Suppose that the current stock price S0 of Facebook is S0 = $100, and the risk-free annual interest rate is 3%. The price (premium) of 1-year European call option (meaning, the expiration date is exactly 1 year from today) with exercise price of K = $90 is $20. You have $10,000 that you would like to invest, and there are 3 different investment options::
1. Invest all $10,000 in Facebook stocks
2. Invest all $10,000 in the aforementioned 1-year European call options with exercise price of $90 (premium = $20)
3. 80% in risk-free rate, 20% in options ($8,000 in T-bills with 3% rate of return and $2,000 in the aforementioned call options)
Plot the payoff (NOT the net profit) 1 year from now of each of the three investment options as a function of S1, the value of the Facebook stock 1 year from now. In other words, you should have three graphs in the same plot, in which each graph has the payoff of one of the 3 investment options on the y-axis and S1 on the x-axis. Also, determine exactly in which range of S1, each investment strategy does better than the others. (It is insufficient to simply indicate on the graph where each investment strategy does the best. You must indicate exactly in which values of S1 each investment does the best.)