$18.$ 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 stock market losses and so cannot run the risk of a stock market collapse, which you recognize is also possible. Your investment adviser therefore 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 $$1,950.$ The stock index is currently at $$2,250.$ However, your uncle suggests you instead buy a three$-$month call option on the index fund with exercise price $$2,100$ and buy three$-$month T$-$bills with face value $$2,100.$

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 $$2,250.)$

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 $$2,250$

T$-$bill $($face value $$2,100)$ $$2,025$

Call $($exercise price $$2,100)$ $$260$

Put $($exercise price $$1,950)$ $$15$

Make a table of profits realized for each portfolio for the following values of the stock price in three months: ST $=$ $$0,$ $$1,750,$ $$2,000,$ $$2,250,$ and $$2,400.$ Graph the profits to each portfolio as a function of S$,$ on a single graph.

D$.$ Which strategy is riskier? Which should have a higher beta?