Mr. Smith used to own a company that was bought by a larger competitor.  The firm was purchased through cash and a significant number of shares of the purchaser.  These shares are restricted and as a result Mr. Smith cannot sell his shares for the next twelve months.  Most of Mr. Smith's net worth is tied to his holdings in this company and he is concerned about how this concentrated equity position might affect his net worth should the market take a turn for the worse.  He currently holds 700,000 shares of Company XYZ.  Mr. Smith wants to protect himself from the stock price going down more than 20% of its current value.  A one-year T-bill is currently priced at $95.12.  The standard deviation of the monthly return is 11.55%.

 

1)  The current stock price is $60. Smith decides to buy some put options.  Using Black-Scholes-Merton option pricing, how much would these options cost?

2)  If Mr. Smith wants to put the hedge in place without any cash outlay, he can put an equity collar in place. What would the corresponding call strike price be associated with the put strike above?

3)  If after six months, the stock price went to $90 and Mr. Smith wanted to unwind the hedge he put in place in question 2) above, what are the economic implications? Will Mr. Smith be paying a termination cost or will he be receiving a termination payment?  How much will this cost/payment be?

4)  Are the strike prices in 2) symmetrical? Why or why not?

5)  A financial advisor approaches Mr. Smith and tells him that based on past performance of Company XYZ shares, technical analysis says that the stock should be going up and there is no need to put a hedge in place for Mr. Smith's holdings. Do you agree with the financial advisor?  Is the financial advisor's analysis consistent with the assumptions we made in class regarding stock prices?

6)  The options that are typically used are European options. Why can you not use American options?  Discuss the risks inherent in an equity collar using American options that is not true of an equity collar using European options.

7)  Keep in mind that these options being used are European options.  Assume that Mr. Smith knew prior to putting the hedge in place that the stock will be paying a dividend of $10 on the sixth month.  Without doing any calculations, how will this affect the call strike price in the equity collar?  Explain why this will necessarily be the case.  Be as detailed as you can in your explanation.