4.3. THE LAW OF ONE PRICE AND COVERED INTEREST PARITY 135
This produces an inequality constraint,Ft,T ≤ St1+1+rrt,T∗
t,T
.Write the no-arbitrage-
profit condition for the counterclockwise trip and express it as another inequality
constraint. Lastly, deriveCIP.
4.3.2 Shopping Around (The Pointlessness of —)
The diagram in Figure 4.2 also tells us that any non-round-trip sequence of trans-
actions can be routed two ways. For instance, you can go directly fromCLPtto
CLPT, or you can go viaNOKtandNOKT. In two earlier examples, 4.7 and 4.8, we
already illustrated our claim that, in perfect markets whereCIPholds, both ways to
implement a trip produce exactly the same outcome. It is simple to show that this
holds for all of the ten other possible trips one could think of, in this diagram; but
it would also be so tedious that we leave this as an exercise to any non-believer in
the audience. It would also be a bit pointless, because in reality shopping around
does matter. As we show in the next chapter, the route you choose for your trip
may matter because of imperfections like bid-ask spreads, taxes (if asymmetric),
information costs (if leading to inconsistent risk spreads asked by home and foreign
banks), and legal subtleties associated with swaps.
4.3.3 Unfrequently Asked Questions onCIP
Before we move on to new challenges like the market value of a forward contract
and the relation of the forward rate with expected future spot rates, a few crucial
comments are in order. We first talk about causality, then about why pros always
quote the swap rate rather than the outright, and lastly about taxes.
Covered Interest Parity and Causality
As we have seen, in perfect markets the forward rate is linked to the spot rate by
pure arbitrage. Such an arbitrage argument, however, does not imply any causality.
CIPis merely an application of the Law of One Price, and the statement that two
perfect substitutes should have the same price does not tell us where that “one
price” comes from. Stated differently, showingFt,T as the left-hand-side variable
(as we did in Equation [4.7]), does not imply that the forward rate is a “dependent”
variable, determined by the spot rate and the two interest rates. Rather, what
Covered Interest Parity says is that the four variables (the spot rate, the forward
rate, and the two interest rates) are determined jointly, and that the equilibrium
outcome should satisfy Equation [4.7]. The fact that the spot market represents less
than 50 percent of the total turnover likewise suggests that the forward market is
not just an appendage to the spot market. Thus, it is impossible to say, either in
theory or in practice, which is the tail and which is the dog, here.