1. Suppose the scenario that the standard deviation of semiannual changes in the price of wheat is $.79, the standard deviation of changes in the futures contract on wheat over the same time period is $.93. and the correlation coefficient relating the asset and futures contract is .86. What is the optimal hedge ratio for the six month contract on wheat? Describe the significance of this.
2. A refiner, for the next two months, has exposure to 3.562 million gallons of ethanol for mixture with gasoline to create a blended fuel. Ethanol is traded on the NYNEX with contract size specifications of 29,000 gallons for each contract. The standard deviations for ethanol and futures contracts on ethanol are .72 and .82 respectively while the correlation coefficient is .75. What would be the optimal number of contracts for the refiner to hedge with?
3. If the spot and futures prices for ethanol in the question above are 1.898 and 1.927 respectively, how many contracts should be used to hedge the exposure in the problem above if you tail the hedge?
4. JP Morgan has a $650 Million portfolio of pension assets for a certain company invested in stocks with a Beta of 1.33. It is interested in using S&P futures contracts to hedge the portfolio as it expects a near term decline in the market. The futures price is currently 1.744 and contract specification call for the delivery of $250 times whatever the index value happens to be. Describe the hedge that minimizes risk. What should JP Morgan do if it wants to reduce Beta to .70? What should it do if it wants to increase Beta to 1.6?