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...

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.Assume that the risk free rate is 10%,and the dividend yield on both the potfolio and the index is 2%. If the portfolio has a beta of 0.5, how many put option contracts should be purchased? If the portfolio has a beta of 0.5 ,what should the strike price of the put option be?