Problem
A portfolio manager in charge of a portfolio worth $10 million is concerned that the market might decline rapidly during the next six months and would like to use options on the S&P 100 to provide protection against the portfolio falling below $9.5 million. The S&P 100 index is currently standing at 500 and each contract is on 100 times the index.
1. If the portfolio has a beta of 1, how many put option contracts should be purchased?
2. If the portfolio has a beta of 1, what should the strike price of the put options be?
3. If the portfolio has a beta of 0.5, how many put option contracts should be purchased?
4. If the portfolio has a beta of 0.5, what should the strike prices of the put options be? Assume that (a) the risk-free rate is 10%, and (b) the dividend yield on both the portfolio and the index is 2%.