A Portfolio Manager in Charge of a Portfolio Worth $10

Short Answer

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/ASX 200 to provide protection against the portfolio falling below $9.5 million. The S&P/ASX 200 is currently standing at 5000 and each contract is on 10 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) When the portfolio has a beta of 0.5, what should the strike prices of the put options be if the insured level of $9.5 million were to include dividends? 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. _ _ _ _ _ _