FNCE 4040 midterm 1 problems

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FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 1. 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. B. One side has the obligation to buy an asset for a certain price in one year's time. explanation: futures and forwards have the OBLIGATION to buy/sell at a certain price 2. 1. Which of the following best de- scribes 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 A. The price for immediate delivery expl:is a contract of buying or sell- ing a commodity, security or currency for immediate settlement on the spot date, which is normally two business days after the trade date. 3. 1. Which of the following is true about a long forward contract? A. The contract becomes more valu- able as the price of the asset declines B. The contract becomes more valu- able 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 con- tract has been entered into B. The contract becomes more valu- able as the price of the asset rises expl: Long position (BUY) gains with an upward movement of a futures price x- initial $ y-futures $ gain= + (y-x) 4. 1 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 1. An investor sells a futures contract of 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 B. The investor has made a loss of $4,000 expl: sells= SHORT... gain= downward movement of fu- tures $... x- initial $ y- futures $ gain= +(x-y) (100*1500)-(1540*100)= -400= LOSS 5. 1. A company enters into a short fu- tures 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 D. 72 cents expl: short=sell, want a downward move- ment...if it goes higher, then you are losing money short=x-y= daily gain/loss margin bal 0= 4,000 -->@72 cents= (.70-.72)*50,000= -1,000 margin bal 1= 4,000-1000= 3,000 -----since new margin bal is at 3,000, if the the futures price increased any higher the margin bal would fall below the maintenance margin and they would receive a margin call to increase bal to the initial margin 6. 1. A company enters into a long fu- tures contract to buy 1,000 units of a commodity for $60 per unit. The ini- B. $62 expl: long= buy= y-x for 2 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 tial margin is $6,000 and the mainte- nance margin is $4,000. What futures price will allow $2,000 to be with- drawn from the margin account? A. $58 B. $62 C. $64 D. $66 gain/loss...need an upward price movement for gain initial margin= 6,000 maint marg= 4,000 --> if you take 2,000 out of margin now, youll get a maint call... so need the price to increase @62-->(62-60)*1000= 2,000 gain --->now 8,000 in margin bal and can withdraw 2000+ 7. 1. 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 con- tract is $1,500. During the next day the futures price rises to $1,012 per unit. What is the balance of your mar- gin account at the end of the day? A. $1,800 B. $3,300 C. $2,200 D. $3,700 A. $1,800 expl: sell= short...gain =downward movement, x-y x= initial, y = futures initial margin: 2,000 day2: (1,010-1,012)*100= loss of $200 margin day 2= 2,000-200= $1800 8. 1. Margin accounts have the effect of A. Reducing the risk of one party re- gretting 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 expl: minimize the possibility of a loss through default of contract, min- imizes the possibility that a counter- party doesnt pay when you get the profit, 9. 1. Futures contracts trade with every month end as a delivery month. A A. The June contract 3 / 20

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FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 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 expl: always choose a date that is closest date after the close out date 10. 1. 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 fu- tures 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 (af- ter taking account of hedging) paid by the company? A. $59.50 B. $60.50 C. $61.50 D. $63.50 A. $59.50 expl: purchase=buy= LONG--> effec- tive price paid= NET AMOUNT PAID S2-(F2-F1)--> 64-(63.50-59)= $59.5 11. 1. A company has a $36 million port- folio 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 expl: to REDUCE beta .... SHORT! K*= (B0-B1)(Va/Vf) where K*= # of contacts B0= current beta B1= desired beta Va= value of current portfolio Vf= current value of one future con- tract 48= (1.2-.9)(36M/{900*250}) 4 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 12. 1. A company has a $36 million port- folio 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 C. LONG 96 contracts expl: to INCREASE beta .... LONG! K*= (B0-B1)(Va/Vf) where K*= # of contacts B0= current beta B1= desired beta Va= value of current portfolio Vf= current value of one future con- tract -96= (1.2-1.8)(36M/{900*250}) 13. 1. On March 1, the spot price of gold is $300 and the December futures price is $315. On November 1, the spot price of gold is $280 and the De- cember futures price is $281. A gold producer entered into a December fu- tures contract on March 1 to hedge the sale of gold on November 1. It closed out its position on November 1. What is the effective sales price re- ceived by the producer for the gold? Gold producer= sell= SHORT .... Ef- fective sales received= net amount Received Effective sales= S2 + (F1-F2) Where: S2= spot rate of date 2à$280 F1= futures rate 1à$315 F2= futures rate 2à$281 = 280 +(315-281)= $314 14. 1. A company will buy 1000 units of a certain commodity in one year. It decides to hedge 80% of its ex- posure using futures contracts. The spot price and the futures price are currently $100 and $90, respectively. The spot price and the futures price in one year turn out to be $112 and $110, respectively. What is the aver- age price paid for the commodity? Buy= LONG=effective purchase $-à net amount PAID Effective sales= S2 - (F2-F1)à HEDGED Where: S1= spot rate of date 1à$100 S2= spot rate of date 2à$112 F1= futures rate 1à$90 F2= futures rate 2à$110 Units= 1000 5 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 Hedged $= S2-(F2-F1)= 112-(110-90)= $92 Unhedged $= S2= 112 Weighted avg price: ($92*80%)+($112*20%)= $96 15. 1. Suppose that the minimum vari- ance hedge ratio (h*) of corn futures is calculated as 0.6. A corn farmer wants to hedge corn price risk by entering into the closest corn futures contracts. He expects his crops will be 100,000 bushels. If the size of fu- tures contract is 5,000 bushels, what would be his optimal number and po- sition of futures contracts? Answer: 12 contracts in the short po- sition The corn farmer wants to sell his crops of corn, so he takes a short futures position. The optimal num- ber of contracts (K*) is the bushels of corn futures needed (NF*) di- vided by the size of corn futures (QF*). The bushels of corn fu- tures needed (NF*) is 0.6´100,000 bushels=60,000 bushels. Therefore, the optimal number of contracts is 60,000 bushels / 5,000 bushels=12. 16. A trader enters into a short cotton fu- tures contract when the futures price is 50 cents per pound. The contract is for the delivery of 50,000 pounds. How much does the trader gain or lose if the cotton price at the end of the contract is (a) 48.20 cents per pound; (b) 51.30 cents per pound? short, sell, want a downward price, a gain/loss = X-Y A) (.5*50,000)-(.482*50000) = $900 gain B) (.5*50000)-(.513*50000)= -$650 loss 17. (based on JH Problem 1.19) A trader enters into a short forward contract on 100 million yen. The for- ward exchange rate is $0.0090 per yen. How much does the trader gain or lose if the exchange rate at the end of the contract is (a) $0.0084 per yen; (b) $0.0101 per yen? SHort= sell, downward movement wanted, X-Y= gain/loss a) (.009 * 100,000,000)- (.0084*100,000,000) = $60,000 gain b)(.009 * 100,000,000)- (.0101*100,000,000) = $110,000 loss 18. (based on JH Problem 2.3)Suppose that you enter into a short futures short= sell= downward= x-y day one margin= 4,000 6 / 20

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FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 contract to sell July silver for $17.20 per ounce. The size of the contract is 5,000 ounces. The initial margin is $4,000, and the maintenance margin is $3,000. What change in the futures price will lead to a margin call? What happens if you do not meet the mar- gin call? cannot lose more than 1000 or will lead to a margin call day 1= ($17.20/oz*5,000)-(X*5000) = -1000 x= $17.4--> if price increases to $17.4 or more, then you will receive a margin call if you do not meet the margin call you can continue to trade without having to add more money into your margin account 19. (based on JH Problem 2.11)A trader buys two July futures contracts on frozen orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin is $6,000 per contract, and the maintenance margin is $4,500 per contract. What price change would lead to a mar- gin call? Under what circumstances could $2,000 be withdrawn from the margin account? buys= long= upward movement= Y-X for gain initial margin= 6000 A) = can only lose 1500 before need- ing to add to initial margin day 1 margin= (Y*15,000)- (1.60*15,000)= -1500 Y= $1.50 or the price could not de- crease more than 150 cents per pound B) change in $= *2 contracts= 1,000 amount to withdraw day 1 margin= (Y*15,000)- (1.60*15,000)= 1000 Y= if the price increased to 166 cents per pound, you would gain 500, enough to withdraw 2000 from the margin accnt 20. (based on JH Problem 2.23)Suppose that on October 24, 2015, a com- pany sells one April 2016 live-cat- tle futures contracts. It closes out its position on January 21, 2016. The futures price (per pound) is 121.20 cents when it enters into the con- sells= short= X-Y= downward 1 contract= 40,0000 lbs cattle futures price= 121.2 cents /lbs--> selling price spot rate= 118.3 cents/lbs---> buying price futures price 2= 118.8 cents/lbs 7 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 tract, 118.30 cents when it closes out its position, and 118.80 cents at the end of December 2015. One contract is for the delivery of 40,000 pounds of cattle. What is the total profit? How is it taxed if the company is (a) a hedger and (b) a speculator? Assume that the company has a December 31 year end. 1) total profit= X-Y= Contract size *(Selling Price-Buying price) = 40,000*(121.2-118.3)= $116,000 a) hedger pays ordinary income tax on the entire gain of %116,000 for the year end of 2016 b) a speculator gets taxed on capi- tal gains for short term capital gain and long term capital gain based on when the gain or loss was realized 2015: 40,000*(121.2-$118.8)= $96,000 short term cap gain 2016: 40,000*($118.8-118.3)= $20,000 short term cap gain 21. (based on JH Problem 2.30)A com- pany enters into a short futures contract to sell 5,000 bushels of wheat for 750 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead to a mar- gin call? Under what circumstances could $1,500 be withdrawn from the margin account? short= sell= X-Y= downward margin call= -1000 loss in daily day1= (7.5*5000)-(Y* 5000)= -1000 A) Y= 7.7--> if price increase to 770 cents per bushell you would need a margin call B) change in $= (Amount to with- draw/contract size) (1,500/5,000) = .30 ----> 750-30= 720 cents OR margin call= 1500 + in daily gain day1= (7.5*5000)-(Y* 5000)= 1500 Y= if price decreased to 720 cents per bushell you could withdraw 1500 from the margin account 22. (based on JH Problem 3.6)Suppose that the standard deviation of quar- terly changes in the prices of a com- modity is $0.65, the standard devia- tion of quarterly changes in a futures h* = Á (Ã S / Ã F ) Á : correlation between ”S and ”F--> .8 ”S, ”F: changes in prices of the asset to be hedged and the asset in futures contract 8 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean? Ã S, Ã F : standard deviations of ”S and ”F--> .65, .81 h*= .6419 expl: in a 3 month hedge, the opti- mal size of the future position should be 64% of the optimal size of the companies exposure... it measures the relationship between change in commodity spot prices and change in future prices 23. (based on JH Problem 3.18)On July 1, an investor holds 50,000 shares of a certain stock. The market price is $30 per share. The investor is interested in hedging against movements in the market over the next month and de- cides to use the September Mini S&P 500 futures contract. The index is cur- rently 1,500 and one contract is for delivery of $50 times the index. The beta of the stock is 1.3. What strategy should the investor follow? Equity Portfolio Hedging - K* = ² (VA /VF) K*: the number of index futures con- tracts VA: current value of the portfolio - (50,000*30)= 1,500,000 VF: current value of the future con- tract (futures price x contract size) = (1,500*50)=75000 beta= 1.3 K*= 1.3(1,500,000/75000)= 26 con- tracts ---> hedging is ALWAYS short 24. (based on JH Problem 3.27)A com- pany wishes to hedge its exposure to a new fuel whose price changes have a 0.6 correlation with gasoline futures price changes. The compa- ny will lose $1 million for each 1 cent increase in the price per gallon of the new fuel over the next three months. The new fuel's price change has a standard deviation that is 50% greater than price changes in gaso- line futures prices. If gasoline futures are used to hedge the exposure what should the hedge ratio be? What is h* = Á (Ã S / Ã F ) P= .6 h* = Á (Ã S / Ã F ) The new fuel's price change has a standard deviation that is 50% greater than price changes in gaso- line futures prices=1.5 h*= .6*1.5= .9 a) hedge ratio = .9--> .9* 100 million gallons = 90 million gallons in gaso- line futures = exposure in fuel b)= h* (NA / QF)--> NA: units of an asset to be hedged - NF*: units of the asset in futures contract 9 / 20

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FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 the company's exposure measured in gallons of the new fuel? What posi- tion measured in gallons should the company take in gasoline futures? How many gasoline futures contracts should be traded? Each contract is on 42,000 gallons. number of futures contracts= (90,0000/42,000) = 2143 gas futures contract 25. (based on JH Problem 3.30)It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.2. The company would like to use the December fu- tures contract on a stock index to change beta of the portfolio to 0.5 during the period July 16 to Novem- ber 16. The index is currently 1,000, and each contract is on $250 times the index.a) What position should the company take?b) Suppose that the company changes its mind and de- cides to increase the beta of the port- folio from 1.2 to 1.5. What position in futures contracts should it take? Equity Portfolio Hedging - Change the beta from --² to ²' -----K* = (² - ²') (VA /VF) K*: the number of index futures con- tracts - VA: current value of the portfolio - VF: current value of the future con- tract (futures price x contract size) a) What position should the company take?--> to reduce beta SHORT a futures contract (1.2-.5)((100,000,000/{1,000*250})= 280 short futures contracts b) Suppose that the company changes its mind and decides to in- crease the beta of the portfolio from 1.2 to 1.5. What position in futures contracts should it take?---> to IN- CREASE beta, but enter the LONG postion (1.2-1.5)((100,000,000/{1,000*250})= 120 futures contracts 26. A US company will pay £10 million for imports from a British supplier in 3 months and decides to enter into a long position of £ in a forward con- tract. Hedger expl: already in business and using a supplier, using to minimize risk 27. An investor with $4,000 to invest feels that Amazon.com's stock price 10 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 will increase over the next 2 months and considers buying options. The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2. Speculator expl: speculator bc in for a profit 28. if investor was in the short position of corn futures contract @day1 and closes out on day 5... enters a long position of a corn fu- tures contract on day 5 with price at day 5 29. On a particular day, there were 2,000 trades in a particular futures con- tract. This means that there were 2,000 buyers (going long) and 2,000 sellers (going short). What is the im- pact of the day's trading on open in- terest? -Of the 2,000 buyers, 1,400 were clos- ing out positions and 600 were enter- ing into new positions. -Of the 2,000 sellers, 1,200 were clos- ing out positions and 800 were enter- ing into new positions. Long open interest = open interest + new long - long closing out X+600-1200= X-600 Short open interest = open interest +new short- short closing out X+800-1400 = x-600 --> open interest decreased by 600. remember closing out is the opposite position 30. Suppose that in September 2015 a company takes a long position in a contract on May 2016 crude oil fu- tures. It closes out its position in March 2016. The futures price (per barrel) is $88.30 when it enters into the contract, $90.50 when it closes out its position, and $89.10 at the end of December 2015. One contact is for the delivery is 1,000 barrels. -What is the company's total profit? -When is it realized?-How is it taxed? LONG= BUY= Y-X hedger: profits realized when posi- tion is closed Mach 2016 total profit realized= (90.50-88.30)*1000= 2200---> taxed like ordinary income for 2016 speculator: profits realized at end of december 2015 then end of march 2016 December: (89.10-88.30)*1000= 800 december march: (90.50-89.1) *1000= 1400 11 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 march = 2,200 total but taxed and realized in diff years 31. One orange juice future contract is on 15,000 pounds of frozen con- centrate. Suppose that in Septem- ber 2014 a company sells a March 2016 orange juice futures contract for 120 cents per pound. In December 2014 the futures price is 140 cents; in December 2015 the futures price is 110 cents; and in February 2016 it is closed out at 125 cents.-What is the company's profit or loss on the contract? sells= Short= x-y (120-125)* 15,000= -750 --> LOSS 32. On March 1, the spot price of gold is $300 and the December futures price is $315. On November 1, the spot price of gold is $280 and the De- cember futures price is $281. A gold producer entered into a December fu- tures contract on March 1 to hedge the sale of gold on November 1. It closed out its position on November 1. What is the effective sales price re- ceived by the producer for the gold? sale= SHORT= X-Y= downward Net amount received= S2 + (F1 - F2) = F1 + b2 280+(315-281)= 314 effective sales $ 33. It is now March 1. A U.S. company expects to receive 50 million Japan- ese yen on July 31. The company wants to convert yen to USD on July 31.•Yen futures contracts have deliv- ery months of March, June, Septem- ber and December, and one contract is for 12.5 million yen.What should the company's futures position be? September--> Closest date AFTER close out SHORT--> selling yen to get USD Net amount received= S2 + (F1 - F2) = F1 + b2 .92+(.98-.925)= .975/Y *50M= $487,500 12 / 20

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FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 After the company receives 50 mil- lion yen on July 31, the company closes out its position.•Suppose F1 = 0.98 (¢/¥) S2 = 0.92 F2 = 0.925 What is the total amount of 50 million yen the company receives in $? 34. An airline expects to purchase 2 mil- lion gallons of jet fuel in 1 month and decides to use heating oil futures for hedging. Given Ã S=0.0263, Ã F=0.0313, and Á=0.928, A)What is the minimum variance hedge ratio?Each heating oil con- tract traded by the CME group is on 42,000 gallons. B)What is the optimal number of con- tracts? (in the nearest whole number) purchase= long A) h* = Á (Ã S / Ã F ) .928(.0263/.0313)= .779--> 78% per- cent exposure B) h* (NA / QF) .78(2,000,000/42,000)= 37 contracts 35. Suppose that the minimum variance hedge ratio (h*) of corn futures is cal- culated as 0.6. A corn farmer wants to hedge corn price risk by entering into the closest corn futures contracts. He expects his crops will be 100,000 bushels. If the size of futures con- tract is 5,000 bushels, what would be his optimal number and position of futures contracts? hedge= short B) h* (NA / QF) .6(100,000/5,000) =12 contract in the short position 36. The std dev. of monthly changes in the spot price of live cattle is 1.2 (cents per pound). The std dev. of monthly changes in the futures price of live cattle for the closest contract is 1.4. The correlation between the purchase= LONG Stdev S= 1.2/lbs stdev F= 1.4/lbs P= .7 units of asset: 200,000 lbs contract delivery: 40,000 lbs 13 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 futures price changes and the spot price changes is 0.7. It is now Oct 15. A beef producer is committed to pur- chasing 200,000 pounds of live cattle on Nov 15. The producer wants to use the Dec live-cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle.What strategy should the beef producer follow? A) h* = Á (Ã S / Ã F ) h*= .7(1.2/1.4)= .6 or 60% B) h* (NA / QF) k*= .6(200,000/40,000)= 3 contracts final answer= enter into 3 long posi- tion contracts 37. S&P 500 futures price is 1,000.The size of one future contract is 250.Val- ue of a portfolio is $5 million.Beta of the portfolio is 1.5.What position in futures contracts on the S&P 500 is necessary to hedge the portfolio completely (beta=0)? TO REDUCE BETA= SHORT/HEDGING K* = ² (VA / VF) Va= value of current portfolio Vf= value of 1 future contract 1.5*(5,000,000/{1,000*250}) = 30 contracts entered in the short position 38. S&P 500 futures price is 1,000.The size of one future contract is 250.Val- ue of a portfolio is $5 million.Beta of the portfolio is 1.5.What position in futures contracts on the S&P 500 is necessary to change the portfolio's beta to 0.75.? REDUCING BETA= HEDGE SHORT K* = (² - ²') (VA / VF) = (1.5-.075)(5,000,000/1,000*250) = 15 contracts short position 39. A company has a $20 million port- folio with a beta of 1.2. It would like to use futures contracts on a stock index to hedge its risk. The index fu- tures is currently standing at 1080, and each contract is for delivery of $250 times the index. What is the hedge that minimizes risk? What should the company do if it HEDGE risk = SHORT K* = ² (VA / VF) A) 1.2(20,000,000/{1080*250})= 89 contracts B) (1.2-.6) (20,000,000/{1080*250})= 44 contracts in the short position 14 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 wants to reduce the beta of the port- folio to 0.6? 40. JH Problem 4.4 •An investor receives $1,100 in one year in return for an investment of $1,000 now. Calculate the percentage return per annum with • -Annual compounding -Semiannual compounding -Continuous compounding 41. JH Problem 4.15 Suppose that the 9-month and 12-month rates are 2% and 2.3%, respectively with continuous com- pounding. What is the forward rate for the period between 9 months and 12 months? 42. •Is there an arbitrage opportunity? Suppose that -The spot price of a non-dividend paying stock is $40. -The 3-month forward price is $43. -The 1-year USD interest rate is 5% per annum. Yes. Borrow $40, Buy the share, and Short the forward. 43. •Is there an arbitrage opportunity? Suppose that -The spot price of a non-dividend paying stock is $40. -The 3-month forward price is $38. -The 1-year USD interest rate is 5% per annum. Yes. Short-sell the share, Invest $40, and Long the forward. 44. •Consider a 4-month forward con- tract to buy a zero-coupon bond that 15 / 20

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FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 will mature 1 year from today. The current price of the bond is $930. We assume that the 4-month risk-free rate of interest is 6% per annum with continuous compounding. - -What would be the delivery price (forward price) in a contract negotiat- ed today? 45. •A long forward contract on a non-dividend-paying stock was en- tered into some time ago. It cur- rently has 6-months to delivery. The risk-free rate of interest with continu- ous compounding is 10% per annum, the stock price today is $25, and the delivery price on the contract is $24. • -What should be the 6-month forward price today? -What is the current value of the for- ward contract? 46. •A known dollar income: Consider a 10-month forward contract on a stock with a price of $50. We as- sume that the risk-free rate of inter- est with continuous compounding is 8% per annum for all maturities. We also assume that dividends of $0.75 per share are expected after 3, 6 and 9 months. • -What is the present value of all divi- dends, I ? -What should be the forward price? 47. 16 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 •A known % yield: Consider a 6-month forward contract on an as- set that is expected to provide in- come equal to 2% of the asset price once during a 6-month period. The yield is 4% per annum with semi- annual compounding. The risk-free rate of interest with continuous com- pounding is 10% per annum. The as- set price is $25. - -What is the yield with continuous compounding, q? -What should be the forward price? 48. •Consider a 3-month futures contract on the S&P 500. Suppose that the stocks underlying the index provide a dividend yield of 1% per annum with continuous compounding. The current value of the index is 800, and the continuously compounded inter- est rate is 6% per annum. • -How is the futures price deter- mined? 49. •Suppose that the 2-year continuous- ly compounded interest rates in Aus- tralia and the United States are 5% and 7%, respectively. The spot ex- change rate between AUD and USD is 0.62 USD per AUD. • -What should be the 2-year forward exchange rate? -What would happen if the current 2-year forward exchange rate is 0.63? 17 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 -What would happen if the current 2-year forward exchange rate is 0.66? 50. •Consider a 1-year futures contract on an investment asset that provides no income. It costs $2 per unit to store the asset, with the payment being made at the end of the year. Assume that the spot price is $450 per unit and the continuously com- pounded risk-free rate is 7% per an- num for all maturities. - -What is the present value of all the storage costs, U ? -How is the theoretical futures price given? 51. JH Problem 5.11 •Assume that the risk-free interest rate is 9% per annum with continu- ous compounding and the dividend yield on a stock index varies through- out the year. In February, May, Au- gust, and November, dividends are paid at a rate of 5% per annum with continuous compounding. In other months, at a rate of 2% per annum with continuous compounding. Sup- pose that the value of the index on July 31 is 1,300. • -What should be the futures price for a contract deliverable on December 31 of the same year? 52. JH Problem 5.12 •Suppose that the risk-free interest rate is 10% per annum with continu- 18 / 20

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FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 ous compounding and that the divi- dend yield on a stock index is 4% per annum with continuous compound- ing. The index is standing at 400, and the futures price for a contract deliv- erable in 4 months is 405. • -What arbitrage opportunities does this create? 53. JH Problem 5.14 •The 2-month interest rates in Switzerland and the United States are 1% and 2% per annum with continuous compounding. The spot price of the Swiss franc is $1.05. The futures price for a contract deliver- able in 2 months is also $1.05. • -What arbitrage opportunities does this create? 54. Interest Rate Swaps Example--> Transform of Liability An agreement by Microsoft , to re- ceive 6-month LIBOR and pay Intel a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million. • •Principal is notional and not gener- ally exchanged. 55. Interest Rate Swaps Example--> Transform of an Asset An agreement by Microsoft , to re- ceive 6-month LIBOR and pay Intel a fixed rate of 5% per annum every 6 months for 3 years on a notional 19 / 20

FNCE 4040 midterm 1 problems Study online at https://quizlet.com/_8p4tv5 principal of $100 million. • •Principal is notional and not gener- ally exchanged. 56. JH Problem 7.1 •Companies A and B have been of- fered the following rates per annum on a $20 million five-year loan. Com- pany A requires a floating-rate loan; company B requires a fixed-rate loan. • A) fixed: 5%, floating:LIBOR +0.1% B) fixed: 6.4%, floating:LIBOR +0.6% -Design a swap that will net a bank, acting as intermediary, 0.1% per an- num profits, and that will appear equally attractive to both companies. 20 / 20