Chapter 5: Q16-42I (page 557)
Use the put-call parity relationship to demonstrate that an at-the-money call option ona non-dividend-paying stock must cost more than an at-the-money put option. Showthat the prices of the put and call will be equal if S =(1 + r)T.
As below
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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.
Donna Donie, CFA, has a client who believes the common stock price of TRT Materials (currently $58 per share) could move substantially in either direction in reaction to an expected court decision involving the company. The client currently owns no TRT shares, but asks Donie for advice about implementing a strangle strategy to capitalize on the possible stock price movement. A strangle is a portfolio of a put and a call with different exercise prices but the same expiration date. Donie gathers the following TRT option price data:
a. Recommend whether Donie should choose a long strangle strategy or a short strangle strategy to achieve the client’s objective.
b. Calculate, at expiration for the appropriate strangle strategy in part ( a ), the:
i. Maximum possible loss per share.
ii. Maximum possible gain per share.
iii. Break-even stock price(s).
Use the following case in answering Problems 10 – 15 :
Mark Washington, CFA, is an analyst with BIC. One year ago, BIC analysts predicted that the U.S. equity market would most likely experience a slight downturn and suggested delta-hedging the BIC portfolio.
As predicted, the U.S. equity markets did indeed experience a downturn of approximately 4% over a 12-month period. However, portfolio performance for BIC was disappointing, lagging its peer group by nearly 10%. Washington has been told to review the options strategy to determine why the hedged portfolio did not perform as expected.
BIC owns 51,750 shares of Smith & Oates. The shares are currently priced at \(69. A call option on Smith & Oates with a strike price of \)70 is selling at $3.50 and has a delta of .69. What is the number of call options necessary to create a delta-neutral hedge?
Turn back to Figure 15.1, which lists the prices of various IBM options. Use the data in the figure to calculate the payoff and the profits for investments in each of the following January 2012 expiration options, assuming that the stock price on the expiration date is $165.
a. Call option, X = 160
b. Put option, X = 160
c. Call option, X = 165
d. Put option, X = 165
e. Call option, X = 170
f. Put option, X = 170
Consider a stock that will pay a dividend of D dollars in one year, which is when a futures contract matures.
Consider the following strategy: Buy the stock, short a futures contract on the stock, and borrow dollars, where is the current price of the stock.
a. What are the cash flows now and in one year? (Hint: Remember the dividend the stock will pay.)
b. Show that the equilibrium futures price must beto avoid arbitrage.
c. Call the dividend yield d = D / , and conclude that .
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