3330%20PS7%20solution - Cornell University Fall 2009...

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Cornell University Fall 2009 Economics 3330: Problem Set 7 Solutions 1. True/False/Explain State whether each of the following is true or false and explain your answer. Please limit your explanations to no more than two sentences. b. From an options perspective, if a company takes on additional debt to buy back some of its equity at the market price, then the value of an outstanding share should increase. True. A share will be a claim on a more volatile asset. 2. You are interested in establishing a long position in a company. The stock of the company currently costs $100. A call option with a strike price of 100 that has six months until maturity costs $10. You have $10,000 to invest. The three portfolios you are considering are 1) all stocks, 2) all options, and 3) 100 options and Treasury bills that would pay 4% over the next six months. Complete the following chart with the value of the portfolio. Price of Stock 6 Months from Now Stock Price $80 $100 $110 $120 All stocks (100 shares) $8,000 $10,000 $11,000 $12,000 All options (1,000 options) $0 $0 $10,000 $20,000 Bills + 100 options $9,360 $9,360 $10,360 $11,360 3. Reconsider the determination of the hedge ratio in the two-state model, where we showed that one-third share of stock would hedge one option. What would be the hedge ratio for each of the following exercise prices: $90, $100, $110, $120? What is the relationship between the hedge ratio and the exercise price? What is the intuition for this result? X Hedge Ratio 120 0 110 1/3 100 2/3 90 1 As the option becomes progressively more in the money, its hedge ratio increases. (This is akin to the effect of the stock price increasing with the exercise price held constant.) 4. Suppose the initial stock price is 100 and next period can take values 80 or 130 with equal
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3330%20PS7%20solution - Cornell University Fall 2009...

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