Chapter 23  Futures, Swaps, and Risk Management
231
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 contract (for the given change in the index). In the bond market,
the comparable calculation is generally thought of in terms of the price value of a basis
point (PVBP) for the bond and the PVBP for the futures contract, rather than in terms of
the total dollar change in both the value of the portfolio and the value of a single futures
contract.
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232
2.
One of the considerations that would enter into the hedging strategy for a U.S. exporting
firm with outstanding bills to its customers denominated in foreign currency is whether
the U.S. firm also has outstanding payables denominated in the same foreign currency.
Since the firm receives foreign currency when its customers’ bills are paid, the firm
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 Spring '10
 MAZUMDER
 Forward contract

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