Chapter 26 Managing Risk 693
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The hedge is not zero-maintenance, however. You can see from Figure 26.4 that the PV
curve for the 7.5-year zero has less curvature (less convexity) than the PV curve for the
lease. The zero has lower duration (shallower slope) at low interest rates and higher duration
(steeper slope) at high interest rates. Thus if interest rates move much higher or lower than
10%, Potterton’s CFO will have to reconsider and reset the hedge. Also she will have to reset
the hedge later even if interest rates do not change because the duration of the 7.5-year zero
will decrease faster than the duration of the 20-year lease. Think forward 7.5 years: The zero
will mature, while the lease will still have 12.5 years to maturity.
You can see why duration is a useful tool for measuring and hedging interest rate risk.^32
The mini-case at the end of this chapter offers another opportunity to use this concept.
Hedge Ratios and Basis Risk
In our example of Potterton Leasing, the CFO matched lease cash flows worth $17 million
against debt worth $17 million. In other words, the hedge ratio for Potterton was exactly 1.
Hedge ratios can be much higher or lower than 1. For example, suppose a farmer owns
100,000 bushels of wheat and wishes to hedge by selling wheat futures. In practice, the wheat
that the farmer owns and the wheat that he sells in the futures markets are unlikely to be identi-
cal. If he sells wheat futures on the Kansas City exchange, he agrees to deliver hard, red winter
wheat in Kansas City in September. But perhaps he is growing northern spring wheat many
miles from Kansas City; in this case, the prices of the two wheats will not move exactly together.
Figure 26.5 shows how changes in the prices of the two types of wheat may have been
related in the past. The slope of the fitted line shows that a 1% change in the price of Kansas
wheat was, on average, associated with an .8% change in the price of the farmer’s wheat.
(^32) Duration is not a complete measure of interest rate risk. It measures only exposure to the level of interest rates, not to changes in the
shape of the term structure. Duration in effect assumes that the term structure is “flat.” Duration is widely used, however, because it is
a good first approximation to interest rate risk exposure.
◗ FIGURE 26.4
Hedging Potterton’s interest rate risk by matching duration. The PV of lease cash inflows is plotted on the left, the PV of
debt on the right. All durations are 7.5 years, so the slopes of the PV curves are identical at the current 10% interest rate.
Therefore, Potterton’s net exposure to small changes in interest rates is zero.
0
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20-year annuity
Yield to maturity, %
Price or value
Yield to maturity, %
PV
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