492 CHAPTER 13. MEASURING EXPOSURE TO EXCHANGE RATES
13.1 The Concepts of Risk and Exposure: a brief survey
In general, we need to distinguish between the terms exchange risk and exchange
exposure. (Some people use them interchangeably, which is not a good idea.)
- Risk We interpretexchange riskas synonymous with uncertainty about the
future spot rate. Possible measures of exchange risk include the standard
deviation or the variance of the future spot rate change. - Exposure A firm is said to beexposedto exchange risk if its financial position
is affected by unexpected exchange rate changes. A large exposure means that
a given exchange rate change has a large impact on the firm. That is, by
exposurewe mean a numerical measure of how sensitive the financial position
of a firm is to changes in the exchange rate.
This concept was already used in Chapter 5, where we generally defined exposure
as a number that tells us by what multiple thehcvalue of an asset or cash flow
changes when the exchange rate moves by ∆S, everything else being the same. We
denoted this multiple byBt,T:
Bt,T=∆V ̃T
∆S ̃T
. (13.1)
Note again theTsubscripts toV andS: we have in mind values atT, so the delta’s
must mean that we compare two possible situations at the same (future) momentT,
not two observations made at different moments in time. (We’re so wont to interpret
∆ as a change over time that explicit notation is in order, here.) Another way of
saying this is that we have in mind a kind ofpartialderivative w.r.t. the exchange
rate, holding constant other items (including time). We used this concept to price
and hedge options (Chapter 9).
The above definition assumes thatV ̃Tis an exact function ofS ̃T. If the relation is
known only up to noise or is otherwise imperfect—for instance because we willingly
ignore non-linearities in the relation—a related concept of exposure crops up: the
variance-minimizing hedge instead of the exact, perfect hedge. We looked at the
variance-minimizing hedge already, notably in Chapter 6 on futures, and we’ll use it
again in this chapter. Recall that this hedge ratio is similar to the above exposure:
a regression coefficient measures the sensitivity ofV ̃T toS ̃T, holding constant the
regression residuals (which is “everything else”, in a regression). So in that sense the
general partial-derivative definition also covers the regression hedge-ratio measure
of exposure.
We already showed thatB has the dimension of a number offcunits. But
what is meant byV ̃T? In the literature one typically lists three alternative possible
specifications of what could be covered by this symbol:
- Contractual exposure In the case of contractual exposure,V ̃Tis defined
as thehcvalue, at maturity, of a net contractual cash flow denominated in a