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.

a) If the portfolio has a beta of 1, how many put option contracts should be purchased? (6 points)

b) If the portfolio has a beta of 0.5, how many put options should be purchased? (4 points)