Question

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 $1,560. The stock index is currently at $1,800. However, your uncle suggests you instead buy a three-month call option on the index fund with exercise price $1,680 and buy three-month T-bills with face value $1,680. (LO 15-2) Stock fund $1,800 T-bill (face value $1,680) 1,620 Call (exercise price $1,680) 240 Put (exercise price $1,560)

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 $1,800.)

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	$1,800
T-bill (face value $1,680)	1,620
Call (exercise price $1,680)	240
Put (exercise price $1,560)	12
Make a table of profits realized for each portfolio for the following values of the stock price in three months: ST = $0, $1,400, $1,600, $1,800, and $1,920. Graph the profits to each portfolio as a function of ST on a single graph. d. Which strategy is riskier? Which should have a higher beta?

Answer 1

a). For the put option + stock strategy, for a given stock price S, the payoff will be as follows:

For the call option + T-bill strategy, for a given stock price S, the payoff will be as follows:

The payoff graph:

b). The call option + T-bill strategy always has a greater payoff than the put option + stock strategy so it has to be more expensive.

c). Put option + stock strategy profit = total payoff - put option price - buying price of stock

Call option + T-bill strategy profit = total payoff - call option price - buying price of T-bill

Profit graph:

d). As can be seen from the profit table, the put + stock strategy is more volatile in the sense that it has higher loss when the stock price is lower and higher profit when stock price is higher, so its beta should be more as it has more risk.