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 cannot afford substantial investment losses and so cannot run the risk of a stock market collapse, which you think is also a possibility. Your investment adviser therefore 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 $$\$ 2,340$$. The stock index fund is currently selling for $$\$ 2,700$$. However, your uncle suggests you instead buy a 3 -month call option on the index fund with exercise price $$\$ 2,520$$ and buy 3-month T-bills with face value $$\$ 2,520$$.
a. On the same graph, draw the payeffs to each of these strategies as a function of the stock fund value in three months. (Hin:: 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 $$\$ 2,700$$.)
b. Which portfolio mast require a greater initial outlay to establish?
c. Suppose the market prices of the securities are as follows:
$$
\begin{array}{ll}
\text { Stock fund } & \$ 2,700 \\
\text { T-bil (face varue } \$ 2,520 \text { ) } & \$ 2,430 \\
\text { Call (owercise price } \$ 2,520 \text { ) } & \$ 360 \\
\text { Pult (exerose price } \$ 2,340 \text { ) } & \$ 18
\end{array}
$$
Make a table of the profits realized for each portfolio for the following values of the stock price in three months: $$S_T=\$ 2,000, \$ 2,520, \$ 2,700, \$ 2,880$$. 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 nor violate the put-call parity relationship.