Parity conditions in International Finance

A summary

Predicting Exchange Rates

International Parity Approach: use arbitrage arguments.

Fundamental Approach: use macro models

Technical Approach: use time series

Objective

Learn how to predict foreign exchange rates using arbitrage arguments

Outline

• On arbitrage and speculation

• Purchasing Power Parity (PPP)

• The International Fisher Effect (IFE)

• Interest Rate Parity (IRP)

ArbitrageENCYCLOPÆDIA BRITANNICA

Business operation involving the purchase of foreign exchange, gold, financial securities, or commodities in one market and their almost simultaneous sale in another market, in order to profit from price differentials existing between the markets.

Arbitrage generally tends to eliminate price differentials between markets.

Mind the distinction

Arbitrage: attempt at exploiting short-term market inconsistencies in order to extract risk-free profits

Speculation: betting that the market will go up or down in the short-term. Speculators take on tremendous risks.

Whenever there is high risk involved, arbitrage becomes speculation

Arbitrage in the foreign exchange market

Uncovered (Speculation)

Covered (True arbitrage)

Example of uncovered arbitrage

i(us) = 5%

i(uk) = 8%

s = $1.5

• Borrow in $ at 5%• Buy pounds and lend at 8%• At maturity exchange back pounds for $• Hope that you’ll have enough to repay the loan and

make an arbitrage profit

Example of covered arbitrage

i(us) = 5%

i(uk) = 8%

s = $1.5

f = $1.48

• Borrow in $ at 5%• Buy pounds and lend at 8%• At maturity exchange back pounds for $

• Repay the loan and make an arbitrage profit

Purchasing Power Parity

Absolute PPP

Goods and services should cost the same regardless of the country

Relative PPP

The exchange rate is expected to adjust in order to reflect expected relative differences in purchasing power.

PPP: Background

The basis for PPP is the "law of one price".

Competitive markets will equalize the price of an identical good in two countries (expressed in the same

currency).

Exemplification

A particular DVD player sells for:

C$ 700 in Sherbrooke

US$ 500 in Burlington

Exchange rate: US$ 1.50/C$.

Consequences

Consumers in Burlington would prefer buying it in Sherbrooke.

Result:

The DVD player price in Sherbrooke should increase to C$750

Caveats

(1) Transportation costs, barriers to trade, and other can make a difference.

(2) There must be competitive markets for the goods and services in question in both countries.

(3) The law of one price only applies to tradable goods.

PPP: Implications

When a country's domestic price level is increasing (inflation), the exchange rate must depreciated in order to return to PPP.

Relative PPP: Calculation

E(st)/s0 = (1+inflationh)t/(1+inflationf)t

when t=1

E(s1)/s0 = (1+inflationh)/(1+inflationf)

The Big Mac Index

Food for thoughtJan 7th 1999

From The Economist print edition For more than a decade, The Economist’s Big Mac index has offered a light-hearted guide to whether currencies are at their “correct” level.

It is based on the theory of purchasing-power parity (PPP)—the notion that a basket of goods and services should cost the same in all countries.

Thus if the price of a Big Mac is lower in one country than in America, this suggests that its currency is undervalued relative to the dollar and vice versa.

The price of a Big Mac varies in the euro area, from euro3.36 in Finland to a bargain euro2.19 in Portugal. The weighted average price in the 11 countries is euro2.53, or $2.98 at current exchange rates.

In America a Big Mac costs only $2.63 (taking the average of three cities).

So the Euro is 13% overvalued against the dollar.

Big MacCurrenciesApr 27th 2000

From The Economist print edition Some people read tea leaves to predict the future. We prefer hamburgers

Some readers beef that our Big Mac index does not cut the mustard. They are right that hamburgers are a flawed measure of PPP, because local prices may be distorted by trade barriers on beef, sales taxes or big differences in the cost of non-traded inputs such as rents. Thus, whereas Big Mac PPPs can be a handy guide to the cost of living in countries, they may not be a reliable guide to future exchange-rate movements. Yet, curiously, several academic studies have concluded that the Big Mac index is surprisingly accurate in tracking exchange rates over the longer term.

Indeed, the Big Mac has had several forecasting successes. When the euro was launched at the start of 1999, most forecasters predicted that it would rise. But the euro has instead tumbled—exactly as the Big Mac index had signaled. At the start of 1999, euro burgers were much dearer than American ones. Burgernomics is far from perfect, but our mouths are where our money is.

The Fisher Effect

The Simple Fisher Effect

The International Fisher Effect

The Fisher Effect

Simple Fisher Effect:

Nominal interest rates equal real interest rates plus inflation premium:

(1+ni) = (1+ ri)(1+inflation)

ni = ri + inflation + (ri)(inflation),

When (ri)(inflation) is a very small number:

ni = ri + inflation

International Fisher Effect (IFE)

The exchange is expected to change in order to reflect expected relative differences in nominal interest rates.

IFE assumes differences in nominal interest rates are driven by expected relative differences in inflation.

E(st)/s0 = (1+nih)t/(1+nif)t

E(s1)/s0 = (1+nih)/(1+nif), when t=1

Interest Rate Parity (IRP)

The forward exchange rate reflects expected relative differences in nominal interest rates.

IRP also assumes differences in nominal interest rates are driven by expected relative differences in inflation.

ft/s0 = (1+nih)t/(1+nif)t

f1/s0 = (1+nih)/(1+nif), when t=1

What is the relationship between forward and future

expected exchange rates?

Some believe f = E(s)

Some believe f = E(s) + risk premium

Summary

The Law of One Price - the arbitrage argument - says that goods and services should be worth the same when compared across borders

An increase in inflation and the resulting increase in the nominal interest rate should cause the domestic currency to depreciate.

And vice-versa.