International Finance: Putting Theory Into Practice

132 CHAPTER 4. UNDERSTANDING FORWARD EXCHANGE RATES FOR CURRENCY

even more marked when we add bid-ask spreads in all markets (next chapter) or
when we study forward forwards or forward rate agreements and their relationship
to forward contracts (Appendix 4.7),^4 or when we explain forward forward swaps
(Chapter 5).

4.3 The Law of One Price and Covered Interest Parity

The sequences of transactions that can be undertaken in the exchange and money
markets, as summarized in Figure 4.2, can be classified into two types.

1. You could do a sequence of transactions that forms a roundtrip. In terms
   of Figure 4.2, a roundtrip means that you start in a particular box, and then
   make four transactions that bring you back to the starting point. For example,
   you may consider the sequenceHCT→HCt→FCt→FCT→HCT. In terms
   of the underlying transactions, this means that you borrowclp, convert the
   proceeds of theclploan intonok, and invest thesenok; the proceeds of the
   investment are then immediately sold forward, back intoclp. The question
   that interests you is whether theclpproceeds of the forward sale are more
   than enough to pay off the originalclploan. If so, you have identified a way
   to make a sure profit without using any of your own capital. Thus, the idea
   behind a round-trip transaction isarbitrage, as defined in Chapter 3.


2. Alternatively, you could consider a sequence of transactions where you end
   up in a box that is not the same as the box from which you start. The two
   examples 4.7 and 4.8 describe such non-round-trip sequences. Trips like that
   have an economic rationale. In the first example, for instance, the investor
   wants to investclp, and the question here is whether the swappednokin-
   vestment (CLPt→NOKt→NOKT →CLPT) yields more than a directclp
   investment (CLPt→CLPT). Using the terminology of Chapter 3, this would
   be an example ofshopping aroundfor the best alternative.

In what follows, we want to establish the following two key results:

1. To rule out arbitrage in perfect markets, the following equality must hold:

Ft,T=St

1 +rt,T

1 +r∗t,T

. (4.7)

[Inimperfect markets, this sharp equality will be watered down to a zone of

admissible values, but the zone is quite narrow.]

(^4) Forward Forwards and forward rate agreements (FRAs) are contracts that fix the interest rate
for a deposit or loan that will be made (say) six months from now, for (say) three months. This can
be viewed as a six-month forward deal on a (then) three-month interest rate. See the Appendix on
forward interest rates.