1. 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.

(i) If the portfolio has a beta of 1, how many put option contracts should be purchased?

(ii) If the portfolio has a beta of 1, what should the strike price of the put options be?

(iii)If the portfolio has a beta of 0.5, how many put options should be purchased?

(iv) If the portfolio has a beta of 0.5, what should the strike prices of the put options be? Assume that the risk-free rate is 10% and the dividend yield on both the portfolio and the index is 2%.