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# Choices for using options to hedge against home purchase in one year.

Mr. and Mrs. Smith plan to buy a house in the near future. Their dream house costs \$240,000 and will be available in a year. The Smiths currently hold \$250,000 in 2,500 shares of Company A. Their financial advisor tells them that they have three options to preserve at best the value of their investment:

(1) create a protective put by buying a put option on stock A, with an exercise price of Xp = \$100 and premium equal to P = \$10.

(2) create a covered call by selling a call option on stock A, with an exercise price of Xc = \$95 and premium equal to C = \$8.

(3) create a collar by buying a put option and selling a call option, both on stock A and both with the same premium, with exercise prices equal to X1 = \$96 for the put option and X2 = \$102 for the call option.

(i) What is the current price of the stock?

(ii) Derive the payout of the protective put as a function of the future price of the stock ST , using the payouts of its components. Show graphically the payout and profit of this investment option (given that the only cost is the premium of the put option). What is the total value (profit) of this investment after one year, as a function of ST ?

(iii) Derive the payout of the covered call as a function of the future price of the stock ST , using the payouts of its components. Show graphically the payout and profit of this investment option (given that the only cost is the premium of the call option). What is the total value (profit) of this investment after one year, as a function of ST ? 1

(iv) Derive the payout of the collar as a function of the future price of the stock ST, using the payouts of its components. Show graphically the payout and profit of this investment option. What is the total value (profit) of this investment after one year, as a function of ST

(v) If you were the financial advisor of the Smiths and you expected the stock price of company A to fall during the year, which strategy would you recommend? How would your recommendation change if you expected the stock price to increase?
Which strategy would you recommend in case the evolution of the price was uncertain?

#### Solution Summary

In multiple Excel sheets, the complex concepts are thoroughly explored and explained. Answers are included.

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