Purchasing Power Parity and the Fisher Effect

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International Parity Relationships and Forecasting Foreign Exchange Rates

Chapter Six

Chapter Outline

Interest Rate Parity

Covered Interest Arbitrage

IRP and Exchange Rate Determination

Currency Carry Trade

Reasons for Deviations from IRP

Purchasing Power Parity

PPP Deviations and the Real Exchange Rate

Evidence on Purchasing Power Parity

Fisher Effects

Forecasting Exchange Rates

Efficient Market Approach

Fundamental Approach

Technical Approach

Performance of the Forecasters

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Law of one price (LOP)

Requirement that similar commodities or securities should be trading at the same or similar prices

Prevails when the same or equivalent things are trading at the same price across different locations or markets, precluding profitable arbitrage opportunities

Arbitrage equilibrium

Arbitrage is the act of simultaneously buying and selling the same or equivalent assets or commodities for the purpose of making certain, guaranteed profits

International Parity Relationships

6-3

Interest rate parity (IRP) is an arbitrage condition that must hold when international financial markets are in equilibrium

Manifestation of the LOP applied to international money market instruments and provides a linkage between interest rates in two different countries

Interest Rate Parity Defined

6-4

Suppose you have $1 to invest over a one-year period, and you will only consider default-free investments.

There are two alternative ways on investing your fund:

Invest domestically at the U.S. interest rate

If you choose this option, the maturity value in one year will be $1(1 + is), where is is the U.S. interest rate

Interest Rate Parity - Example

6-5

Suppose you have $1 to invest over a one-year period. There are two alternative ways on investing your fund:

Invest in a foreign country, say, the U.K., at the foreign interest rate and hedge the exchange risk by selling the maturity value of the foreign investment forward. This option requires the following steps:

Exchange $1 for a pound, that is, £(1/S) amount at the prevailing spot exchange rate (S)

Invest the pound amount at the U.K. interest rate (i£), with the maturity value of £(1/S)(1+i£)

Sell the maturity value of the U.K. investment forward in exchange for a predetermined dollar amount, that is, $[(1/S)(1+i£)]F, where F denotes the forward exchange rate

Interest Rate Parity – Example (Continued)

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Interest Rate Parity: Equivalent Investments

Effective dollar interest rate from the U.K. investment alternative is given by:

U.S. and U.K. investment examples are equivalent

Future dollar proceeds from investing in the two equivalent investments must be the same, implying the following:

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Arbitrage

IRP can be derived by constructing an arbitrage portfolio, which involves the following:

No net investment

No risk

No net cash flow generated in equilibrium

When IRP does not hold, the situation gives rise to covered interest arbitrage opportunities, allowing certain arbitrage profits to be made without the arbitrageur investing any money out of pocket or bearing any risk

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IRP and Exchange Rate Determination

Reformulating the IRP relationship in terms of the spot exchange rate yields:

Forward exchange rate can be viewed as the expected future spot exchange rate conditional on all relevant information being available

Combining the two equations yields the following:

6-9

St+1 is the future spot rate when the forward contract matures

It denotes the set of information currently available

IRP and Exchange Rate Determination Continued

Two things are noteworthy from the following equation (presented on previous slide):

“Expectation” plays a key role in exchange rate determination (i.e., when people “expect” the exchange rate to go up in the future, it goes up now)

Exchange rate behavior will be driven by news events

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Uncovered Interest Rate Parity

When the forward exchange rate F is replaced by the expected future spot exchange rate, E(St+1), we obtain:

Uncovered interest rate parity

Interest rate differential between a pair of countries is (approximately) equal to the expected rate of change in the exchange rate

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E(e) is the expected rate of change in the exchange rate

Currency Carry Trade

Unlike IRP, the uncovered interest rate parity often does not hold, giving rise to uncovered interest arbitrage opportunities

Currency carry trade involves buying a high-yielding currency and funding it with a low-yielding currency, without any hedging

The carry trade is profitable if the interest rate differential is greater than the appreciation of the funding currency against the investment currency

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Since the interest rate in Japan has been near zero since the mid-1990s, the yen has been the most popular funding currency for carry trade, followed by the Swiss franc.

EXHIBIT 6.3 Interest Rate Spreads and Exchange Rate Changes: Six-Month Carry Trade Periods for Australian Dollar–Japanese Yen Pair

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Note: For interest rates, interbank six-month rates are used for both countries. The interest rate spread and the rate of change in the exchange rate are plotted at the beginning of each six-month carry period.

Source: Interest rates and exchange rates are obtained from Datastream.

Reasons for Deviations from IRP

IRP holds quite well, but it may not hold precisely all the time due to (primarily) two main reasons:

Transaction costs

Interest rate at which the arbitrager borrows tends to be higher than the rate at which he lends, reflecting the bid-ask spread

There exist bid-ask spreads in the foreign exchange market as well, as the arbitrager must buy currencies at the higher ask price and sell at the lower bid price

Capital controls

Governments sometimes restrict capital flows, inbound and/or outbound via jawboning, imposing taxes, or outright bans

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EXHIBIT 6.4 Interest Rate Parity with Transaction Costs

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EXHIBIT 6.5: Deviations from Interest Rate Parity: Japan, 1978-1981 (in percent)

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Note: Daily data were used in computing the deviations. The zone bounded by +0.339 and −0.339 represents the average width of the band around the IRP for the sample period.

Source: Otani, I., and S. Tiwari. (1981). “Capital Controls and Interest Rate Parity: The Japanese Experience, 1978–81,” IMF Staff Papers 28: pp. 793−816.

Purchasing Power Parity

When the law of one price is applied international to a standard consumption basket, we obtain the theory of purchasing power parity (PPP)

PPP states the exchange rate between currencies of two countries should be equal to the ratio of the countries’ price levels of a commodity basket

Let P$ be the dollar price of the standard consumption basket in the U.S. and P£ the pound price of the same basket in the U.K.

Absolute version of PPP states the exchange rate between the dollar and pound should be:

6-17

S is the dollar price of one pound.

Purchasing Power Parity Continued

When the PPP relationship is presented in the “rate of change” form, instead of price level as in the absolute version of PPP, we obtain the relative version of PPP:

Where:

e is the rate of change in the exchange rate

π$ and π£ are the inflation rates in the United States and U.K., respectively

6-18

e is the rate of change in the exchange rate

π$ and π£ are the inflation rates in the United States and U.K., respectively

PPP Deviations and the Real Exchange Rate

If there are deviations from PPP, changes in nominal exchange rates cause changes in the real exchange rates, affecting the international competitive positions of countries

Real exchange rate, q, is found by:

If PPP holds, the real exchange rate will be unity (i.e., q = 1), but when PPP is violated, the real exchange rate will deviate from unity

6-19

Evidence on PPP

PPP has been the subject of a series of tests, yielding generally negative results, especially over short horizons

Generally unfavorable evidence about PPP suggests that substantial barriers to international commodity arbitrage exist

As long as there are nontradables (e.g., haircuts, housing, etc.), PPP will not hold in its absolute version

If PPP holds for tradables and the relative prices between tradables and nontradables are maintained, then PPP can hold in its relative version

6-20

Fisher Effects

The Fisher effect holds that an increase (decrease) in the expected inflation rate in a country will cause a proportionate increase (decrease) in the interest rate in the country

Formally, the Fisher effect is written as follows:

Fisher effect implies that the expected inflation rate is the different between the nominal and real interest rates in each country, that is,

6-21

ρ$ denotes the equilibrium expected “real” interest rate in the United States

Fisher Effects Continued

If we assume the real interest rate is the same between countries, that is, ρ$ = ρ£, we obtain the international Fisher effect (IFE), which suggests the nominal interest rate differential reflects the expected change in exchange rate

When the international Fisher effect is combined with IRP, we obtain the forward expectations parity (FEP), which states any forward premium or discount is equal to the expected change in the exchange rate

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EXHIBIT 6.9: International Parity Relationships among Exchange Rates, Interest Rates, and Inflation Rates

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Notes:

1. With the assumption of the same real interest rate, the Fisher effect (FE) implies that the interest rate differential is equal to the expected inflation rate differential.

2. If both purchasing power parity (PPP) and forward expectations parity (FEP) hold, then the forward exchange premium or discount will be equal to the expected inflation rate differential. The latter relationship is denoted by the forward-PPP, i.e., FPPP in the exhibit.

3. IFE stands for the international Fisher effect.

Forecasting Exchange Rates

Many business decisions are now made based on forecasts, implicit or explicit, of future exchange rates

Forecasting techniques can be classified into three distinct approaches:

Efficient market approach

Fundamental approach

Technical approach

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Efficient Market Approach

Efficient market hypothesis (EMH) states that financial markets are informationally efficient in that the current asset prices reflect all the relevant and available information

Implies that the exchange rate will change only when the market receives new information

Random walk hypothesis suggests today’s exchange rate is the best predictor of tomorrow’s exchange rate

To the extent that interest rates are different between two countries, the forward exchange rate will be different from the current spot exchange rate

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Fundamental Approach

Uses various models to forecast exchange rates

Three main difficulties of this approach:

One must forecast a set of independent variables to forecast the exchange rates, and forecasting the former will certainly be subject to errors and may not be necessarily easier than forecasting the latter

Parameter values that are estimated using historical data may change over time because of changes in government policies and/or the underlying structure of the economy

Model itself can be wrong

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Technical Approach

First analyzes the past behavior of exchange rates for the purpose of identifying “patterns” and then projects them into the future to generate forecasts

Based on the premise that history repeats itself

At odds with the efficient market approach

Differs from fundamental approach in that it does not use the key economic variables, like money supplies or trade balances, for purpose of forecasting

Two examples of technical analysis:

Moving average crossover rule

Head-and-shoulders pattern

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EXHIBIT 6.10: Moving Average Crossover Rule: Golden Cross vs. Death Cross

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EXHIBIT 6.11: Head-and-Shoulders Pattern: A Reversal Signal

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Performance of the Forecasters

Can professional forecasters outperform the market?

Eun and Sabherwal (2002) study found that banks as a whole could not outperform the random walk model, but some banks significantly outperformed the random walk model, especially in the longer run

Beckmann and Czudaj (2017) suggest professionals have a hard time predicting exchange rates, and uncertainty regarding economic policy and macroeconomic and financial conditions significantly affects professionals’ forecast errors

Purchasing Power Parity and the Fisher Effect

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