Raha CHAPTER 3 Hedging Strategies Using Futures Problem 3.6. Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.45, the standard deviation of quarterly changes in a fuatures price on the commodity is SO.S1, and the coefficient of correlation between the two changes is 0.6. What is the optimal hedge ratio for a three-month contract? What does it mean? Problem 3.7 A company has a $10 million portfolio with a beta of 1.4. It would like to use futures contracts on the S&P 500 to hedge its risk. The index futures is currently standing at 1040, and each contract is for delivery of $150 times the index. What is the hedge that minimizes risk? What should the company do ifit wants to reduce the beta of the portfolio to 0.6 Problem 3.16. The standard deviation of monthly changes in the spot price of live catle is (in cents per pound) 1.3. The standard deviation of monthly changes in the futures price of live cattle for the closest contract is 1.5. The correlation between the futures price changes and the spot price changes is 0.8. It is now October 15. A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15. The producer wants to use the December live-cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle. What is the optimal hedge ratio ?What strategy should the beef producer follow