Chapter 11, Forward and Futures Hedging, Spread, and Target Strategies Video Solutions, An Introduction to Derivatives and Risk Management: With Stock-Trak Coupon

Problem 1

On June 17 of a particular year, an American watch dealer decided to import 100,000 Swiss watches. Each watch costs SF225. The dealer would like to hedge against a change in the dollar/Swiss franc exchange rate. The forward rate was $$\$ 0.3881$$. Determine the outcome from the hedge if it was closed on August 16, when the spot rate was $\$ 0.4434$.

Narayan Hari

Numerade Educator

Problem 2

On January 31 , a firm learns that it will have $$\$ 5$$ million available on May 31 . It will use the funds to purchase the APCO $91 / 2$ percent bonds maturing in about 21 years. Interest is paid semiannually on March 1 and September 1 . The bonds are rated A2 by Moody's and are selling for $787 / 8$ per 100 and yielding 12.32 percent. The modified duration is 7.81 .
The firm is considering hedging the anticipated purchase with September T-bond futures. The futures price is $718 / 32$. The firm believes the futures contract is tracking the Treasury bond with a coupon of $123 / 4$ percent and maturing in about 25 years. It has determined that the implied yield on the futures contract is 11.40 percent and the modified duration of the contract is 8.32 .
The firm believes the APCO bond yield will change 1 point for every l-point change in the yield on the bond underlying the futures contract.
a. Determine the transaction the firm should conduct on January 31 to set up the hedge.
b. On May 31, the APCO bonds were priced at $823 / 4$. The September futures price was 76 14/32. Determine the outcome of the hedge.

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Problem 3

For each of the following hedge termination dates, identify the appropriate contract expiration. Assume the available expiration months are March, June, September, and December.
a. August 10
b. December 15
c. February 20
d. June 14

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Problem 4

For each of the following situations, determine whether a long or short hedge is appropriate. Justify your answers.
a. A firm anticipates issuing stock in three months.
b. An investor plans to buy a bond in 30 days.
c. A firm plans to sell some foreign currency denominated assets and convert the proceeds to domestic currency.

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Problem 5

Explain how to determine whether to buy or sell futures when hedging.

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02:14

Problem 6

Explain the difference between a short hedge and a long hedge.

James Kiss

Numerade Educator

05:04

Problem 7

You are the manager of a stock portfolio. On October 1 , your holdings consist of the eight stocks listed in the following table, which you intend to sell on December 31. You are concerned about a market decline over the next three months. The number of shares, their prices, and the betas are shown, as well as the prices on December 81 .
$$
\begin{array}{lcccc}
\hline \text { Stock } & \text { Number of Shares } & \text { Beta } & \text { 10/1 Price } & \text { 12/31 Price } \\
\hline \text { R. R. Donnelley } & 10,000 & 1.00 & 19.63 & 27.38 \\
\text { B. F. Goodrich } & 6,200 & 1.05 & 31.38 & 32.88 \\
\text { Rrytheon } & 15,300 & 1.15 & 49.38 & 53.68 \\
\text { Maytag } & 8,900 & 0.90 & 55.38 & 77.85 \\
\text { Kroger } & 11,000 & 0.85 & 42.13 & 47.89 \\
\text { Comdisco } & 14,500 & 1.45 & 19.38 & 28.63 \\
\text { Cessna } & 9,900 & 1.20 & 29.75 & 30.13 \\
\text { Foxboro } & 4,500 & 0.95 & 24.75 & 26.00 \\
\hline
\end{array}
$$
On October 1, you decide to execute a hedge using a stock index futures contract, which has a $$\$ 500$$ multiplier. The March contract price is 376.20 . On December 31, the March contract price is 424.90 . Determine the outcome of the hedge.

James Kiss

Numerade Educator

Problem 8

On July 1, a portfolio manager holds $$\$ 1$$ million face value of Treasury bonds, the $11 \mathrm{1} / 4 \mathrm{~s}$ maturing in about 29 years. The price is $10714 / 32$. The bond will need to be sold on August 30. The manager is concerned about rising interest rates and believes a hedge would be appropriate. The September T-bond futures price is $7715 / 32$. The price sensitivity hedge ratio suggests that the firm should use 13 contracts.
a. What transaction should the firm make on July I?
b. On August 30, the bond was selling for $10112 / 32$ and the futures price was $775 / 32$. Determine the outcome of the hedge.

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Problem 9

On March 1, a securities analyst recommended General Cinema stock as a good purchase in the early summer. The portfolio manager plans to buy 20,000 shares of the stock on June 1 but is concerned that the market as a whole will be bullish over the next three months. General Cinema's stock currently is at 32.88, and the beta is 1.10.
Construct a hedge that will protect against movements in the stock market as a whole. Use the September stock index futures, which is priced at 375.30 on March 1 and which has a $$\$ 500$$ multiplier. Evaluate the outcome of the hedge if on June 1 the futures price is 887.30 and General Cinema's stock price is 38.63 .

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Problem 10

During the first six months of the year, yields on long-term government debt have fallen about 100 basis points. You believe the decline in rates is over, and you are interested in speculating on a rise in rates. You are, however, unwilling to assume much risk, so you decide to do an intramarket spread. Use the following information to construct a T-bond futures spread on July 15, and determine the profit when the position is closed on November 15 .
July 15
December futures price: 769/32 March futures price: 75 9/92
November 15
December futures price: 79 13/32
March futures price: 78 9/32

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Problem 11

The manager of a $$\$ 20$$ million portfolio of domestic stocks with a beta of 1.10 would like to begin diversifying internationally. He would like to sell $$\$ 5$$ million of domestic stock and purchase $$\$ 5$$ million of foreign stock. He learns that he can do this using a futures contract on a foreign stock index. The index is denominated in dollars, thereby eliminating any currency risk. He would like the beta of the new foreign asset class to be 1.05 . The domestic stock index futures contract is priced at $$\$ 250,000$$ and can be assumed to have a beta of 1.0 . The foreign stock index futures contract is priced at $$\$ 150,000$$ and can also be assumed to have a beta of 1.0 .
a. Determine the number of contracts he would need to trade of each type of futures in order to achieve this objective.
b. Determine the value of the portfolio if the domestic stock increases by 2 percent, the domestic stock futures contract increases by 1.8 percent, the foreign stock increases by 1.2 percent, and the foreign stock futures contract increases by 1.4 percent.

Rashmi Sinha

Numerade Educator

05:04

Problem 12

On November 1 , an analyst who has been studying a firm called Computer Sciences believes the company will make a major new announcement before the end of the year. Computer Sciences currently is priced at 27.63 and has a beta of 0.95 . The analyst belicves the stock can advance about 10 percent if the market does not move. The analyst thinks the market might decline by as much as 5 percent, leaving the stock with a return of $0.10+(-0.05)(0.95)=0.0525$. To capture the full 10 percent alpha, the analyst recommends the sale of stock index futures. The March contract currenty is priced at 393. Assume the investor owns 100,000 shares of the stock. Set up a transaction by determining the appropriate number of futures contracts. Then determine the effective return on the stock if, on December 31 , the stock is sold at 28.88 , the futures contract is at 432.90 , and the multiplier is 500. Explain your results.

James Kiss

Numerade Educator

05:04

Problem 13

You are the manager of a stock portfolio worth $$\$ 10,500,000$$. It has a beta of 1.15 . During the next three months, you expect a correction in the market that will take the market down about 5 percent; thus, your portfolio is expected to fall about 5.75 percent ( 5 percent times a beta of 1.15 ). You wish to lower the beta to 1 . A stock index futures contract with the appropriate expiration is priced at 425.75 with a multiplier of $$\$ 500$$.
a. Should you buy or sell futures? How many contracts should you use?
b. In three months, the portfolio has fallen in value to $$\$ 9,870,000$$. The futures has fallen to 402.35 . Determine the profit and portfolio return over the quarter. How close did you come to the desired result?

James Kiss

Numerade Educator

Problem 14

On January 2 of a particular year, an American firm decided to close out its account at a Canadian bank on February 28. The firm is expected to have 5 million Canadian dollars in the account at the time of the withdrawal. It would convert the funds to U.S. dollars and transfer them to a New York bank. The relevant forward exchange rate was $$\$ 0.7564$$. The March Canadian dollar futures contract was priced at $$\$ 0.7541$$. Determine the outcome of a futures hedge if on February 28 the spot rate was $$\$ 0.7207$$ and the futures rate was $$\$ 0.7220$$. All prices are in U.S. dollars per Canadian dollar. The Canadian dollar futures contract covers CD 100,000 .

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Problem 15

Suppose you are a dealer in sugar. It is September 26 , and you hold 112,000 pounds of sugar worth $$\$ 0.0479$$ per pound. The price of a futures contract expiring in January is $$\$ 0.0550$$ per pound. Each contract is for 112,000 pounds.
a. Determine the original basis. Then calculate the profit from a hedge if it is held to expiration and the basis converges to zero. Show how the profit is explained by movements in the basis alone.
b. Rework this problem, but assume the hedge is closed on December 10, when the spot price is $$\$ 0.0574$$ and the January futures price is $$\$ 0.0590$$.

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Problem 16

You are the manager of a bond portfolio of $$\$ 10$$ million face value of bonds worth $$\$ 9,448,456$$. The portfolio has a yield of 12.25 percent and a duration of 8.33 . You plan to liquidate the portfolio in six months and are concerned about an increase in interest rates that would produce a loss on the portfolio. You would like to lower its duration to 5 years. A T-bond futures contract with the appropriate expiration is priced at $723 / 32$ with a face value of $$\$ 100,000$$, an implied yield of 12 percent, and an implied duration of 8.43 years.
a. Should you buy or sell futures? How many contracts should you use?
b. In six months, the portfolio has fallen in value to $$\$ 8,952,597$$. The futures price is $6816 / 32$. Determine the profit from the transaction.

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Problem 17

(Concept Problem) As we discussed in the chapter, futures can be used to eliminate systematic risk in a stock portfolio, leaving it essentially a risk-free portfolio. A portfolio manager can achieve the same result, however, by selling the stocks and replacing them with T-bills. Consider the following stock portfolio.
$$
\begin{array}{lcrr}
\hline \text { Stock } & \text { Number of Shares } & \text { Price } & \text { Beta } \\
\hline \text { Northrop Grumman } & 14,870 & 18.13 & 1.10 \\
\text { H.J. Heinz } & 8,755 & 36.19 & 1.05 \\
\text { Washington Post } & 1,945 & 264.00 & 1.05 \\
\text { Disney } & 8,750 & 134.50 & 1.25 \\
\text { Wang Labs } & 38,995 & 4.25 & 1.20 \\
\text { Wisconsin Energy } & 12,480 & 29.00 & 0.65 \\
\text { Ceneral Motors } & 14,750 & 48.75 & 0.95 \\
\text { Union Pacific } & 12,900 & 71.50 & 1.20 \\
\text { Royal Datch Shell } & 7,500 & 78.75 & 0.75 \\
\text { Illinois Power } & 3,550 & 15.50 & 0.60 \\
\hline
\end{array}
$$
Suppose the porffolio manager wishes to convert this portfolio to a riskless portfolio for a period of one month. The price of a stock index futures with a $$\$ 500$$ multiplier is 369.45 . To sell each share would cost $$\$ 20$$ per order plus $$\$ 0.03$$ per share. Each company's shares would constitute a separate order. The futures contract would entail a cost of $$\$ 27.50$$ per contract, round-trip. T-bill purchases cost $$\$ 25$$ per trade for any number of T-bills. Determine the most cost-effective way to accomplish the manager's goal of converting the portfolio to a risk-free position for one month and then converting it back.

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Problem 18

What factors must one consider when deciding on the appropriate underiying asset for a hedge?

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Problem 19

State and explain two reasons why firms hedge.

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Problem 20

a. Define the minimum variance hedge ratio and the measure of hedging effectiveness? What do these two values tell us?
b. What is the price sensitivity hedge ratio? How are the price sensitivity and minimum variance hedge ratios alike? How do they differ?

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Problem 21

a. What is the basis?
b. How is the basis expected to change over the life of a futures contract?
c. Explain why a strengthening basis benefits a short hedge and hurts a long hedge.

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Problem 22

(Concept Problem) You plan to buy 1,000 shares of Swiss International Airlines stock. The current price is SF950. The current exchange rate is $$\$ 0.7254 / \mathrm{SF}$$. You are interested in speculating on the stock but do not wish to assume any currency risk. You plan to hold the position for six months. The appropriate futures contract currently is trading at $$\$ 0.7250$$. Construct a hedge and evaluate how your investment will do if in six months the stock is at SF926.50, the spot exchange rate is $$\$ 0.7301$$, and the futures price is $$\$ 0.7295$$. The Swiss franc futures contract size is SF125,000. Determine the overall profit from the transaction. Then break down the profit into the amount earned solely from the performance of the stock, the loss or gain from the currency change while holding the stock, and the loss or gain on the futures transaction.

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