A portfolio manager in charge of a portfolio worth $8 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 $7 million. The S&P 100 index is currently valued at 400 and each contract is on 100 times the index.

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

2. If the portfolio has a beta of 1, what should the strike price of the put options be?

3. If the portfolio has a beta of 0.5, how many put options should be purchased?

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