5.3. USING FORWARD CONTRACTS (2): HEDGING CONTRACTUAL EXPOSURE 179
and the choice of (1 +r∗) has an impact of +0.18 percent. Add all this up (the
effect of compounding these percentages is tiny) and we get the 0.40 percent spread
in the earlier calculations.
In the example, about 0.35 of this 0.40 percent comes from interest spreads. Bid-
ask spreads in money markets fluctuate over time and vary across currencies, but
they rise fast with time to maturity. For example, theWall Street Journal Europe,
January 25, 2005, mentions a Eurodollar spread of just 0.01 %p.a.for 30d and 0.04
%p.a. for 180d, implying effective spreads of less than one-tenth basis points for
30 days and 2 basis points for 180 days. So at the one-month end, interest spreads
for both currencies add little to the spread between the Worst Combinations, but
at 180 days most of that spread already comes from money markets. For currencies
with smaller markets, spot spreads are higher but so are money-market spreads, so
it is hard to come up with a general statement. Still, synthetic spreads do rise fast
with time to maturity.
The widening of the spread between the Worst Combinations does give banks
room to also widen the bid-ask spread on their actual quotes. As we already argued,
there are good economic reasons why equilibrium spreads would go up with the
horizon: markets are thinning, and the compound risk of default and exchange
losses increases.^4 All this, then, explains the Second Law: banks have not only the
room to widen the spreads with time to maturity but also an economic reason to do
so.
This finishes our discussion of arbitrage and the Law of One Price. The second
usage to which forward contracts are put is hedging, as discussed in the next section.
5.3 Using Forward Contracts (2): Hedging Contractual Exposure
Exposure
The issue in this section is how to measure and hedge contractual exposure from a
particular transaction. There is said to be contractual exposure when the firm has
signed contracts that ensure a known in- or outflow offcon a well-defined date.
There are other exposures too, as discussed in Chapter 13; but contractual exposure
is the most obvious type, and most easily hedged.
We describe how to measure the exposure from a single transaction, how to add
up the contractual exposures from different contracts if these contracts mature on
the same date and are denominated in the same currency and how the resulting
(^4) Note that the risk is compound, a risk on a risk. The simple exchange risk under normal
circumstances (i.e. assuming no failure) is hedged by closing out in the forward or, if necessary,
synthetically. Exchange risk pops back up only if there is default and the bank unexpectedly needs
to reverse its earlier hedge.