4.3. THE LAW OF ONE PRICE AND COVERED INTEREST PARITY 137
depends on the sign ofrt,T−rt,T∗ :
[swap rate]t,T def= Ft,T−St,= St[
1 +rt,T
1 +rt,T∗− 1
]
,
= St[
1 +rt,T
1 +rt,T∗−
1 +r∗t,T
1 +r∗t,T]
,
= St[
rt,T−r∗t,T
1 +r∗t,T]
; (4.12)
⇒
∂·
∂St=
[
rt,T−r∗t,T
1 +r∗t,T]
≈rt,T−r∗t,T. (4.13)Thus, a higher domestic return means that the forward rate is at a premium, and
vice versa. To a close approximation (with low foreign interest rates and/or short
maturities), the percentage swap rate even simply is the effective return differential.
To easily remember this, think of the following. If there would be a pronounced
premium, we would tend to believe that this signals an expected appreciation for the
foreign currency.^7 That is, the foreign currency is “strong”. But strong currencies
are also associated with low interest rates: it’s the weak moneys that have to offer
high rates to shore up their current value. In short, a positive forward premium
goes together with a low interest rate because both are traditionally associated with
a strong currency.
A second corollary from theCIPtheorem is that, whenever the spot rate changes,
all forward rates must change in lockstep. In old, pre-computer days, this meant
quite a burden to traders/market makers, who would have to manually recompute
all their forward quotes. Fortunately, traders soon noticed that the swap rate is
relatively insensitive to changes in the spot rate. That is, when you quote a spot
rate and a swap rate, then you make only a small error if you do not change the
swap rate every timeSchanges.
Example 4.9
Let thep.a. simple interest rates be 4 and 3 percent (hcandfc, respectively). If
Stchanges from 100 to 100.5—a huge change—the theoretical one-month forward
changes too, and so does the swap rate, but the latter effect is minute:
(^7) Empirically, the strength of a currency is predicted by the swap rate only in the case of pro-
nounced premia. When interest are quite similar and expectations rather diffuse, as is typically the
case among OECD mainstream countries, the effects risk premia and transaction costs appear to
swamp any expectation effect. See Chapter 10.