Suppose that you are a portfolio manager. Your portfolio consists of $150 million of stocks with a beta of 0.90, and $10 million invested in Treasury bills. The spot S&P500 index is 1300.

i. What is the overall beta of your portfolio?

ii. You believe that the probability of a stock market decline has increased. Therefore, you wish to reduce the beta of your portfolio to 0.60. Outline the right strategy. The index multiple is 100.

iii. Suppose instead that you wish to reduce the beta of your portfolio to zero. How many futures contracts should you use?

iv. For the portfolio formed in (iii), what should the expected return on this portfolio approximate and why?