## Putting It All Together

We have developed three relationships, PPP, IRP, and UFR, that describe the interaction between key financial variables such as interest rates, exchange rates, and inflation rates. We now explore the implications of these relationships as a group.

Uncovered Interest Parity To start, it is useful to collect our international financial market relationships in one place:

PPP: E(Si) = S0 X [1 + (hFc - hus)] IRP: Fi = S0 X [1 + (Rfc - Rus)] UFR: F1 = E(S1)

We begin by combining UFR and IRP. Because we know that F1 = E(S1) from the UFR condition, we can substitute E(S1) for F1 in IRP. The result is:

This important relationship is called uncovered interest parity (UIP), and it will play a key role in our international capital budgeting discussion that follows. With t periods, UIP becomes:

The International Fisher Effect Next, we compare PPP and UIP. Both of them have E(S1) on the left-hand side, so their right-hand sides must be equal. We thus have that:

IFE: Ru hu

Rf hF

uncovered interest parity (UIP)

The condition stating that the expected percentage change in the exchange rate is equal to the difference in interest rates.

This tells us that the difference in returns between the United States and a foreign country is just equal to the difference in inflation rates. Rearranging this slightly gives us the international Fisher effect (IFE):

The IFE says that real rates are equal across countries.2

The conclusion that real returns are equal across countries is really basic economics. If real returns were higher in, say, Brazil than in the United States, money would flow out of U.S. financial markets and into Brazilian markets. Asset prices in Brazil would rise and their returns would fall. At the same time, asset prices in the United States would fall and their returns would rise. This process acts to equalize real returns.

Having said all this, we need to note a couple of things. First of all, we really haven't explicitly dealt with risk in our discussion. We might reach a different conclusion about real returns once we do, particularly if people in different countries have different tastes and attitudes towards risk. Second, there are many barriers to the movement of money and capital around the world. Real returns might be different in two different countries for long periods of time if money can't move freely between them.

Despite these problems, we expect that capital markets will become increasingly internationalized. As this occurs, any differences in real rates that do exist will probably diminish. The laws of economics have very little respect for national boundaries.

international Fisher effect (IFE)

The theory that real interest rates are equal across countries.

2Notice that our result here is in terms of the approximate real rate, R — h (see Chapter 7), because we used approximations for PPP and IRP. For the exact result, see Problem 15 at the end of the chapter.

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

VIII. Topics in Corporate Finance

22. International Corporate Finance

© The McGraw-Hill Companies, 2002

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