502 CHAPTER 13. MEASURING EXPOSURE TO EXCHANGE RATES
Thus, operating exposure comes in all kinds of shapes & sizes. How, then, can
one still hedge it? What is the measure of exposure? This depends on the type
of hedge instrument one has in mind. When hedging is done with a linear tool
like a spot or forward position, we have to approximate the (noisy, non-linear—
remember?) relation by a linear one, using regression. If a non-linear hedge is used,
for instance a portfolio of options, things are different. We begin with linear hedges.
13.3.2 The Minimum-Variance Approach to Measuring and Hedg-
ing Operating Exposure
Note from the definition of operating exposure given in Section 3 that exposure tells
us by how much the cash flows of the firm change, for a unit change in the exchange
rate. Adler and Dumas (1983) suggest the use of simulations to compute the eco-
nomic exposure. The simulation requires that we come up with a number of possible
future values for the spot exchange rate and compute the value, in home currency,
of the cash flows for each possible future exchange-rate value. The exposure of the
firm to the exchange rate can then be computed by decomposing thehcvalue of
the asset or cash flow,V ̃T,sin scenarios= 1,...n, into a part linearly related to the
spot rate in that scenario and a part uncorrelated with the spot rate—a technique
commonly called linear regression:
V ̃T,s = At,T+Bt,TS ̃T,s+ ̃t,T,s,
= At,T+ ̃t,T,s
︸ ︷︷ ︸
uncorrelated
withS ̃+ Bt,TS ̃T,s
︸ ︷︷ ︸
exactly linear
inS ̃. (13.3)
IfV ̃ were truly linear inS ̃, we could have used the familiar conditional-expectation
equation, E(V ̃T,s|ST,s) =At,T+Bt,TST, but that is usually not appropriate: the
above is just a linear approximation or linear decomposition or linear projection of
something that is really non-linear. But we need the linear approximation rather
than the true relation because our hedge instrument is linear anyway. We start with
a number of examples where the situation is so simple that the regression can be
done naked-eye, almost. In the first illustration there isn’t even any noise ( ̃):
A Problem with just two Possible Exchange Rates, no Noise
Example 13.7
Belgium’s Android MetaProductsNV/SAwishes to hedge its exposure to the ex-
change rate stemming from its ownership of a marketing affiliate located inuk.
This is 1992, and thegbphas just formally joined theermafter maintaining a con-
stant rate for two years. Still there is risk: what worries Android is that, in the past
few years, inflation has been substantially higher in theukthan on the continent,
raising the question whether the current exchange rate,bef/gbp60, is sustainable.
After discussion with its bankers, Android ends up with two possible outcomes: