Reference no: EM133072203

The Protective Put

Question

The following problem reviews the usefulness and limitations of the put-call parity relationship. In the process it also revisits the protective put strategy that is widely adopted by portfolio managers as an alternative method of implementing portfolio insurance.

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 also think is a possibility. Your investment horizon is the next three months.

Your investment advisor suggests a protective put position: Buy shares in the market index stock fund and European put options on those shares with three-month maturity and exercise price of $260. The stock index is currently selling at $300.

However, your uncle suggests that you should instead buy a three-month European call option on the index fund with exercise price $280 and buy three-month Treasury bills with face value $280. (All Treasury bills - obligations of the US Treasury with maturity one year or less - are like zero coupon bonds and therefore pay only at maturity.)

a. On the same graph, draw the dollar 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 $300.)

b. Which of these two portfolios must require a greater initial outlay to establish? Why?

c. Suppose the market price of the securities are as follows:

Stock fund $300

T-bill (face value $280) $270

Call (exercise price $280) $35

Put (exercise price $260) $2

Explain why the prices for these securities do not violate the put-call parity relationship.