《《Investment 8th Chap023》.docVIP

CHAPTER 23: FUTURES, SWAPS, AND RISK MANAGEMENT PROBLEM SETS 1. In formulating a hedge position, a stock’s beta and a bond’s duration are used similarly to determine the expected percentage gain or loss in the value of the underlying asset for a given change in market conditions. Then, in each of these markets, the expected percentage change in value is used to calculate the expected dollar change in value of the stock or bond portfolios, respectively. Finally, the dollar change in value of the underlying asset, along with the dollar change in the value of the futures contract, determines the hedge ratio. The major difference in the calculations necessary to formulate a hedge position in each market lies in the manner in which the first step identified above is computed. For a hedge in the equity market, the product of the equity portfolio’s beta with respect to the given market index and the expected percentage change in the index for the futures contract equals the expected percentage change in the value of the portfolio. Clearly, if the portfolio has a positive beta and the investor is concerned about hedging against a decline in the index, the result of this calculation is a decrease in the value of the portfolio. For a hedge in the fixed income market, the product of the bond’s modified duration and the expected change in the bond’s yield equals the expected percentage change in the value of the bond. Here, the investor who has a long position in a bond (or a bond portfolio) is concerned about the possibility of an increase in yield, and the resulting change in the bond’s value is a loss. A secondary difference in the calculations necessary to formulate a hedge position in each market arises in the calculation of the hedge ratio. In the equity market, the hedge ratio is typically calculated by dividing the total expected dollar change in the value of the portfolio (for a given change in the index) by the profit (i.e., the dollar change in value) on one futures