You have $10m to invest, and you are considering the returns associated with different trading strategies centering on the S&P 500 index, as well as puts and calls on the index. Currently, the index is trading at 2,449.86.

Strike Call Put

2440 32.00 21.50

2445 29.60 23.10

2450 26.96 25.70

2455 24.10 27.42

You are debating the risks and rewards associated with the following trad- ing strategies:

• Invest the $10m directly in the index.
• Use the $10m to buy call options on the index with a strike of 2445 and, for each call bought, write call option on the index with a strike of 2455.
• Use the $10m to buy put options on the index with a strike of 2450 and, for each put bought, write put option on the index with a strike of 2445.
• Study the returns from each of these strategies, for values of the index in the range of 2440 to 2455 (i.e. assume that the index can take on any value between 2440 and 2460. If you look at only integer values of the index, that will be sufficient).

(a) Compute the return from each strategy as a function of the index price. (Recall that returns are defined as (value of the portfolio at the final date minus cost of the portfolio at the initial date)/(cost of the portfolio at the initial date).)

(b) Which strategy would you deem most risky? Assuming that the index has a positive beta (which it should), what would be the sign of the betas of each of the strategies? Can you rank the trading strategies in terms of their expected returns in a CAPM world?