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%. _ _ _ _ _ _