Chapter 5: Q20I (page 504)
Would you expect a \(1 increase in a call option’s exercise price to lead to a decrease inthe option’s value of more or less than \)1?
Decrease in call price by less than $1
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The multiplier for a futures contract on the stock-market index is \(250. The maturity of the contract is one year, the current level of the index is 800, and the risk-free interest rate is .5% per month. The dividend yield on the index is .2% per month. Suppose that after one month, the stock index is at 810.
a. Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly.
b. Find the one-month holding-period return if the initial margin on the contract is \)10,000.
estion: A member of an investment committee interested in learning more about fixed-income investment procedures recalls that a fixed-income manager recently stated that derivative instruments could be used to control portfolio duration, saying, “A futures like position can be created in a portfolio by using put and call options on Treasury bonds.”
a. Identify the options market exposure or exposures that create a “futures-like
position” similar to being long Treasury-bond futures. Explain why the position you created is similar to being long Treasury-bond futures.
b. Explain in which direction and why the exposure(s) you identified in part (a) would affect portfolio duration.
c. Assume that a pension plan’s investment policy requires the fixed-income manager to hold portfolio duration within a narrow range. Identify and briefly explain circumstances or transactions in which the use of Treasury-bond futures would be helpful in managing a fixed-income portfolio when duration is constrained.
You are attempting to formulate an investment strategy. On the one hand, you think there is great upward potential in the stock market and would like to participate in the upward move if it materializes. However, you are not able to afford substantial stock market losses and so cannot run the risk of a stock market collapse, which you recognize is also possible. Your investment adviser suggests a protective put position:
Buy shares in a market-index stock fund and put options on those shares with three months until expiration and exercise price of \(1,040. The stock index is currently at \)1,200. However, your uncle suggests you instead buy a three-month call option on the index fund with exercise price \(1,120 and buy three-month T-bills with face value \)1,120.
a. On the same graph, draw the payoffs to each of these strategies as a function of the stock fund value in three months. (Hint: Think of the options as being on one “share” of the stock index fund, with the current price of each share of the index equal to \(1,200.)
b. Which portfolio must require a greater initial outlay to establish?
( Hint: Does either portfolio provide a final payoff that is always at least as great as the payoff of the other portfolio?)
c. Suppose the market prices of the securities are as follows:
Stock Fund | \)1200 |
T -bill (Face value \(1,120 | \)1080 |
Call (Exercise price \(1,120 | \)160 |
Put (Exercise price \(1040 | \)8 |
Make a table of profits realized for each portfolio for the following values of the stock price in three months: S T = \(0, \)1,040, \(1,120, \)1,200, and $1,280. Graph the profits to each portfolio as a function of S T on a single graph.
d. Which strategy is riskier? Which should have a higher beta?
You are a portfolio manager who uses options positions to customize the risk profile of your clients. In each case, what strategy is best given your client’s objective?
a. Performance to date: Up 16%.
Client objective: Earn at least 15%.
Your scenario: Good chance of large stock price gains or large losses between now and end of year.
i. Long straddle
ii. Long bullish spread
iii. Short straddle
b. Performance to date: Up 16%.
Client objective: Earn at least 15%.
Your Scenario: Good chance of large stock price losses between now and end of year.
i. Long put options
ii. Short call options
iii. Long call options
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).
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