Question

Suppose you think that Boeing (BA) stock is going to appreciate substantially in value over the next 1.5 months. The stock’s current price is S₀ = 87.37. The call option expiring in 1.5 months with exercise price X = 85 is trading at an option premium of C = 5.00. You have 10,000 to invest and are considering three alternatives:

1) All stocks: invest all 10,000 in the stock (you buy 114.46 shares).

2) All options: invest all 10,000 in options (you buy 2,000 options).

3) Bills and options: buy 114 options for 570 and invest the remaining 9,430 in a money market fund that pays 4% (annual rate) in interest. Assume that this means that over the 1.5 months of your investment the money market fund pays 0.5% in interest.

What is the payoff and rate of return for each alternative (1-3) for the following 3 stock prices in 1.5 months: 85, 90, 95? Summarize your results in a table (8 points).

stock price	85	90	95
Payoff
1) stock only
2) options only
3) bills and options
Return
1) stock only
2) options only
3) bills and options

b. What are the minimum possible payoffs and returns for the three strategies? (3 points)

The minimum possible payoff to the three strategies is:

Answer 1

Return on stock (absolute return since less than a year is not annualised) = (S_1.5 - S₀)/S₀

Payoff on call option = Max (S_1.5 - X, 0) (pay off only includes expiry cash flows and not the premium which has already been paid)

Money market pay off in 1.5 months = 9430 * (1+0.5%) = 9477.15

Now we can populate the table, as below:

Part (b) As we can see from the table above:

• Minimum possible pay off is at 85, when the options will expire worthless and hence 100% loss. The all stock will have a loss of 2.71% and bills and options at negative 5.23%
• Except in case of options which expire worthless, both in case of stock and bills & options there will be residual value for the portfolio