Chapter 5: Q4B (page 588)
You purchase a Treasury-bond futures contract with an initial margin requirement of 15% and a futures price of \(115,098. The contract is traded on a \)100,000 underlying par value bond. If the futures price falls to $108,000, what will be the percentage loss on your position?
Answer
Loss of 41.11%
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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.
You are very bullish (optimistic) on stock EFG, much more so than the rest of the market.
In each question, choose the portfolio strategy that will give you the biggest dollar profit if your bullish forecast turns out to be correct. Explain your answer.
a. Choice A: \(100,000 invested in calls with X = 50.
Choice B: \)100,000 invested in EFG stock.
b. Choice A: 10 call options contracts (for 100 shares each), with X = 50.
Choice B: 1,000 shares of EFG stock.
Consider the following options portfolio: You write a January 2012 expiration calloption on IBM with exercise price \(170. You also write a January expiration IBM putoption with exercise price \)165.
a. Graph the payoff of this portfolio at option expiration as a function of IBM’s stockprice at that time.
b. What will be the profit/loss on this position if IBM is selling at \(167 on the optionexpiration date? What if IBM is selling at \)175? Use The Wall Street Journal listingfrom Figure 15.1 to answer this question.
c. At what two stock prices will you just break even on your investment?
d. What kind of “bet” is this investor making; that is, what must this investor believeabout IBM’s stock price in order to justify this position?
A bearish spread is the purchase of a call with exercise price X 2 and the sale of a call with exercise price X 1, with X 2 greater than X 1. Graph the payoff to this strategy and compare it to Figure 15.10 .
The common stock of the P.U.T.T. Corporation has been trading in a narrow price range for the past month, and you are convinced it is going to break far out of that range in the next three months. You do not know whether it will go up or down, however. The current price of the stock is \(100 per share, the price of a three-month call option with an exercise price of \)100 is \(10, and a put with the same expiration date and exercise price costs \)7.
a. What would be a simple options strategy to exploit your conviction about the stock price’s future movements?
b. How far would the price have to move in either direction for you to make a profit on your initial investment?
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