gain of $4,000
The investor has made a loss of $4,000
The investor has made a gain of $2,000
The investor has made a loss of $2,000
The investor has made a loss of $4,000
In contrast to contingent claims, forward commitments provide the:
right to buy or sell the underlying asset in the future.
obligation to buy or sell the underlying asset in the future.
promise to provide credit protection in the event of default.
obligation to buy or sell the underlying asset in the future.
Compared with the underlying spot mar-
ket, derivative markets are more likely to have:
greater liquidity.
higher transaction costs.
higher capital requirements.
greater liquidity.
Derivative markets typically have greater liquidity than the underlying spot market as a result of the lower capital required to trade derivatives compared with the underlying. Derivatives also have lower transaction costs and lower capital re-
quirements than the underlying.
The law of one price is best described as:
the true fundamental value of an asset.
earning a risk-free profit without commit-
ting any capital.
two assets that will produce the same cash flows in the future must sell for equivalent prices.
two assets that will produce the same cash flows in the future must sell for equivalent prices.
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An interest rate swap is a derivative con-
tract in which:
two parties agree to exchange a series of cash flows.
the credit seller provides protection to the credit buyer.
the buyer has the right to purchase the underlying from the seller.
two parties agree to exchange a series of cash flows.
"two parties" is correct. An interest rate swap is defined as a derivative in which two parties agree to exchange a series of cash flows: One set of cash flows is vari-
able, and the other set can be variable or fixed. "the credit seller ..." is incorrect because a credit derivative is a derivative contract in which the credit protection seller provides protection to the credit protection buyer. Choice "the buyer ..." is incorrect because a call option, not a swap, gives the buyer the right to pur-
chase the underlying from the seller.
Which of the following is approximately true when size is measured in terms of the underlying principal amounts or val-
ue of the underlying assets
The exchange-traded market is twice as big as the over-the-counter market.
The over-the-counter market is twice as big as the exchange-traded market.
The exchange-traded market is ten times as big as the over-the-counter market.
The over-the-counter market is ten times as big as the exchange-traded market.
The over-the-counter market is ten times as big as the exchange-traded market.
Which of the following is the best exam-
ple of a derivative? A global equity mutual fund
A non-callable government bond
A contract to purchase Apple Computer at a fixed price
A contract to purchase Apple Computer at a fixed price
Mutual funds and government bonds are *not* derivatives. A government bond is a fundamental asset on which derivatives might be created, but it is not a derivative itself. A mutual fund can technically meet the definition of a derivative, it's value is determined by the value of the "under-
2 / 54
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lying"stocks it contains, but derivatives transform the value of a payoff of an un-
derlying asset. Mutual funds merely pass those payoffs through to their holders.
Which of the following characteristics is not associated with exchange-traded de-
rivatives?
Margin or performance bonds are re-
quired.
The exchange guarantees all payments in the event of default.
All terms except the price are cus-
tomized to the parties' individual needs.
All terms except the price are customized to the parties' individual needs.
Exchange-traded contracts are stan-
dardized, meaning that the exchange de-
termines the terms of the contract ex-
cept the price. The exchange guarantees against default and requires margins or performance bonds.
Which of the following statements most accurately describes exchange-traded derivatives relative to over-the-counter derivatives? Exchange-traded deriva-
tives are more likely to have:
greater credit risk.
standardized contract terms.
greater risk management uses.
standardized contract terms.
Standardization of contract terms is a characteristic of exchange-traded deriv-
atives. Credit risk is well-controlled in ex-
change markets. Risk management uses are not limited by being traded over the counter.
Which of the following characteristics is least likely to be a benefit associated with using derivatives?
More effective management of risk
Payoffs similar to those associated with the underlying
Greater opportunities to go short com-
pared with the spot market
Payoffs similar to those associated with the underlying
A one-year call option on a stock with a strike price of $30 costs $3; a one-year put option on the stock with a strike price of $30 costs $4. Suppose that a trader buys two call options and one put option. The breakeven stock price below which $20
When the stock price is $20 the two call options provide no payoff. The put option provides a payoff of 3020 or $10. The 3 / 54
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the trader makes a profit is
$25
$28
$26
$20
total cost of the options is 2×3+ 4 or $10. The stock price in D, $20, is therefore the breakeven stock price below which the position is profitable because it is the price for which the cost of the options equals the payoff.
A derivative is best described as a fi-
nancial instrument that derives its perfor-
mance by:
passing through the returns of the under-
lying.
replicating the performance of the under-
lying.
transforming the performance of the un-
derlying.
transforming the performance of the un-
derlying.
Answer "transforming the performance of the underlying" is correct. A deriva-
tive is a financial instrument that trans-
forms the performance of the underlying. The transformation of performance func-
tion of derivatives is what distinguishes it from mutual funds and exchange traded funds that pass through the returns of the underlying. Answer "passing through ..." is incorrect because derivatives, in contrast to mutual funds and exchange traded funds, do not simply pass through the returns of the underlying at payout. Answer "replicating the ..." is incorrect because a derivative transforms rather than replicates the performance of the underlying
Exchange-traded derivatives are:
largely unregulated.
traded through an informal network.
guaranteed by a clearinghouse against default.
guaranteed by a clearinghouse against default.
A trader has a portfolio worth $5 million that mirrors the performance of a stock index. The stock index is currently 1,250. Futures contracts trade on the index with one contract being on 250 times the in-
dex. To remove market risk from the port-
folio the trader should
Sell 16 contracts
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Buy 16 contracts
Sell 16 contracts
Buy 20 contracts
Sell 20 contracts
Which of the following derivatives is least likely to have a value of zero at initiation of the contract?
Futures
Options
Forwards
Options
"Options" is correct. The buyer of the option pays the option premium to the seller of the option at the initiation of the contract. The option premium represents the value of the option, whereas futures and forwards have a value of zero at the initiation of the contract. Answer "futures" is incorrect because no money changes hands between parties at the initiation of the futures contract, thus the value of the futures contract is zero at initiation. Same for forwards.
Which of the following is *not* a charac-
teristic of a derivative
An underlying
A low degree of leverage
Two parties - a buyer and a seller
A low degree of leverage
All derivatives have an underlying and must have a buyer and a seller. More im-
portantly, derivatives have high degrees of leverage, not low degrees of leverage.
The price of a stock on July 1 is $57. A trader buys 100 call options on the stock with a strike price of $60 when the option price is $2. The options are exercised when the stock price is $65. The trader's net profit is
$700
$500
$300
$600
$300
Which of the following best describes the term "spot price"
The price for immediate delivery
The price for delivery at a future time
The price for immediate delivery
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The price of an asset that has been dam-
aged
The price of renting an asset
Which of the following is NOT true
A call option gives the holder the right to buy an asset by a certain date for a certain price
A put option gives the holder the right to sell an asset by a certain date for a certain price
The holder of a call or put option must exercise the right to sell or buy an asset
The holder of a forward contract is oblig-
ated to buy or sell an asset
The holder of a call or put option must exercise the right to sell or buy an asset
A company knows it will have to pay a certain amount of a foreign currency to one of its suppliers in the future. Which of the following is true?
A forward contract can be used to lock in the exchange rate
A forward contract will always give a bet-
ter outcome than an option
An option will always give a better out-
come than a forward contract
An option can be used to lock in the exchange rate
A forward contract can be used to lock in the exchange rate
The price of a stock on February 1 is $84. A trader buys 200 put options on the stock with a strike price of $90 when the option price is $10. The options are exercised when the stock price is $85. The trader's net profit or loss is
Loss of $1,000
Loss of $2,000
Loss of $1,000
The payoff is 9085 or $5 per option. For 200 options the payoff is therefore 5×200 or $1000. However the options cost 10×200 or $2000. There is therefore a net loss of $1000
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Gain of $200
Gain of $1000
Which of the following derivatives pro-
vide payoffs that are non-linearly related to the payoffs of the underlying?
Options
Forwards
Interest rate swaps
Options
"Options" is correct. Options are clas-
sified as a contingent claim which pro-
vides payoffs that are non-linearly relat-
ed to the performance of the underlying. "Forwards" is incorrect because forwards are classified as a forward commitment, which provides payoffs that are linearly related to the performance of the under-
lying. "Interest rate swaps" is incorrect because interest-rate swaps are classi-
fied as a forward commitment, which pro-
vides payoffs that are linearly related to the performance of the underlying.
Which of the following describes Euro-
pean options?
Sold in Europe
Priced in Euros
Exercisable only at maturity
Calls (there are no European puts)
Exercisable only at maturity
A short forward contract on an asset plus a long position in a European call option on the asset with a strike price equal to the forward price is equivalent to
A short position in a call option
A short position in a put option
A long position in a put option
None of the others
A long position in a put option
A credit derivative is a derivative contract in which the:
clearinghouse provides a credit guaran-
tee to both the buyer and the seller.
seller provides protection to the buyer against the credit risk of a third party.
seller provides protection to the buyer against the credit risk of a third party.
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the buyer and seller provide a perfor-
mance bond at initiation of the contract.
The price of a stock on February 1 is $124. A trader sells 200 put options on the stock with a strike price of $120 when the option price is $5. The options are exercised when the stock price is $110. The trader's net profit or loss is
Gain of $1,000
Loss of $2,000
Loss of $2,800
Loss of $1,000
Loss of $1,000
The payoff that must be made on the options is 200×(120110) or $2000. The amount received for the options is 5×200 or $1000. The net loss is therefore 20001000 or $1000.
Which of the following derivatives is clas-
sified as a contingent claim?
Futures contracts
Interest rate swaps
Credit default swaps
Credit default swaps
Which of the following is most likely to be a destabilizing consequence of specula-
tion using derivatives?
Increased defaults by speculators and creditors
Market price swings resulting from arbi-
trage activities
The creation of trading strategies that result in asymmetric performance
Increased defaults by speculators and creditors
The benefits of derivatives, such as low transaction costs, low capital require-
ments, use of leverage, and the ease in which participants can go short, also can result in excessive speculative trad-
ing. These activities can lead to defaults on the part of speculators and creditors. Arbitrage activities tend to bring about a convergence of prices to intrinsic val-
ue. Asymmetric performance is not itself destabilizing.
Market makers earn a profit in both ex-
change and over-the-counter derivatives markets by:
charging a commission on each trade.
a combination of commissions and buying at one price, selling at a higher price, and hedging any risk.
Market makers buy at one price (the bid), sell at a higher price (the ask), and 8 / 54
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markups.
buying at one price, selling at a higher price, and hedging any risk.
hedge whatever risk they otherwise as-
sume. Market makers do not charge a commission.
Which of the following statements about derivatives is *not* true?
They are created in the spot market.
They are used in the practice of risk man-
agement.
They take their values from the value of something else.
They are created in the spot market.
Derivatives are used to practice risk management and they take (derive) their values from the value of something else, the underlying. They are not created in the spot market, which is where the un-
derlying trades.
A one-year call option on a stock with a strike price of $30 costs $3; a one-year put option on the stock with a strike price of $30 costs $4. Suppose that a trader buys two call options and one put option. The breakeven stock price above which the trader makes a profit is:
$35
$40
$30
$36
$35
The price of a stock on February 1 is $48. A trader sells 200 put options on the stock with a strike price of $40 when the option price is $2. The options are exercised when the stock price is $39. The trader's net profit or loss is
Loss of $800
Loss of $200
Gain of $200
Loss of $900
Gain of $200
Arbitrage opportunities exist when:
two identical assets or derivatives sell for different prices.
combinations of the underlying asset and a derivative earn the risk-free rate.
arbitrageurs simultaneously buy two identical assets or derivatives sell for different prices.
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takeover targets and sell takeover ac-
quirers.
A one-year forward contract is an agree-
ment where
One side has the right to buy an asset for a certain price in one year's time.
One side has the obligation to buy an asset for a certain price in one year's time.
One side has the obligation to buy an asset for a certain price at some time during the next year.
One side has the obligation to buy an asset for the market price in one year's time.
One side has the obligation to buy an asset for a certain price in one year's time.
A one-year forward contract is an obliga-
tion to buy or sell in one year's time for a predetermined price. By contrast, an option is the right to buy or sell.
Which of the following best describes a central clearing party
It is a trader that works for an exchange
It stands between two parties in the over-the-counter market
It is a trader that works for a bank
It helps facilitate futures trades
It stands between two parties in the over-the-counter market
Which of the following is NOT true about call and put options:
An American option can be exercised at any time during its life
A European option can only be exercised only on the maturity date
Investors must pay an upfront price (the option premium) for an option contract
The price of a call option increases as the strike price increases
The price of a call option increases as the strike price increases
Which of the following characteristics is associated with over-the-counter deriva-
tives?
They are less transparent than ex-
change-listed derivatives.
OTC derivatives have a lower degree of transparency than exchange-listed deriv-
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Trading occurs in a central location.
They are more regulated than ex-
change-listed derivatives.
They are less transparent than ex-
change-listed derivatives.
atives. Trading does not occur in a central location but, rather, is quite dispersed. Al-
though new national securities laws are tightening the regulation of OTC deriv-
atives, the degree of regulation is less than that of exchange-listed derivatives.
Forward commitments subject to default are:
forwards and futures.
futures and interest rate swaps.
interest rate swaps and forwards.
interest rate swaps and forwards.
Choice "interest rate swaps and for-
wards" is correct. Interest rate swaps and forwards are over-the-counter con-
tracts that are privately negotiated and are both subject to default. Futures con-
tracts are traded on an exchange, which provides a credit guarantee and pro-
tection against default. Futures are ex-
change-traded contracts which provide daily settlement of gains and losses and a credit guarantee by the exchange through its clearinghouse.
Which of the following is true about a long forward contract
The contract becomes more valuable as the price of the asset declines
The contract becomes more valuable as the price of the asset rises
The contract is worth zero if the price of the asset declines after the contract has been entered into
The contract is worth zero if the price of the asset rises after the contract has been entered into
The contract becomes more valuable as the price of the asset rises
Compared with exchange-traded deriva-
tives, over-the-counter derivatives would most likely be described as:
standardized.
less transparent.
more transparent.
less transparent.
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A haircut of 20% means that
A bond with a market value of $100 is considered to be worth $80 when used to satisfy a collateral request
A bond with a face value of $100 is con-
sidered to be worth $80 when used to satisfy a collateral request
A bond with a market value of $100 is considered to be worth $83.3 when used to satisfy a collateral request
A bond with a face value of $100 is con-
sidered to be worth $83.3 when used to satisfy a collateral request
A bond with a market value of $100 is considered to be worth $80 when used to satisfy a collateral request
In the corn futures contract a number of different types of corn can be delivered (with price adjustments specified by the exchange) and there are a number of different delivery locations. Which of the following is true
This flexibility tends increase the futures price.
This flexibility tends decrease the futures price.
This flexibility may increase and may de-
crease the futures price.
This flexibility has no effect on the futures price
This flexibility tends decrease the futures price.
One futures contract is traded where both the long and short parties are clos-
ing out existing positions. What is the resultant change in the open interest?
No change
Decrease by one
Decrease by two
Decrease by one
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Increase by one
Which of the following best describes central clearing parties
Help market participants to value deriva-
tive transactions
Must be used for all OTC derivative transactions
Are used for futures transactions
Perform a similar function to exchange clearing houses
Perform a similar function to exchange clearing houses
You sell one December futures contracts when the futures price is $1,010 per unit. Each contract is on 100 units and the initial margin per contract that you pro-
vide is $2,000. The maintenance margin per contract is $1,500. During the next day the futures price rises to $1,012 per unit. What is the balance of your margin account at the end of the day?
$1,800
$3,300
$2,200
$3,700
$1,800
Which of the following are cash settled
All futures contracts
All option contracts
Futures on commodities
Futures on stock indices
Futures on stock indices
The frequency with which margin ac-
counts are adjusted for gains and losses is
Daily
Daily
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Weekly
Monthly
Quarterly
A speculator takes a long position in a futures contract on a commodity on No-
vember 1, 2012 to hedge an exposure on March 1, 2013. The initial futures price is $60. On December 31, 2012 the fu-
tures price is $61. On March 1, 2013 it is $64. The contract is closed out on March 1, 2013. What gain is recognized in the accounting year January 1 to December 31, 2013? Each contract is on 1000 units of the commodity.
$0
$1,000
$3,000
$4,000
$3,000
Which of the following is true?
Both forward and futures contracts are traded on exchanges.
Forward contracts are traded on ex-
changes, but futures contracts are not.
Futures contracts are traded on ex-
changes, but forward contracts are not.
Neither futures contracts nor forward contracts are traded on exchanges.
Futures contracts are traded on ex-
changes, but forward contracts are not.
A company enters into a long futures contract to buy 1,000 units of a com-
modity for $60 per unit. The initial margin is $6,000 and the maintenance margin is $4,000. What futures price will allow $2,000 to be withdrawn from the margin $62
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account?
$58
$62
$64
$66
Which entity in the United States takes primary responsibility for regulating fu-
tures market?
Federal Reserve Board
Commodities Futures Trading Commis-
sion (CFTC)
Security and Exchange Commission (SEC)
US Treasury
Commodities Futures Trading Commis-
sion (CFTC)
A hedger takes a long position in a fu-
tures contract on a commodity on No-
vember 1, 2012 to hedge an exposure on March 1, 2013. The initial futures price is $60. On December 31, 2012 the fu-
tures price is $61. On March 1, 2013 it is $64. The contract is closed out on March 1, 2013. What gain is recognized in the accounting year January 1 to December 31, 2013? Each contract is on 1000 units of the commodity.
$0
$1,000
$3,000
$4,000
$4,000
A company enters into a short futures contract to sell 50,000 units of a com-
modity for 70 cents per unit. The initial margin is $4,000 and the maintenance margin is $3,000. What is the futures price per unit above which there will be a 72 cents
Margin call when $1000 or more has been lost
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margin call?
78 cents
76 cents
74 cents
72 cents
Because the company is short, each one cent rise in the price leads to a loss of 0.01x50,000 = $500
Margin accounts have the effect of
Reducing the risk of one party regretting the deal and backing out
Ensuring funds are available to pay traders when they make a profit
Reducing systemic risk due to collapse of futures markets
All the answers
All the answers
Which of the following is NOT true
Futures contracts nearly always last longer than forward contracts
Futures contracts are standardized; for-
ward contracts are not.
Delivery or final cash settlement usually takes place with forward contracts; the same is not true of futures contracts.
Forward contracts usually have one specified delivery date; futures contract often have a range of delivery dates.
Futures contracts nearly always last longer than forward contracts
For a futures contract trading in April 2012, the open interest for a June 2012 contract, when compared to the open in-
terest for Sept 2012 contracts, is usually
Higher
Lower
The same
Equally likely to be higher or lower
Higher
Who initiates delivery in a corn futures contract
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The party with the long position
The party with the short position
Either party
The exchange
The party with the short position
On a particular day, there were 2,000 trades in a particular futures contract. This means that there were 2000 buy-
ers (going long) and 2000 sellers (going short). Of the 2,000 buyers, 1,400 were closing out positions and 600 were enter-
ing into new positions. Of the 2,000 sell-
ers, 1,200 were closing out positions and 800 were entering into new positions. What is the impact of the day's trading on open interest?
down by 1200
down by 1400
up by 800
down by 600
down by 600
The open interest went down by 600. We can see this in two ways. First, 1,400 shorts closed out and there were 800 new shorts. Second, 1,200 longs closed out and there were 600 new longs.
A company enters into a short futures contract to sell 5,000 bushels of wheat for 750 cents per bushel. The initial mar-
gin is $3,000 and the maintenance mar-
gin is $2,000. What price change would lead to a margin call?
Price up by 30 cents
Price down by 20 cents
Price up by 20 cents
Price down by 25 cents
Price up by 20 cents
The open interest usually decline during the month preceding the delivery month.
True
False
True
Open interest is the number of contract outstanding. Many traders close out their positions just before the delivery month is reached. This is why the open interest 17 / 54
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declines during the month preceding the delivery month.
Trader A enters into futures contracts to buy 1 million euros for 1.1 million dollars in three months. Trader B enters in a forward contract to do the same thing. The exchange rate (dollars per euro) de-
clines sharply during the first two months and then increases for the third month to close at 1.1300. Which of the following in NOT true.
Trader A's profit is realized day-by-day during the three months. Substantial losses are made during the first two months and profits are made during the final month.
The total profit of each trader in dollars is $3,000.
Trader B's profit is realized at the end of the three months.
It is likely that Trader B has done better because Trader A had to finance its loss-
es during the first two months.
The total profit of each trader in dollars is $3,000.
Suppose that there are no storage costs for crude oil and the interest rate for borrowing or lending is 4% per annum. Could you make money risk free if the June and December futures contracts for a particular year trade at $50 and $56?
True
False
True
You could go long one June oil con-
tract and short one December contract. In June you take delivery of the oil bor-
rowing $50 per barrel at 4% to meet cash outflows. The interest accumulated in six months is about 50×0.04×1/2 or $1 per barrel. In December the oil is sold for $56 per barrel which is more than the $51 that has to be repaid on the loan. The strategy therefore leads to a profit. Note that this profit is independent of the actual price of oil in June and December. It will be 18 / 54
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slightly affected by the daily settlement procedures.
A company has derivatives transactions with Banks A, B, and C which are worth +$20 million, $15 million, and $25 mil-
lion, respectively to the company. How much margin or collateral does the com-
pany have to provide? The transactions are cleared bilaterally and are subject to one-way collateral agreements where the company posts variation margin, but no initial margin. The banks do not have to post collateral.
$20 million
$10 million
$60 million
$40 million
$30 million
$40 million
If the transactions are cleared bilaterally, the company has to provide collateral to Banks A, B, and C of (in millions of dollars) 0, 15, and 25, respectively. The total collateral required is $40 million. If the transactions are cleared centrally they are netted against each other and the company's total variation margin (in millions of dollars) is -20 + 15 + 25 or $20 million in total. The total margin required (including the initial margin) is therefore $30 million.
A company has derivatives transactions with Banks A, B, and C which are worth +$20 million, $15 million, and $25 mil-
lion, respectively to the company. How much margin or collateral does the com-
pany have to provide? The transactions are cleared bilaterally and are subject to one-way collateral agreements where the company posts variation margin, but no initial margin. The transactions are cleared centrally through the same CCP and the CCP requires a total initial mar-
gin of $10 million.
$20 million
$10 million
$60 million
$40 million
$30 million
$30 million
If the transactions are cleared bilaterally, the company has to provide collateral to Banks A, B, and C of (in millions of dollars) 0, 15, and 25, respectively. The total collateral required is $40 million. If the transactions are cleared centrally they are netted against each other and the company's total variation margin (in millions of dollars) is -20 + 15 + 25 or $20 million in total. The total margin required (including the initial margin) is therefore $30 million.
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The forward price on the Swiss franc for delivery in 45 days is quoted as 1.1000. The futures price for a contract that will be delivered in 45 days is 0.9000. Ex-
plain these two quotes. Which is more fa-
vorable for a trader wanting to sell Swiss francs?
The forward market is more attractive for a trader wanting to sell Swiss francs.
The futures market is more attractive for a trader wanting to sell Swiss francs.
The forward and futures market are equally attractive for a trader wanting to sell Swiss francs.
The Swiss frank is expected to decline relative to the US dollar.
The forward market is more attractive for a trader wanting to sell Swiss francs.
1) The forward price on the Swiss franc for delivery in 45 days is quoted as 1.1000. Here, The 1.1000 forward quote is the number of Swiss francs per dollar.
2) The futures price for a contract that will be delivered in 45 days is 0.9000.
But here, The 0.9000 futures quote is the number of dollars per Swiss franc.
so, if we quote forward price in the same way of futures price then,
=1/1.1000
=0.9091
Therefore Swiss francs is more valu-
able in the forward market than futures market. Therefore the forward market is more favorable for a trader wanting to sell Swiss francs.
.9091 is more favorable because the trader can get more units of USD for each unit of francs when using the forward contract
A speculator sells a July 2013 wheat fu-
tures contract at 721 cents per bushel. Each futures contract is for 5,000 bushels. The futures price drops to 676 on December 31, 2012 and rises to 712 in May 2013 when she closes the con-
tract. What is the gain or loss for account-
ing purposes in 2013?
$45,000 gain
$45,000 loss
$225,000 gain
$180,000 loss
$180,000 gain
$180,000 loss
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In July 2012, a small chocolate factory receives a large order for chocolate bars to be delivered in November. The spot price for Cocoa is $2,400 per metric ton. It will need 10 metric tons of Cocoa in September to fill this order. Because of limited storage capacity and volatility in the world cocoa prices, the company de-
cides the best strategy is to buy 10 call options for $53 each with strike price of $2,400 (equal to the current price) with a maturity date of September 2012. When the options expire in September, how much will the company pay (including the cost of the options) for cocoa if the spot price in September proves to be $2,600
$22,470
$23,000
$24,530
$23,530
$23,470
$24,530
In July 2012, a small chocolate factory receives a large order for chocolate bars to be delivered in November. The spot price for Cocoa is $2,400 per metric ton. It will need 10 metric tons of Cocoa in September to fill this order. Because of limited storage capacity and volatility in the world cocoa prices, the company de-
cides the best strategy is to buy 10 call options for $53 each with strike price of $2,400 (equal to the current price) with a maturity date of September 2012. When the options expire in September, how much will the company pay (including the cost of the options) for cocoa if the spot price in September proves to be $2,300.
$23,530
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$23,000
$23,530
$24,530
$22,470
$23,470
A company has a $36 million portfolio with a beta of 1.2. The index futures price is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to increase beta to 1.8?
Long 192 contracts
Short 192 contracts
Long 96 contracts
Short 96 contracts
Long 96 contracts
Which of the following does NOT de-
scribe beta?
A measure of the sensitivity of the return on an asset to the return on an index
The slope of the best fit line when the return on an asset is regressed against the return on the market
The hedge ratio necessary to remove market risk from a portfolio
Measures correlation between futures prices and spot prices
Measures correlation between futures prices and spot prices
Which of the following is true?
Gold producers should always hedge the price they will receive for their production of gold over the next three years
Gold producers should always hedge the price they will receive for their production of gold over the next one year
The hedging strategies of a gold produc-
er should depend on whether it share-
The hedging strategies of a gold produc-
er should depend on whether it share-
holders want exposure to the price of gold
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holders want exposure to the price of gold
Gold producers can hedge by buying gold in the forward market
Which of the following is a reason for hedging a portfolio with an index futures?
The investor believes the stocks in the portfolio will perform better than the mar-
ket but is uncertain about the future per-
formance of the market
The investor believes the stocks in the portfolio will perform better than the mar-
ket and the market is expected to do well
The portfolio is not well diversified and so its return is uncertain
All
The investor believes the stocks in the portfolio will perform better than the mar-
ket but is uncertain about the future per-
formance of the market
Futures contracts trade with every month as a delivery month. A company is hedg-
ing the purchase of the underlying as-
set on June 15. Which futures contract should it use?
The June contract
The July contract
The May contract
The August contract
The July contract
Which of the following increases basis risk?
A large difference between the futures prices when the hedge is put in place and when it is closed out
Dissimilarity between the underlying as-
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set of the futures contract and the hedgerâ s exposure
A reduction in the time between the date when the futures contract is closed and its delivery month
None of the other
Dissimilarity between the underlying as-
set of the futures contract and the hedger's exposure
The basis is defined as spot minus fu-
tures. A trader is hedging the sale of an asset with a short futures position. The basis increases unexpectedly. Which of the following is true?
The hedgerâ s position improves.
The hedgerâ s position worsens.
The hedgerâ s position sometimes wors-
ens and sometimes improves.
The hedgerâ s position stays the same.
The hedgerâ s position improves.
The price received by the trader is the futures price plus the basis. It follows that the trader's position improves when the basis increases.
Net amount received:
S2 + (F1 - F2)
Which of the following is true?
Hedging can always be done more easily by a company's shareholders than by the company itself
If all companies in an industry hedge, a company in the industry can sometimes reduce its risk by choosing not to hedge
If all companies in an industry do not hedge, a company in the industry can reduce its risk by hedging
If all companies in an industry do not hedge, a company is liable increase its risk by hedging
If all companies in an industry do not hedge, a company is liable increase its risk by hedging
A silver mining company has used fu-
tures markets to hedge the price it will 24 / 54
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receive for everything it will produce over the next 5 years. Which of the following is true?
It is liable to experience liquidity prob-
lems if the price of silver falls dramatical-
ly
It is liable to experience liquidity prob-
lems if the price of silver rises dramati-
cally
It is liable to experience liquidity prob-
lems if the price of silver rises dramati-
cally or falls dramatically
The operation of futures markets pro-
tects it from liquidity problems
It is liable to experience liquidity prob-
lems if the price of silver rises dramati-
cally
A company will buy 1000 units of a cer-
tain commodity in one year. It decides to hedge 80% of its exposure using futures contracts. Spot price and futures price are currently $100 and $90. The one year futures price of the commodity is $90. If the spot price and the futures price in one year turn out to be $112 and $110, respectively. What is the average price paid for the commodity?
$92
$96
$102
$106
$96
Hedged portion price: S2 - (F2 - F1) = $112 - ($110 - $90) = $92
Unhedged portion price:
$112
($92 x .8) + ($112 x .2) = $96
Which of the following best describes the capital asset pricing model?
Determines the amount of capital that is needed in particular situations
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Is used to determine the price of futures contracts
Relates the return on an asset to the return on a stock index
Is used to determine the volatility of a stock index
Relates the return on an asset to the return on a stock index
Which of the following is true?
The optimal hedge ratio is the slope of the best fit line when the spot price (on the y-axis) is regressed against the fu-
tures price (on the x-axis).
The optimal hedge ratio is the slope of the best fit line when the futures price (on the y-axis) is regressed against the spot price (on the x-axis).
The optimal hedge ratio is the slope of the best fit line when the change in the spot price (on the y-axis) is regressed against the change in the futures price (on the x-axis).
The optimal hedge ratio is the slope of the best fit line when the change in the futures price (on the y-axis) is regressed against the change in the spot price (on the x-axis).
The optimal hedge ratio is the slope of the best fit line when the change in the spot price (on the y-axis) is regressed against the change in the futures price (on the x-axis).
A company has a $36 million portfolio with a beta of 1.2. The index futures price is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to reduce beta to 0.9?
Long 192 contracts
Short 192 contracts
Short 48 contracts
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Long 48 contracts
Short 48 contracts
On March 1 a commodity's spot price is $60 and its August futures price is $59. On July 1 the spot price is $64 and the August futures price is $63.50. A com-
pany entered into futures contracts on March 1 to hedge its purchase of the commodity on July 1. It closed out its position on July 1. What is the effective price (after taking account of hedging) paid by the company?
$59.50
$60.50
$61.50
$63.50
$59.50
On March 1 the price of a commodity is $1,000 and the December futures price is $1,015. On November 1 the price is $980 and the December futures price is $981. A producer of the commodity entered into a December futures con-
tracts on March 1 to hedge the sale of the commodity on November 1. It closed out its position on November 1. What is the effective price (after taking account of hedging) received by the company for the commodity?
$1,016
$1,001
$981
$1,014
$1,014
A company due to pay a certain amount of a foreign currency in the future de-
cides to hedge with futures contracts. Which of the following best describes the 27 / 54
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advantage of hedging?
It leads to a better exchange rate being paid
It leads to a more predictable exchange rate being paid
It caps the exchange rate that will be paid
It provides a floor for the exchange rate that will be paid
It leads to a more predictable exchange rate being paid
Suppose that the standard deviation of monthly changes in the price of com-
modity A is $2. The standard deviation of monthly changes in a futures price for a contract on commodity B (which is similar to commodity A) is $3. The cor-
relation between the futures price and the commodity price is 0.9. What hedge ratio should be used when hedging a one month exposure to the price of commod-
ity A?
0.60
0.67
1.45
0.90
0.60
Beta * (SD of change in price / SD of change in futures price)
Which of the following best describes â stack and rollâ ?
Creates long-term hedges from short term futures contracts
Can avoid losses on futures contracts by entering into further futures contracts
Involves buying a futures contract with one maturity and selling a futures con-
tract with a different maturity
Involves two different exposures simulta-
neously
Creates long-term hedges from short term futures contracts
28 / 54
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Which of the following is true for a con-
sumption commodity?
There is no limit to how high or low the futures price can be, except that the fu-
tures price cannot be negative
There is a lower limit to the futures price but no upper limit
There is an upper limit to the futures price but no lower limit, except that the futures price cannot be negative
The futures price can be determined with reasonable accuracy from the spot price and interest rates
There is an upper limit to the futures price but no lower limit, except that the futures price cannot be negative
The spot price of an investment asset is $30 and the risk-free rate for all maturi-
ties is 10% with continuous compound-
ing. The asset provides an income of $2 at the end of the first year and at the end of the second year. What is the three-year forward price?
$19.67
$35.84
$45.15
$40.50
$35.84
Income to subtract:
2*e^(-.1*1) + 2*e^(-.1*2) = $3.45
F0:
($30-$3.45)*e^(.1*3) = 35.84
Which of the following describes the way the futures price of a foreign currency is quoted?
The number of U.S. dollars per unit of the foreign currency
The number of the foreign currency per U.S. dollar
Some futures prices are always quoted as the number of U.S. dollars per unit The number of U.S. dollars per unit of the foreign currency
29 / 54
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of the foreign currency and some are always quoted the other way round
There are no quotation conventions for futures prices
Which of the following describes the way the forward price of a foreign currency is quoted?
The number of U.S. dollars per unit of the foreign currency
The number of the foreign currency per U.S. dollar
Some forward prices are always quoted as the number of U.S. dollars per unit of the foreign currency and some are always quoted the other way round
There are no quotation conventions for forward prices
Some forward prices are always quoted as the number of U.S. dollars per unit of the foreign currency and some are always quoted the other way round
Which of the following is true?
The convenience yield is always positive or zero.
The convenience yield is always positive for an investment asset.
The convenience yield is always nega-
tive for a consumption asset.
The convenience yield measures the av-
erage return earned by holding futures contracts.
The convenience yield is always positive or zero.
As the convenience yield increases, which of the following is true?
The one-year futures price as a percent-
age of the spot price increases
30 / 54
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The one-year futures price as a percent-
age of the spot price decreases
The one-year futures price as a percent-
age of the spot price stays the same
Any of the above can happen
The one-year futures price as a percent-
age of the spot price decreases
An investor shorts 100 shares when the share price is $50 and closes out the position six months later when the share price is $43. The shares pay a dividend of $3 per share during the six months. How much does the investor gain?
$1,000
$400
$700
$300
$400
(100 * 50) - (100 * 43) - (100 * 3) = 400
A short forward contract that was ne-
gotiated some time ago will expire in three months and has a delivery price of $40. The current forward price for three-month forward contract is $42. The three month risk-free interest rate (with continuous compounding) is 8%. What is the value of the short forward contract?
+$2.00
-$2.00
+$1.96
-$1.96
-$1.96
(40-42)*e^(-.08 * 3/12) = -1.96
Which of the following describes contan-
go?
The futures price is below the expected future spot price
The futures price is below todayâ s spot The futures price is above the expected future spot price
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price
The futures price is a declining function of the time to maturity
The futures price is above the expected future spot price
Which of the following is a consumption asset?
The S&P 500 index
The Canadian dollar
Copper
IBM stock
Copper
As inventories of a commodity decline, which of the following is true?
The one-year futures price as a percent-
age of the spot price increases
The one-year futures price as a percent-
age of the spot price decreases
The one-year futures price as a percent-
age of the spot price stays the same
Any of the above can happen
The one-year futures price as a percent-
age of the spot price decreases
^^ Because storage costs included in the futures will reduce
Which of the following is NOT true?
Gold and silver are investment assets
Investment assets are held by significant numbers of investors for investment pur-
poses
Investment assets are never held for consumption
The forward price of an investment asset can be obtained from the spot price, in-
terest rates and the income paid on the asset
Investment assets are never held for con-
sumption
An exchange rate is 0.7000 and the six-month domestic and foreign risk-free 32 / 54
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interest rates are 5% and 7% (both ex-
pressed with continuous compounding). What is the six-month forward rate?
0.7070
0.7177
0.7249
0.6930
0.6930
.7000 * e^((.05 - .07) * (6/12)) = .6930
Which of the following is an argument used by Keynes and Hicks?
If hedgers hold long positions and spec-
ulators holds short positions, the futures price will tend to be higher than expected future spot prices
If hedgers hold long positions and spec-
ulators holds short positions, the futures price will tend to be lower than expected future spot prices
If hedgers hold long positions and spec-
ulators holds short positions, the futures price will tend to be lower than todayâ s spot prices
If hedgers hold long positions and spec-
ulators holds short positions, the futures price will tend to be higher than todayâ s spot prices
If hedgers hold long positions and spec-
ulators holds short positions, the futures price will tend to be higher than expected future spot prices
Which of the following is NOT a reason why a short position in a stock is closed out?
The investor with the short position chooses to close out the position
The lender of the shares issues instruc-
tions to close out the position
The broker is no longer able to borrow shares from other clients
The lender of the shares issues instruc-
tions to close out the position
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The investor does not maintain margins required on his/her margin account
Which of the following describes a known dividend yield on a stock?
The size of the dividend payments each year is known
Dividends per year as a percentage of todayâ s stock price are known
Dividends per year as a percentage of the stock price at the time when divi-
dends are paid are known
Dividends will yield a certain return to a person buying the stock today
Dividends per year as a percentage of the stock price at the time when divi-
dends are paid are known
Which of the following is NOT true about forward and futures contracts?
Forward contracts are more liquid than futures contracts
The futures contracts are traded on exchanges while forward contracts are traded in the over-the-counter market
In theory forward prices and futures prices are equal when there is no uncer-
tainty about future interest rates
Taxes and transaction costs can lead to forward and futures prices being different
Forward contracts are more liquid than futures contracts
What should a trader do when the one-year forward price of an asset is too low? Assume that the asset provides no income.
The trader should borrow the price of the asset, buy one unit of the asset and enter into a short forward contract to sell the 34 / 54
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asset in one year.
The trader should borrow the price of the asset, buy one unit of the asset and enter into a long forward contract to buy the asset in one year.
The trader should short the asset, invest the proceeds of the short sale at the risk-free rate, enter into a short forward contract to sell the asset in one year
The trader should short the asset, invest the proceeds of the short sale at the risk-free rate, enter into a long forward contract to buy the asset in one year
The trader should short the asset, invest the proceeds of the short sale at the risk-free rate, enter into a long forward contract to buy the asset in one year
The spot price of an investment asset that provides no income is $30 and the risk-free rate for all maturities (with con-
tinuous compounding) is 10%. What is the three-year forward price?
$40.50
$22.22
$33.00
$33.16
$40.50
The spot price of an asset is positively correlated with the market. Which of the following would you expect to be true?
The forward price equals the expected future spot price.
The forward price is greater than the ex-
pected future spot price.
The forward price is less than the expect-
ed future spot price.
The forward price is less than the expect-
ed future spot price.
35 / 54
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The forward price is sometimes greater and sometimes less than the expected future spot price.
Assume an asset pays no dividends or interest, and also assume that the asset does not yield any non-financial benefits or incur any carrying cost. At initiation, the price of a forward contract on that asset is:
lower than the value of the contract.
equal to the value of the contract.
greater than the value of the contract.
greater than the value of the contract.
At the initiation of a forward contract on an asset that neither receives benefits nor incurs carrying costs during the term of the contract, the forward price is equal to the:
spot price.
future value of the spot price.
present value of the spot price.
future value of the spot price.
If the present value of storage costs ex-
ceeds the present value of its conve-
nience yield, then the commodity's for-
ward price is most likely:
less than the spot price compounded at the risk-free rate.
the same as the spot price compounded at the risk-free rate.
higher than the spot price compounded at the risk-free rate.
higher than the spot price compounded at the risk-free rate.
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An arbitrage transaction generates a net inflow of funds:
throughout the holding period.
at the end of the holding period.
at the start of the holding period.
at the start of the holding period.
Arbitrage is a type of transaction under-
taken when two assets or portfolios pro-
duce identical results but sell for different prices. A trader buys the asset or port-
folio with the lower price and sells the asset or portfolio with the higher price, generating a net inflow of funds at the start of the holding period. Because the two assets or portfolios produce identical results, a long position in one and short position in the other means that at the end of the holding period, the payoffs off-
set. Therefore, there is no money gained or lost at the end of the holding period, so there is no risk.
If the net cost of carry of an asset is pos-
itive, then the price of a forward contract on that asset is most likely:
lower than if the net cost of carry was zero.
the same as if the net cost of carry was zero.
higher than if the net cost of carry was zero.
lower than if the net cost of carry was zero.
An asset's forward price is increased by the future value of any costs and de-
creased by the future value of any ben-
efits. If the net cost of carry (benefits less costs) is positive, the forward price is lower than if the net cost of carry was zero.
An arbitrageur will most likely execute a trade when:
transaction costs are low.
costs of short-selling are high.
prices are consistent with the law of one price.
transaction costs are low.
37 / 54
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To the holder of a long position, it is more desirable to own a forward contract than a futures contract when interest rates and futures prices are:
negatively correlated.
uncorrelated.
positively correlated.
negatively correlated.
The price of a forward contract:
is the amount paid at initiation.
is the amount paid at expiration.
fluctuates over the term of the contract.
is the amount paid at expiration
If you expect a stock market downturn, one potential defensive strategy would be to ________.
sell foreign exchange futures
buy stock-index options
buy stock-index futures
sell stock-index futures
sell stock-index futures
A 1-year gold futures contract is selling for $1,645. Spot gold prices are $1,592 and the 1-year risk-free rate is 3%. The arbitrage profit implied by these prices is ________.
$4.39
$5.24
$6.72
$5.24
Parity F0 = S0(1 + rf d)T = $1,592(1 + 0.03 0)1 = $1,639.76
The arbitrage profit is $1,645 1,639.76 = $5.24
An established value below which a trad-
er's margin may not fall is called the ________.
convergence limit
maintenance margin
daily limit
daily margin
maintenance margin
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The overwhelming majority of trading in futures contracts is done via ________.
electronic networks
open outcry
trading pits
phone
electronic networks
An investor who is hedging a corporate bond portfolio using a T-bond futures contract is said to have ________.
a spread hedge
an arbitrage
a cross-hedge
an over hedge
a cross-hedge
A long hedge is a simultaneous ________ position in the spot market and a ________ position in the futures market.
long; long
short; long
long; short
short; short
short; long
The current level of the S&P 500 is 1,250. The dividend yield on the S&P 500 is 3%. The risk-free interest rate is 6%. The futures price quote for a contract on the S&P 500 due to expire 6 months from now should be ________.
1,274.33
1,286.95
1,291.29
1,268.61
1,268.61
F0 = S0(1 + rf d)T = $1,250(1 + 0.06 0.03)0.5 = $1,268.61
You take a long position in a futures con-
tract of one maturity and a short position in a contract of a different maturity, both 39 / 54
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on the same commodity. This is called a ________.
spread position
cross-hedge
reversing trade
straddle
spread position
Which one of the following contracts re-
quires no cash to change hands when initiated?
listed put option
forward contract
short futures contract
listed call option
forward contract
Margin requirements for futures con-
tracts can be met by ________.
cash or warehouse receipts for an equiv-
alent quantity of the underlying commodity
cash or any marketable securities
cash or highly marketable securities such as Treasury bills
cash only
cash or highly marketable securities such as Treasury bills
Which one of the following refers to the daily settlement of obligations on future positions?
marking to market
the open interest
the convergence property
the triple witching hour
marking to market
A speculator will often prefer to buy a fu-
tures contract rather than the underlying 40 / 54
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asset because:
I.
Gains in futures contracts can be larger due to leverage.
II.
Transaction costs in futures are typically lower than those in spot markets.
III.
Futures markets are often more liquid than the markets of the underlying
commodities.
I and III only
II and III only
I and II only
I, II, and III
I, II, and III
A hypothetical futures contract on a non-
dividend-paying stock with a current spot price of $100 has a maturity of 1 year. If the T-bill rate is 5%, what should the futures price be?
$95.24
$100
$107
$105
$105
F0 = S0(1 + r)T = $100(1.05)1 = $105
At maturity of a futures contract, the spot price and futures price must be approxi-
mately the same because of ________.
the open interest
marking to market
the convergence property
the triple witching hour
the convergence property
Which one of the following exploits differ-
ences between actual future prices and 41 / 54
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their theoretically correct parity values?
index arbitrage
marking to market
reversing trades
settlement transactions
index arbitrage
The fact that the exchange is the coun-
terparty to every futures contract is-
sued is important because it eliminates ________ risk.
credit
interest rate
basis
market
credit
An investor who goes long in a futures contract will ________ any increase in value of the underlying asset and will ________ any decrease in value in the underlying asset.
pay; pay
receive; receive
receive; pay
pay; receive
receive; pay
At contract maturity the basis should equal ________.
1
1
the risk-free interest rate
0
0
Investors who take short positions in fu-
tures contract agree to ________ de-
livery of the commodity on the delivery date, and those who take long positions agree to ________ delivery of the com-
modity.
make; take
42 / 54
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make; take
make; make
take; take
take; make
On January 1, you sold one April S&P 500 Index futures contract at a futures price of 1,300. If the April futures price is 1,250 on February 1, your profit would be ________ if you close your position. (The contract multiplier is 250.)
$12,500
$15,000
$12,500
$15,000
$12,500
Violation of the spot-futures parity rela-
tionship results in ________.
fines and other penalties imposed by the SEC
suspension of delivery privileges
arbitrage opportunities for investors who spot them
suspension of trading
arbitrage opportunities for investors who spot them
Which of the following provides the profit to a long position at contract maturity?
zero
basis
original futures price Spot price at matu-
rity
spot price at maturity Original futures price
spot price at maturity Original futures price
Single stock futures, as opposed to stock index futures, are ________.
not yet being offered by any exchanges
scheduled to begin trading in 2015 on 43 / 54
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several exchanges
currently trading on OneChicago, a joint venture of several exchanges
offered overseas but not in the United States
currently trading on OneChicago, a joint venture of several exchanges
You believe that the spread between the September T-bond contract and the June T-bond futures contract is too large and will soon correct. This market exhibits positive cost of carry for all contracts. To take advantage of this, you should ________.
buy the September contract and buy the June contract
sell the September contract and buy the June contract
buy the September contract and sell the June contract
sell the September contract and sell the June contract
sell the September contract and buy the June contract
The open interest on silver futures at a particular time is the number of ________.
silver futures contracts traded during the day
silver futures contracts traded the previ-
ous day
long and short silver futures positions counted separately on a particular trad-
ing day
all outstanding silver futures contracts
all outstanding silver futures contracts
In the futures market the short position's loss is ________ the long position's gain.
less than
sometimes less than and sometimes greater than
equal to
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equal to
greater than
At year-end, taxes on a futures position ________.
must be paid regardless of whether the position has been closed out or not
must be paid if the position has been closed out
need not be paid if the position supports a hedge
must be paid if the position has not been closed out
must be paid regardless of whether the position has been closed out or not
A hypothetical futures contract on a non-
dividend-paying stock with a current spot price of $100 has a maturity of 4 years. If the T-bill rate is 7%, what should the futures price be?
$131.08
$107
$76.29
$93.46
$131.08
F0 = S0(1 + r)4 = $100(1.07)4 = $131.08
The ________ contract dominates trad-
ing in stock-index futures.
Nasdaq 100
DJIA
Russell 2000
S&P 500
S&P 500
A futures contract ________.
is a contract to be signed in the future by the buyer and the seller of a commodity
is an agreement to buy or sell a specified amount of an asset at whatever the spot price happens to be on the expiration 45 / 54
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date of the contract
gives the buyer the right, but not the obligation, to buy an asset some time in the future
is an agreement to buy or sell a specified amount of an asset at a predetermined price on the expiration date of the con-
tract
is an agreement to buy or sell a specified amount of an asset at a predetermined price on the expiration date of the con-
tract
An investor who goes short in a futures contract will ________ any increase in value of the underlying asset and will ________ any decrease in value in the underlying asset.
pay; receive
pay; pay
receive; receive
receive; pay
pay; receive
A person with a long position in a com-
modity futures contract wants the price of the commodity to ________.
remain unchanged
decrease substantially
increase substantially
increase or decrease substantially
increase substantially
A 1-year gold futures contract is selling for $1,645. Spot gold prices are $1,592 and the 1-year risk-free rate is 3%.Based on the above data, which of the following set of transactions will yield positive risk-
less arbitrage profits?
Buy gold spot with borrowed money, and buy the futures contract.
Buy gold in the spot with borrowed mon-
Buy gold in the spot with borrowed mon-
ey, and sell the futures contract.
Actual F0 = $1,645, but according to spot-futures parity it should be $1,639.76, so the futures contract is 46 / 54
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ey, and sell the futures contract.
Buy the futures contract, and buy the gold spot using borrowed money.
Buy the futures contract, and sell the gold spot and invest the money earned.
overpriced. Sell futures today, and buy gold spot with borrowed money.
An investor establishes a long position in a futures contract now (time 0) and holds the position until maturity (time T). The sum of all daily settlements will be ________.
F0 S0
FT S0
FT F0
F0 FT
FT F0
On May 21, 2012, you could have pur-
chased a futures contract from Intrade for a price of $5.70 that would pay you $10 if Barack Obama won the 2012 presidential election. This tells you ________.
that the market believed Obama's chances of winning were about 43%
that the market believed that Obama had a 57% chance of winning
that the market believed that Obama would not win the election
nothing about the market's belief con-
cerning the odds of Obama winning
that the market believed that Obama had a 57% chance of winning
Forward contracts ________ traded on an organized exchange, and futures con-
tracts ________ traded on an organized exchange.
are not; are
47 / 54
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are not; are
are; are not
are; are
are not; are not
________ are likely to close their po-
sitions before the expiration date, while ________ are likely to make or take de-
livery.
Speculators; hedgers
Investors; regulators
Hedgers; speculators
Regulators; investors
Speculators; hedgers
The price of a corn futures contract is $2.65 per bushel when the contract is issued, and the commodity spot price is $2.55. When the contract expires, the two prices are identical. What principle is represented by this price behavior?
convergence
volatility
basis
margin
convergence
If the risk-free rate is greater than the dividend yield, then we know that ________.
arbitrage profits are possible
FT > ST
F0 < S0
the futures price will be higher as con-
tract maturity increases
the futures price will be higher as con-
tract maturity increases
A wheat farmer should ________ in or-
der to reduce his exposure to risk asso-
ciated with fluctuations in wheat prices.
sell wheat futures if the basis is currently 48 / 54
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positive and buy wheat futures if the ba-
sis is currently negative
sell wheat futures
buy a contract for delivery of wheat now and sell a contract for delivery of wheat at harvest time
buy wheat futures
sell wheat futures
The spot price for gold is $1,550 per ounce. The dividend yield on the S&P 500 is 2.5%. The risk-free interest rate is 3.5%. The futures price for gold for a 6-month contract on gold should be ________.
$1,557.73
$1,554.04
$1,569.08
$1,504.99
$1,557.73
F0 = S0(1 + rf - d)T = $1,550(1 + 0.035 - 0.025)0.5 = $1,557.73
Futures markets are regulated by the ________.
CFTC
SEC
CFA Institute
CIA
CFTC
The S&P 500 Index futures contract is an example of a(n) ________ delivery contract. The pork bellies contract is an example of a(n) ________ delivery con-
tract.
cash; actual
actual; cash
cash; cash
actual; actual
cash; actual
Synthetic stock positions are common-
ly used by ________ because of their ________.
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money market funds; limited exposure
banks; lower risk
wealthy investors; tax treatment
market timers; lower transaction cost
market timers; lower transaction cost
Which one of the following is a true state-
ment?
The maintenance margin is the amount of money you post with your broker when you buy or sell a futures contract.
All futures contracts require the same margin deposit.
The maintenance margin is the value of the margin account below which the holder of a futures contract receives a margin call.
A margin deposit can be met only by cash.
The maintenance margin is the value of the margin account below which the holder of a futures contract receives a margin call.
Approximately ________ of futures con-
tracts result in actual delivery.
less than 60% to 80%
less than 1% to 3%
0%
less than 5% to 15%
less than 1% to 3%
A hog farmer decides to sell hog futures. This is an example of ________ to limit risk.
speculating
spreading
short hedging
cross-hedging
short hedging
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Initial margin is usually set in the region of ________ of the total value of a fu-
tures contract.
20%-30%
10%-20%
15%-25%
5%-15%
5%-15%
A short hedge is a simultaneous ________ position in the spot market and a ________ position in the futures market.
long; short
short; long
long; long
short; short
long; short
A farmer sells futures contracts at a price of $2.75 per bushel. The spot price of corn is $2.55 at contract expiration. The farmer harvested 12,500 bushels of corn and sold futures contracts on 10,000 bushels of corn.What are the farmer's proceeds from the sale of corn?
$35,950
$31,875
$27,500
$33,875
$33,875
Net proceeds = (2.75 × 10,000) + (2.55 × 2,500) = 33,875
A company that mines bauxite, an alu-
minum ore, decides to short aluminum futures. This is an example of ________ to limit its risk.
cross-hedging
long hedging
spreading
speculating
cross-hedging
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The CME weather futures contract is an example of ________.
a financial future
an agricultural contract
a cash-settled contract
a commodity future
a cash-settled contract
Futures contracts have many advan-
tages over forward contracts except that ________.
futures contracts are tailored to the spe-
cific needs of the investor
counterparty credit risk is not a concern on futures
futures trading preserves the anonymity of the participants
futures positions are easier to trade
futures contracts are tailored to the spe-
cific needs of the investor
The daily settlement of obligations on futures positions is called ________.
the initial margin requirement
marking to market
a margin call
a variation margin check
marking to market
When dividend-paying assets are in-
volved, the spot-futures parity relation-
ship can be stated as ________.
F1 = S0(1 + rf)
F0 = S0(1 + rf)T
F0 = S0(1 + rf d)T
F0 = S0(1 + rf + d)T
F0 = S0(1 + rf d)T
The only money exchanged by both the long and short at the creation of a futures contract is called the ________.
spot price
futures price
Margin
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collateral
Margin
Which of the following provides the profit to a short position at contract maturity?
original futures price Spot price at matu-
rity
basis
zero
spot price at maturity Original futures price
original futures price Spot price at matu-
rity
The advantage that standardization of futures contracts brings is that ________ is improved because ________.
trading cost; trading volume is reduced
credit risk; all traders understand the risk of the contracts
liquidity; all traders must trade a small set of identical contracts
pricing; convergence is more likely to take place with fewer contracts
liquidity; all traders must trade a small set of identical contracts
From the perspective of determining profit and loss, the long futures position most closely resembles a levered invest-
ment in a ________.
long call
short call
short stock position
long stock position
long stock position
You are currently long in a futures con-
tract. You instruct a broker to enter the short side of a futures contract to close your position. This is called ________.
marking to market
a reversing trade
a reversing trade
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a speculation
a cross-hedge
Margin must be posted by ________.
buyers of futures contracts only
speculators only
both buyers and sellers of futures con-
tracts
sellers of futures contracts only
both buyers and sellers of futures con-
tracts
If an asset price declines, the investor with a ________ is exposed to the largest potential loss.
long put option
long futures contract
long call option
short futures contract
long futures contract
A farmer sells futures contracts at a price of $2.75 per bushel. The spot price of corn is $2.55 at contract expiration. The farmer harvested 12,500 bushels of corn and sold futures contracts on 10,000 bushels of corn.Ignoring the transaction costs, how much did the farmer improve his cash flow by hedging sales with the futures contracts?
$33,875
$31,875
$0
$2,000
$2,000
Gain = (2.75 2.55)10,000 = 2,000
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Check Progress
QUESTION
FINANCING AND SETTLEMENT » FINANCING LEGISLATION
32 c
When a buyer goes in to apply for a loan on a new first mortgage, what must the lender give to the buyer?
Glossary Terms
Mortgage,
ANSWERS
EXPLANATION
A > The broker's commission amount
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C> An estimate of the seller's closing costs
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Question 1
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machine:
Lease Alternative
Seroja can lease the machine under a 5-year lease requiring lease payment of RM5,000 at the
beginning of each year. All maintenance costs will be borne by the lessor and the insurance and
other costs will be borne by the lessee.
"Borrowing to Buy" Alternative
The machine costs RM20,000 and will have a 5-year life. The purchase will be financed by a 5-
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and other costs.
Seroja Berhad plans to keep the machine and use it beyond its 5-year life.
The machine will be depreciated as given below:
Year Depreciation
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3,000
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5
1,000
Given that the corporate tax rate is 30%.
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P2,000,00
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Fair,value of building
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120,000
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C
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$479,079
Right-of-Use Asset
*Present value of an annuity due of $1: n=6, i=10%
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mortgage
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one who pays to use an asset
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purchase
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On January 1, 2019, the Okanagan Flight Institute, which reports its financial results in
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Lease term
Economic life of equipment
Lease payment
Fair value of asset
Implicit rate in the lease (not known by lessee)
Incremental borrowing rate
Option to purchase
Guaranteed residual value
Year end is December 31
Expected payout under guarantee
5 years
7 years
$7,800, first due January 1, 2019
$40,000
6%
7%
No
$5,000
$0
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