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 materialises. 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 and put options on the index 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.$

What are the payoffs to each of these strategies as a function of the stock fund value in three months $($payoffs when Stock over $1,040$ and Stock below $1,040).$