Question

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 materializes. 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 fund and put options on those shares 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.

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 \(1,200.)

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	\)1200
T -bill (Face value \(1,120	\)1080
Call (Exercise price \(1,120	\)160
Put (Exercise price \(1040	\)8

Make a table of profits realized for each portfolio for the following values of the stock price in three months: S _T = \(0, \)1,040, \(1,120, \)1,200, and $1,280. Graph the profits to each portfolio as a function of S _T on a single graph.

d. Which strategy is riskier? Which should have a higher beta?

Short answer

As below

Step-by-step solution

Calculation of Strategy one

Protective Put

Protective Put	ST < 1040	ST > 1040
Stock	ST	ST
Put	1040 - ST	0
Total	1040	ST

Calculation of Strategy two

Bills plus calls

Protective Put	ST < 1,120	ST < 1,120
Bills	1,120	1,120
Call	0	ST –1,120
Total	1,120	ST

Calculation of initial outlay ‘b’

Protective Put	ST = 0	ST = 1400	ST = 1600	ST = 1800	ST = 1920
Stock	0	1400	1600	1800	1920
+ Put	1560	0	0	0	0
Payoff	1560	1400	1600	1800	1920
Profit	-252	-412	-212	-12	108

Profit = Payoff – initial outlay

Initial outlay = 1560 + 252 = $1,812

Calculation of initial outlay ‘b’

Position	ST = 0	ST = 1400	ST = 1600	ST = 1800	ST = 1920
Bill	1680	1680	1680	1680	1680
+ Call	0	0	0	120	240
Payoff	1680	1680	1680	1800	1920
Profit	-180	-180	-180	-60	-60

Profit = Payoff – initial outlay

Initial outlay = 1680 + 180 = $1,860

Graphical representation of profits ‘c’

Explanation on riskier strategy

The stock and put strategy would be riskier as its beta would be higher based on the market conditions.