Chapter 5: Q26I (page 555)
If the time to expiration falls and the put price rises, then what has happened to the put option’s implied volatility?
Increased
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The margin requirement on the S&P 500 futures contract is 10%, and the stock index is currently 1,200. Each contract has a multiplier of $250. How much margin must be put up for each contract sold? If the futures price falls by 1% to 1,188, what will happen to the margin account of an investor who holds one contract? What will be the investor’s percentage return based on the amount put up as margin?
Joe Finance has just purchased a stock-index fund, currently selling at \(1,200 per share. To protect against losses, Joe plans to purchase an at-the-money European put option on the fund for \)60, with exercise price \(1,200, and three-month time to expiration. Sally Calm, Joe’s financial adviser, points out that Joe is spending a lot of money on the put. She notes that three-month puts with strike prices of \)1,170 cost only $45, and suggests that Joe use the cheaper put.
a. Analyze Joe’s and Sally’s strategies by drawing the profit diagrams for the stock-plus put positions for various values of the stock fund in three months.
b. When does Sally’s strategy do better? When does it do worse?
c. Which strategy entails greater systematic risk?
a. Turn to Figure 17.1 and locate the contract on the Standard & Poor’s 500 Index. If the margin requirement is 10% of the futures price times the multiplier of $250, how much must you deposit with your broker to trade the September contract?
b. If the September futures price were to increase to 1,200, what percentage return would you earn on your net investment if you entered the long side of the contract at the price shown in the figure?
c. If the September futures price falls by 1%, what is the percentage gain or loss on your net investment?
The hedge ratio of an at-the-money call option on IBM is .4. The hedge ratio of an at-the-money put option is -6. What is the hedge ratio of an at-the-money straddle position on IBM?
An executive compensation scheme might provide a manager a bonus of $1,000 for every dollar by which the company’s stock price exceeds some cut off level. In what way is this arrangement equivalent to issuing the manager calls options on the firm’s stock?
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