Parity Conditions

International Corporate Finance

P.V. Viswanath

P.V. Viswanath 2

Learning Objectives

Law of One Price How arbitrage links good prices and asset returns Relations between spot and forward exchange rates,

inflation rates and interest rates Difference between real and nominal exchange

rates

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Arbitrage

Law of One Price – in competitive markets with many buyers and sellers with low-cost access to information, exchange-adjusted prices of identical tradable goods and financial assets must be within transaction costs worldwide.

Risk-adjusted expected returns on financial assets in different markets should be equal.

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Shapiro/Multinational Financial Management, 7e

Effects of Arbitrage

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Effects of Differential Inflation

If inflation in Mexico is expected to exceed inflation in the US by 3% for the coming year, then The Mexican peso should decline in value by about 3%

relative to the dollar (Purchasing Power Parity) The one-year forward Mexican peso should sell at a 3%

discount relative to the US dollar. (Forward Market Efficiency)

One-year interest rates should be higher in Mexico relative to the US by about 3% (Fisher Effect)

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Money Supply and Inflation

As the supply of one good increases relative to supplies of other goods, the price of the first good declines relative to the prices of other goods.

Similarly, if the supply of dollars increases relative to the amount individuals wish to hold, they will increase their spending on goods, services and securities, causing US goods prices to rise.

Thus, as the US money supply expands, the purchasing power of US dollars – the exchange rate between dollars and goods – declines, i.e. there is inflation in the US.

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Domestic inflation and exchange rates

In the same manner, as the supply of the US dollar exceeds the quantity of dollars that investors wish to hold relative to other currencies, investors move to reduce their relative holdings of the dollar. They will do this, in part, by buying foreign goods, thus increasing demand for the foreign currency.

They may also simply seek to directly exchange dollars for foreign currencies.

This will cause the value of the dollar to depreciate relative to other currencies.

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Purchasing Power Parity

Individuals can buy goods domestically or abroad. If there is to be no international arbitrage, then the exchange

rate between the home currency and domestic goods must equal the exchange rate between the home currency and foreign goods.

For this to happen, the foreign exchange rate must change by approximately the difference between the domestic and foreign rates of inflation.

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Shapiro/Multinational Financial Management, 7e

Purchasing Power Parity

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Shapiro/Multinational Financial Management, 7e

Purchasing Power Parity

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Monetary Approach to PPP

M = money supply; P = price level; y = real GNP; v = money velocity.

i = inflation rate; growth rate of money supply; gy = growth rate of real GNP; gv = change in velocity of money

Combining with PPP, we get:

PyMV

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Fisher Effect

The nominal interest rate determines the exchange rate between current and future dollars.

However, individuals are not interested in dollars per se. They are more interested in what they can purchase with dollars. In other words, they are interested in the inflation-adjusted or real interest rate.

Hence, if the value of a nominal dollar is expected to decrease over time, the equilibrium nominal rate of interest has to adjust for the inflation in order to keep the real interest rate where market participants want it to be.

Consequently, if rates of inflation vary across countries, their nominal interest rates also have to vary accordingly, in order to keep real interest rates constant across countries.

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Fisher Effect

(1+nominal rate) = (1+real rate)(1+expected inflation rate)

Or approximately, r = a + i, where

r = nominal rate, a = real rate and i = expected inflation rate

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Shapiro/Multinational Financial Management, 7e

Fisher Effect: Empirical Evidence

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Capital Market Integration

The international Fisher effect assumes that real interest rates are equalized across countries.

However, that will only happen if people are allowed to move capital freely across countries.

If capital markets in different countries are segregated, then real interest in different countries might very well differ.

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Shapiro/Multinational Financial Management, 7e

Capital Market Integration

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International Fisher Effect (IFE)

If we combine the Fisher effect and Purchasing Power Parity, we get the International Fisher effect.

The Fisher effect equates inflation rate differentials to interest rate differentials. PPP equates inflation rates to changes in exchange rates.

The International Fisher effect equates changes in exchange rates to interest rate differentials.

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International Fisher Effect

The IFE says that the interest rate differential between two countries is an unbiased predictor of the future change in the spot rate of exchange.

An implicit assumption of the IFE is that investors view foreign and domestic assets as perfect substitutes.

However, investors may require a risk premium in the form of a higher expected real return to hold foreign assets; if so, the IFE will not hold exactly.

Furthermore, the Fisher effect, itself, need not hold exactly, since investors may require a risk premium to bear inflation risk.

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Interest Rate Parity (IRP)

According to IRP, the currency of the country with a lower interest rate should be at a forward premium in terms of the currency of the country with the higher rate. The interest differential should equal the forward premium.

IRP ensures that the return on a hedged foreign investment will just equal the domestic interest rate on investments of identical risk.

If f1 = forward exchange rate for delivery at time 1, the forward

premium = .

We can write IRP as or, approx.,f

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Forward Rate Unbiasedness

The forward rate is greatly influenced by current expectations of future movements in exchange rates.

The Unbiased Forward Rate (UFR) hypothesis holds that the forward rate equals the expected future spot rate on the date of settlement of the forward contract:

However, risk averse investors might require a risk premium on forward contracts. If so, the UFR hypothesis will not hold. However, it is argued that exchange rate risk should be diversifiable, and hence the UFR should hold.

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