Chapter 5: Q17I (page 590)
Desert Trading Company has issued \(100 million worth of long-term bonds at a fixed rate of 7%. The firm then enters into an interest rate swap where it pays LIBOR and receives a fixed 6% on notional principal of \)100 million. What is the firm’s overall cost of funds?
Answer
LIBOR + 1%
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A collar is established by buying a share of stock for \(50, buying a six-month put option with exercise price \)45, and writing a six-month call option with exercise price \(55. Based on the volatility of the stock, you calculate that for an exercise price of \)45 and maturity of six months, N (d1) = .60, whereas for the exercise price of \(55, N (d1) = .35.
a. What will be the gain or loss on the collar if the stock price increases by \)1?
b. What happens to the delta of the portfolio if the stock price becomes very large? Very small?
You are attempting to value a call option with an exercise price of \(100 and one year to expiration. The underlying stock pays no dividends, its current price is \)100, and you believe it has a 50% chance of increasing to \(120 and a 50% chance of decreasing to \)80.
The risk-free rate of interest is 10%. Calculate the call option’s value using the two-state stock price model.
Ken Webster manages a $200 million equity portfolio benchmarked to the S&P 500 Index. Webster believes the market is overvalued when measured by several traditional fundamental/economic indicators. He is therefore concerned about potential losses but recognizes that the S&P 500 Index could nevertheless move above its current 883 level.
Webster is considering the following option collar strategy:
The information in the following table describes the two options used to create the collar.
a. Describe the potential returns of the combined portfolio (the underlying portfolio plus the option collar) if after 30 days the S&P 500 Index has:
i. Risen approximately 5% to 927.
ii. Remained at 883 (no change).
iii. Declined by approximately 5% to 841.
(No calculations are necessary.)
b. Discuss the effect on the hedge ratio (delta) of each option as the S&P 500 approaches the level for each of the potential outcomes listed in part ( a ).
c. Evaluate the pricing of each of the following in relation to the volatility data provided:
i. The put
ii. The call
The S&P 500 Index is currently at 1,200. You manage a \(6 million indexed equityportfolio. The S&P 500 futures contract has a multiplier of \)250.
a. If you are temporarily bearish on the stock market, how many contracts should yousell to fully eliminate your exposure over the next six months?
b. If T-bills pay 2% per six months and the semi-annual dividend yield is 1%, what is theparity value of the futures price? Show that if the contract is fairly priced, the totalrisk-free proceeds on the hedged strategy in part (a) provide a return equal to theT-bill rate.
c. How would your hedging strategy change if, instead of holding an indexed portfolio,you hold a portfolio of only one stock with a beta of .6? How many contracts wouldyou now choose to sell? Would your hedged position be riskless? What would be thebeta of the hedged position?
a. How should the parity condition (Equation 17.2) for stocks be modified for futures contracts on Treasury bonds? What should play the role of the dividend yield in that equation?
b. In an environment with an upward-sloping yield curve, should T-bond futures prices on more distant contracts be higher or lower than those on near-term contracts?
c. Confirm your intuition by examining Figure 17.1.
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