4.3. THE LAW OF ONE PRICE AND COVERED INTEREST PARITY 133
Figure 4.3:Spot/Forward/Money Market Diagram: Arbitrage Computa-
tions
121,000 1100
100.000 1000
× 1.^121 ×1.21
HCmoney market× 1.^110 ×1.10FCmoney market× 110
× 1 / 110
forward market× 100
× 1 / 100
spot market?6 6?- If equation (4.7) holds, shopping-around computations are a waste of time
since the two routes that lead from a given initial position A to a desired end
position B produce exactly the same. Stated positively, shopping around can
(and will) be useful only because of imperfections.
4.3.1 Arbitrage and Covered Interest Parity
In this section, we use an arbitrage argument to verify equation (4.7), a relationship
called theCovered Interest Parity(CIP) Theorem. The theorem is evidently satisfied
in our example:
110 =Ft,T=St1 +rt,T
1 +r∗t,T= 100
1. 21
1. 10
= 110. (4.8)
Arbitrage, we know, means full-circle roundtrips through the diagram. There are
two ways to go around the entire diagram: clockwise, and counterclockwise. Follow
the trips on Figure 4.3, where the symbols for amounts have been replaced by the
specific numbers used in the numerical examples. We should not make any profit if
the rate is 110, and we should make free money as soon as the rate does deviate.
Clockwise roundtripThe starting point of a roundtrip is evidently immaterial,
but let’s commence with ahcloan: this makes it eminently clear that no own capital
is being used. Also the starting amount is immaterial, so let’s pick an amount that
produces conveniently round numbers all around: we write apnwith face value