694 Part Eight Risk Management
bre44380_ch26_673-706.indd 694 09/30/15 12:09 PM
Because the price of the farmer’s wheat is relatively insensitive to changes in Kansas prices,
he needs to sell .8 × 100,000 bushels of wheat futures to minimize risk.
Let us generalize. Suppose that you already own an asset, A (e.g., wheat), and you wish to
hedge against changes in the value of A by making an offsetting sale of another asset, B (e.g.,
wheat futures). Suppose also that percentage changes in the value of A are related in the fol-
lowing way to percentage changes in the value of B:
Expected change in value of A = α + δ(change in value of B)
Delta (δ) measures the sensitivity of A to changes in the value of B. It is also equal to the
hedge ratio—that is, the number of units of B that should be sold to hedge the purchase of A.
You minimize risk if you offset your position in A by the sale of delta units of B.
The trick in setting up a hedge is to estimate the delta or hedge ratio. Our farmer could use
past experience to do so, but often a strong dose of judgment is called for. For example, sup-
pose that Antarctic Air would like to protect itself against a hike in oil prices. As the financial
manager, you need to decide how much a rise in oil price would affect firm value.
Suppose the company spent $200 million on fuel last year. Other things equal, a 10%
increase in the price of oil will cost the company an extra .1 × 200 = $20 million. But
perhaps you can partially offset the higher costs by charging higher ticket prices, in which
case earnings will fall by less than $20 million. Or perhaps an oil price rise will lead to a
slowdown in business activity and therefore lower passenger numbers. In that case earn-
ings will decline by more than $20 million. Working out the likely effect on firm value is
even trickier because it depends on whether the rise is likely to be permanent. Perhaps the
price rise will induce an increase in production or encourage consumers to economize on
energy usage.
Whenever the two sides of the hedge do not move exactly together, there will be some
basis risk. That is not a problem for the CFO of Potterton. As long as interest rates do
not change sharply, any changes in the value of Potterton’s lease should be exactly offset
by changes in the value of the debt. In this case there is no basis risk, and Potterton is per-
fectly hedged.
Our wheat farmer is less fortunate. The scatter of points in Figure 26.5 shows that it is not
possible for the farmer to construct a perfect hedge using wheat futures. Since the underlying
commodity (the farmer’s wheat) and the hedging instrument (Kansas City wheat futures) are
imperfectly correlated, some basis risk remains.BEYOND THE PAGE
mhhe.com/brealey12eJet fuel and basis
riskBEYOND THE PAGE
mhhe.com/brealey12eWTI and Brent oil
futures◗ FIGURE 26.5
Hypothetical plot of past changes
in the price of the farmer’s wheat
against changes in the price of
Kansas City wheat futures. A 1%
change in the futures price implies,
on average, a .8% change in the
price of the farmer’s wheat.–2–10123–2 –1 0 1 2 3
Price change in wheat futures, %Price change infarmer’s wheat, %