Question 6 Assume no transaction costs. A stock has a price of $17 on 1/1/2006.

Question

Question 6 Assume no transaction costs. A stock has a price of $17 on 1/1/2006. Vicki sells 1,000 shares of stock short with an expiration date of 1/1/2007. Valerie buys 1,000 put options expiring 1/1/2007 with a strike price of $17. These options cost S1.25. The stock closes at S15 on 1/1/2007 and both Vickie and Valerie make money. What is the difference between their gains? Assume a continuous discount rate of 5% annually, and assume that Valerie is allowed to invest the proceeds of the short sale at this risk-free rate

Explanation / Answer

If Vicki will short sale then he will make = 1000 * 17 = $17000

and if he inves at 5% for one year then value of $17000 = $17000 * e^(.05*1) = $17871.6

Valerie will pay for options = $1.25 * 1000 = $1250

payoff for Valerie at the time of expiration = number of options * (strike price - stock price)

= 1000 * (17 - 15) = 2000

so total profit for Valerie = $2000 - $1250 = $750

Vickie will earn = $17871.60 - ($15 * 1000) = $2871.60

Difference between gain after one year = $2871.6 - $750 = $2121.6

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