Suppose that the risk-free rate of interest is equal to 5.5% per year continuously compounded and that a stock index has a constant dividend yield equal to 2.25% per year. Suppose that the futures price on a futures contract written on the stock index with maturity of 1 year is $1250. The size of the contract is standard: 500 times the index.

1. What is the current market value of the index?

2. A mutual fund manages a portfolio with market value $150M. This portfolio has an expected return equal to 18%. If the risk premium on the market portfolio of risky assets is 10% what is the beta of the managed portfolio?

3. The mutual fund manager seeks to reduce the beta of her portfolio to 0.60. Find the number of futures contracts required if the return on the index underlying the futures is perfectly correlated with the return on the market portfolio of risky assets?

4. Calculate the effects of the hedging strategy on the fund managers 1 year return if the index level in 1 year is 1000. Do the same for if the index is 1500.