1. You manage a $10 million stock portfolio with a beta of 1.4. The futures price for a contract on the Mini S&P index is 4000 times $50. (a) Suppose you wish to protect the portfolio against market volatility. How many futures contracts do you need to buy or sell to accomplish this objective? (b) How many futures contract do you need to buy or sell to lower the beta to 0.5? (c) You are a risk-taker. Starting with (a) above, how many futures contract do you need to buy or sell to increase beta to 2? (d) How much risk would you be able to hedge in (a) if the correlation between the spot and futures price changes is 0.8? (e) Do you think it is wise to use this futures contract to hedge price fluctuations in a bond portfolio? (25 points)