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)
Arbitrage
ENCYCLOPÆDIA 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 thought
Jan 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 MacCurrencies
Apr 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 nontraded 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 exchangerate 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.