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A corporation plans to issue $10 million of 10-year bonds in three months. At current yields the bonds would have modified duration of eight years. The T-note futures contract is selling at F0 = 100 and has modified duration of six years. How can the firm use this futures contract to hedge the risk surrounding the yield at which it will be able to sell its bonds? Both the bond and the contract are at par value.

Short Answer

Expert verified

Sale 133 contracts to offset losses

Step by step solution

01

Given information

Bond value = $10,000,000

Modified duration = 8 years

Since the contracts and yield changes on bond are 1 basis point, hence the change in bond value = $10,000,000 x 0.0001 x 8

=$8,000

02

Calculation of cash flow

The cash flow on account of contract = $100,000 x .0001 x 6 (given)

= $60

This implies that the manager should sell 8000 / 60 = 133 contracts

This sale would offset losses in case the interest rates increase.

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Most popular questions from this chapter

Futures contracts and options contracts can be used to modify risk. Identify the fundamental distinction between a futures contract and an option contract, and briefly explain the difference in the manner that futures and options modify portfolio risk.

Why might individuals purchase futures contracts rather than the underlying asset?

Joseph Jones, a manager at Computer Science, Inc. (CSI), received 10,000 shares of company stock as part of his compensation package. The stock currently sells at \(40 a share. Joseph would like to defer selling the stock until the next tax year. In January, however, he will need to sell all his holdings to provide for a down payment on his new house. Joseph is worried about the price risk involved in keeping his shares. At current prices, he would receive \)40,000 for the stock. If the value of his stock holdings falls below \(35,000, his ability to come up with the necessary down payment would be jeopardized.

On the other hand, if the stock value rises to \)45,000, he would be able to maintain a small cash reserve even after making the down payment. Joseph considers three investment strategies:

a. Strategy A is to write January call options on the CSI shares with strike price \(45. These calls are currently selling for \)3 each.

b. Strategy B is to buy January put options on CSI with strike price \(35. These options also sell for \)3 each.

c. Strategy C is to establish a zero-cost collar by writing the January calls and buying the January puts.

Evaluate each of these strategies with respect to Joseph’s investment goals. What are the advantages and disadvantages of each? Which would you recommend?

The Excel Applications box in the chapter (available at www.mhhe.com/bkm ; link to Chapter 17 material) shows how to use the spot-futures parity relationship to find a “term structure of futures prices,” that is, futures prices for various maturity dates.

a. Suppose that today is January 1, 2012. Assume the interest rate is 1% per year and a stock index currently at 1,200 pays a dividend yield of 2%. Find the futures price for contract maturity dates of February 14, 2012, May 21, 2012, and November 18, 2012.

b. What happens to the term structure of futures prices if the dividend yield is lower than the risk-free rate? For example, what if the interest rate is 3%?

Why do you think the most actively traded options tend to be the ones that are near the money?

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