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 think is also a possibility. Your investment adviser suggests a protective put position: Buy both shares in a market index stock fund and put options on those shares with 3-month expiration and exercise price of $780. The stock index fund is currently selling for $900. However, your uncle suggests you instead buy a 3-month call option on the index fund with exercise price $840 and buy 3-month T-bills with face value $840.
a. On the same graph, draw the payoffs to each of these strategies as a function of the stock fund value in 3 months. Think of the options as being on one “share” of the stock index fund, with the current price of each share of the fund equal to $900.)
b. Which portfolio must require a greater initial outlay to establish? (Does either portfolio provide a final payout 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 ............... $900
T-bill (face value $840) ........... $810
Call (exercise price $840) .......... $120
Put (exercise price $780) ......... $ 6
Make a table of the profits realized for each portfolio for the following values of the stock price in 3 months: ST = $700, $840, $900, $960.
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?
e. Explain why the data for the securities given in part (c) do not violate the put-call parity relationship.