13.3. MEASURING AND HEDGING OF OPERATING EXPOSURE 503
Figure 13.4:Android and the PoundBB -655 60
93
99
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Z Z Z Z Z Z Z Z Z Z ZZZ- Theukgovernment may switch to a strongly deflationary policy and stabilize
the exchange rate at 60. Such a deflationary policy is expected to depress sales
and would decrease the net cash flow of the marketing affiliate togbp1.55m. - Alternatively, theukgovernment may let thegbpdepreciate and follow a
moderately deflationary policy. In this case, the exchange rate would bebef
gbp55, and management expects a cash flow ofgbp1.8m.
How can we hedge this? Obviously, as we have an asset denominated in pounds,
the exposure seems bound to be positive—but should we hedge the lower amount,
or the higher one, or something in between? The message below will be that the
above “obvious” diagnosis is totally off the mark: the exposure is nowhere near the
1.55-1.80m range. In fact, it is massively negative. We see this by computing the
two possiblehcvalues:
(no devaluation:) VT = 1. 55 m×60 =bef 93 m,
(devaluation:) VT = 1. 80 m×55 =bef 99 m.This tells us that we win if the pound loses value, which means the exposure is
negative. Figure 13.4 illustrates this. It is quite easy to compute the slope of the
line connecting the two possible outcome points:
slope =93 m− 99 m
60 − 55=
− 6 m
5
=−gbp 1. 2 m. (13.4)This slope is, of course, none other than our exposure,B: if there are just two
possible points, the regression is the line through those two points. We now show
that if Android takes a position in the forward market with the opposite sign—minus
minus 1.2m, that is, buying forward 1.2m—it is hedged. Suppose that the forward
rate is 58. The outcomes are analyzed as follows:
case raw cash flow outcome of hedge hedged cash flow
S=60 93m 1. 2 m×(60−58) = +2. 4 m 93 m+ 2. 4 m=bef 95. 4 m
S=55 99m 1. 2 m×(55−58) =− 3. 6 m 99 m− 3. 6 m=bef 95. 4 m