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

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 an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What should the strike price of options on the index be the portfolio has a beta of 0.5? Assume that the risk-free rate is 10% per annum and the dividend yield on both the portfolio and the index is 2% per annum.