MSF Derivatives Homework 1
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FIN 5537-01: Financial Derivatives - Homework 1 You may complete this homework individually or as a group assignment. 1.
Trader A enters into futures contracts to buy 4.0 million euros for 4.4 million dollars in three months. Trader B enters into a forward contract to do the same thing. The exchange (dollars per euro) declines sharply during the first two months and then increases in the third month to close at 1.1120. Ignoring daily settlement, what is the total profit of each trader? When the impact of daily settlement at the exchange is considered, which trader does better? 2.
A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for $2,029 per ounce and sell gold for $2,028 per ounce. The trader can borrow funds at 5.5% per year and invest funds at 5.3% per year. (Both interest rates are expressed with annual compounding.) For what range of one-year forward prices of gold will the trader have no arbitrage opportunities? Assume there is no bid
–
offer spread for forward prices. 3.
A company wishes to hedge its exposure to a new fuel whose price changes have a 0.94 correlation with crude oil futures price changes. The company will lose $2,350,000 for each $0.01 increase in the price per gallon of the new fuel over the next three months. The new fuel's price changes have an estimated standard deviation 12% greater than the standard deviation of crude oil futures prices. a.
What is the company's total exposure measured in gallons of the new fuel? b.
If crude oil futures are to be used to hedge the fuel exposure, what should the hedge ratio be? c.
What position measured - in barrels
- should the company take in crude oil futures? Assume there are 42 gallons to a barrel. d.
How many crude oil futures contracts should be traded? Assume each crude oil contract represents 1,000 barrels. 4.
A trader owns 28,000 troy oz. of silver and decides to hedge price exposure with 3-month silver futures contracts. Each futures contract is for 5,000 troy oz. The standard deviation of the change in the spot price of silver is 0.25. The standard deviation of the change in silver futures prices is 0.27. The coefficient of correlation between the two is 0.96. a.
What is the minimum variance hedge ratio? b.
What is the optimal number of futures contracts? 5.
A stock provides a dividend yield of 1.75% paid semi-annually (equivalent to 1.74% continuously compounded). The spot price of the stock is currently $64, and the risk-free rate is 4.60% with continuous compounding. a.
What is the two-year forward price for a stock? b.
What is the continuously compounded cost of carry for the stock?
6.
A US investor sees an arbitrage opportunity in the currency markets. The spot exchange rate between the Swiss Franc and US Dollar is 0.9624 ($ per CHF). Assume the continuously compounded interest rates in the US and Switzerland are 4.35% and 3.85%, respectively. The 3-month currency forward price is 0.9585 ($ per CHF). a.
What is the theoretically correct forward price? b.
What is the investor’s total profit (in $), assuming she begins by borrowing 4,000,000 CHF? 7.
The following table gives data on 12 monthly changes in the spot price and the futures price for a certain commodity. Use this data to calculate a minimum variance hedge ratio. Spot Price Change -0.3734 -0.4511 1.1818 -0.1499 -0.3560 -0.0676 Futures Price Change -0.4221 -0.6031 1.4676 -0.2218 -0.3207 -0.1388 Spot Price Change 0.0048 -0.0837 0.3906 1.9142 -0.0958 0.3503 Futures Price Change -0.1023 -0.2634 -0.0766 2.1223 0.4797 0.3637 8.
The current price of a stock is $57, and three-month call options with a strike price of $60 currently sell for $2.85. An investor who feels that the price of the stock will increase is trying to decide between buying 100 shares and buying 2,000 call options (20 contracts). Both strategies involve an investment of $5,700. What advice would you give? How high does the stock price have to rise for the all-option strategy to be profitable if the options are held until expiration? 9.
An interest rate is quoted as 5.2% per annum with semiannual compounding. What is the equivalent rate with (a) annual compounding, (b) monthly compounding, and (c) continuous compounding? 10.
Suppose that LIBOR rates for maturities of one month, two months, three months, four months, five months and six months are 4.30%, 4.65%, 4.90%, 5.15%, 5.35%, and 5.50% with continuous compounding? What are the forward rates for the five future one-month periods? 11.
The 6-month, 12-month, 18-month, and 24-month zero rates are 4.60%, 4.90%, 5.20%, and 5.45%, with semiannual compounding. a.
What are the rates with continuous
compounding? b.
What is the forward rate for the 6-month period beginning in 18 months? 12.
Assume the risk-free rates are as described in Question 11. What is the value of an FRA where the holder pays LIBOR and receives 5.5% (semiannually compounded) for a six-
month period beginning in 18 months? The current forward rate for this period is 4.0% (semiannually compounded) and the principal is $75 million.
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Related Questions
Suppose you observe the following one-year interest rates, spot exchange rates and futures prices. Futures contracts are available on €10,000. How much risk-free arbitrage profit could
you make on one contract at maturity from this mispricing?
Exchange Rate
Interest Rate
APR
So($/EL
F380(S/E)
$1.45 €1.00
is
4%
$1.48 = €1.00
3%
(Note: If you are unable to view the image shown above, you can download it: interestTable.PNG)
O $159.22.
O $153.10.
$439.42.
Onone of the options.
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You Answered
Correct Answer
(mark-to-market) You enter a short position in a € future contract with the size
of €125,000 today. The futures expire in 90 days. The interest rates are
i$=5.9% and ic=6.1%. The current spot rate is $1.38/€. Assume 360 days a year.
If the spot rate is $1.37/€ the next day and interest rates remain the same, your
profit or loss for this day is $
___. (Keep the sign and two decimal
places.)
1,250
1,248.46 margin of error +/-0.05
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This morning (Day 0) you take a short position in a pound futures contract that matures
in 3 days (Day 3). The future price is $1.9750 today. The contract size is £62,500 and its
initial performance bond and maintenance bond are $2,430 and $1,830, respectively.
a.
(b)
Assuming that the daily settlement prices are indicated below, how would the
daily change in settlement future prices affect your account? Show the daily
gain/loss and account balance.
Day
0
1
2
3
Settlement
1.9750
1.9700
1.9815
1.9907
Total
Gain/Loss
Account Balance
b. During this period, did you receive a margin call? If you did, on what day?
c. At the end of Day 3, how much in total did you make/lose on this futures
contract?
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KA.
Please answer fast
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am. 122.
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Q1-13
If a speculator observes that the current 3-month forward rate on Swiss francs is 20¢ = 1 franc, but he/she expects that the spot rate in 3 months will be 30¢ = 1 franc, then this speculator would now
a. buy dollars on the forward market.
b. buy francs on the forward market.
c. sell francs on the forward market.
d. buy francs on the spot market and simultaneously sell francs on the 3-month forward market if the current spot rate is 25¢ = 1 franc.
arrow_forward
Assume today’s settlement price on a CME EUR futures contract is $1.3144 per euro. You have a short position in one contract. EUR125,000 is the contract size of one EUR contract. Your performance bond account currently has a balance of $1,900. The next three days’ settlement prices are $1.3130, $1.3137, and $1.3053. Calculate the changes in the performance bond account from daily marking-to-market and the balance of the performance bond account after the third day.
Required:
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
arrow_forward
Assume today's settlement price on a CME EUR futures contract is $1.3154 per euro. You have a short
position in one contract. EUR125,000 is the contract size of one EUR contract. Your performance bond
account currently has a balance of $2,400. The next three days' settlement prices are $1.3140, $1.3147,
$1.3063. Calculate the changes in the performance bond account from daily marking-to-market and the
balance of the performance bond account after the third day.
Required:
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Balance of the performance bond account
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Give typing answer with explanation and conclusion
arrow_forward
You Answered
Correct Answer
(mark-to-market) You enter a long position in a € future contract with the size
of €125,000 today. The futures expire in 90 days. The interest rates are
is=2.6% and ic=5.5%. The current spot rate is $1.38/€. Assume 360 days a year.
If the spot rate is $1.36/€ the next day and interest rates remain the same, your
profit or loss for this day is $
___. (Keep the sign and two decimal
places.)
-2,500
-2,468.79 margin of error +/- 0.02
arrow_forward
Q1-11
Suppose that a speculator notes that the current 3-month forward rate on the euro is $1.26 and the speculator expects that, in 3 months, the euro will have a value of $1.30. In this situation, the speculator would _______ euros on the forward market, and this activity ______ for the speculator.
a. buy / involves risk
b. buy / involves no possible risk
c. sell / involves risk
d. sell / involves no possible risk
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Yesterday, you entered into a futures contract to buy €62,500 at $1.50/€. Your initial margin was $3,750 (-0.04 x €62,500 ×
$1.50/€ -4 percent of the contract value in dollars). Your maintenance margin is $2,000 (meaning that your broker leaves you
alone until your account balance falls to $2.000). At what settle price (use 4 decimal places) do you get a margin call?
O $1.5280/€
O $1.4720/€
O none of the options
$1.500/€
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As a US exporter selling to Europe. You wish to hedge a 1,040,000 Euro to be received in 3 months with futures or forwards. Futures contract sizes for the Euro are 125,000E each. How many dollars will you receive/pay for the goods if you hedge with futures, forwards, and not hedging? Also, rank them?
Now End
Spot 1.100-01 $/E 1.300-01 $/E
Futures 1.120 $/E 1.315 $/E
Forwards 1.130-31 $/E
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Q20: Company ABC enters a 50 million notional principal interest rate swap. The
swap requires ABC to pay a fixed rate and receive a floating rate equal to LIBOR The
swap contract specifies that payments are made every twelve months with the
floating payments determined by LIBOR at the begin of the twelve months. The
period of the swap is four
years.
The following zero coupon curve prevails in the market (annual compounding).
Time (years) 1
2
3
Rate 0.015 0.018 0.020 0.022
What is the swap rate? (the fixed rate that will make the interest rate swap zero NPY
at the beginning)
Select one:
a 1.99%
b 2.09%
c1.89%
d 2.19%
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You are to receive €360,000 on May 16. Today’s spot rate is $1.10/€. The forward rate is $1.12/€. On May 16 the spot rate is $1.11/€. Futures contracts are for €125,000 each.
On May 16 you, 1) close out the forward contracts, and 2) receive the €360,000 and exchange them for dollars.
Q4. How much money did you make or lose on the contracts?
Q5. When you combine the gain or loss on the futures contracts with the dollars exchanged for the €360,000 what was the dollar/euro total exchange rate?
Q6. Why was the amount you received per euro more than the $1.12 future contract hedge amount?
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Assume that today the euro futures contracts with a September 15th delivery date are priced at $1.3680/€ . Suppose that you sold 15 contracts of the euro futures today. If, by September 15th the spot rate is $1.3260/€ , your total profit/loss on your position is (the euro futures contract size is €125,000).
$78,750 loss $78,750 gain €78,750 loss €5,250 loss None of the abov
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You entered into a futures contract to buy €62,500 at $1.20/€ yesterday. Your initial margin was
$4,200. Your maintenance margin is $2,500 (meaning that your broker leaves you alone until your
account balance falls to $2,500). At what settle price will you get a margin call?
$1.2750/€
$1.0272/€
$1.1728/€
O $1.5800/€
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(mark-to-market) You enter a short position in a € future contract with the size of €125,000
today. The futures expire in 90 days. The interest rates are i$=5.9% and iç-6.1%. The current
spot rate is $1.38/€. Assume 360 days a year. If the spot rate is $1.37% € the next day and
interest rates remain the same, your profit or loss for this day is $___________ __.(Keep the
sign and two decimal places.)
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Yesterday, you entered into a futures contract to buy €62,500 at $1.50 per €. Your initial performance bond is $1,500 and your maintenance level is $500. At what settle price will you get a demand for additional funds to be posted? ANSWER D IS CORRECT BUT WHAT IS THE PROCEDURE BUT HOW DO I GET THERE?
a) $1.5160 per €.
b)$1.208 per €.
c)$1.1920 per €.
d)$1.4840 per €. Correct
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Laura Cervantes. Laura Cervantes, the currency speculator we met in the chapter, sells eight June futures contracts for 500,000 pesos (Ps) at the closing price quoted in:
a. What is the value of her position at maturity if the ending spot rate is $0.12003 = Ps1.00?
b. What is the value of her position at maturity if the ending spot rate is $0.09809 = Ps1.00?
c. What is the value of her position at maturity if the ending spot rate is $0.11002 = Ps1.00?
(Round to the nearest cent. Use a minus sign if value is negative.)
a. What is the value of her position at maturity if the ending spot rate is $0.12003 = Ps1.00?
The value of Amber's position is $
b. What is the value of her position at maturity if the ending spot rate is $0.09809 = Ps1.00?
The value of Amber's position is $
The value of Amber's position is $ (Round to the nearest cent. Use a minus sign if value is negative.)
c. What is the value of her position at maturity if the ending spot rate is $0.11002 = Ps1.00?
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