Expectations, Money and
Determination of the Exchange Rate
IMQF course in International Finance
Caves, Frankel and Jones (2007) World Trade and Payments, 10e, Pearson
Introduction
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Determination of exchange rate in interantional financial markets: no transaction costs and capital
controls, no other barriers
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Portofolio investors’ decision is driven by:
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the interest rates, and
expectations about future changes in the exchange rates
Outline
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Interest rate parity conditions
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Monetary Model of Exchange Rates with Flexible Prices
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The exchange rate and price of money
Expectations of money growth
Hyperinflation
When money supply follows the random walk
When money supply is expected to rise in the future
Interest Rate Parity Condition
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Depreciation of USD to Yen to be substracted from return Japanese investors will make by investing in
the US assets, and the other way around
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Investors will keep buying and selling assets until the expected returns are equalized across countries
(arbitrage condition)
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i.e. expected rate of depreciation to equal nominal interest differential – uncovered interest parity
i  i*  s e
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Investors buying foreing asset with high rate of return expose themselves to the risk of loss of earnings
due to foreign currency depreciation
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It will hold if investors treat domestic and foreign currency as perfect substitutes, i.e. if FX risk is not important or if
investors are risk neutral
Uncovered interest parity does not suggest causality, i.e. it does not describe determination of interest
rates
Monetary Model of Exchange Rates
with Flexible Prices
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Two sets of assumptions:
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No transaction costs, capital controls and other barrers
Different countries’ bonds can be aggregated together, as long as they all pay the same expected rate of return
(perfect substitutes)
Recall PPP assimption:
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S
P
P*
S being the level of exchange rate
Exchange rate determined by relative prices in home and foreign country?
Monetary Model of Exchange Rates
with Flexible Prices
THE EXCHANGE RATE AND PRICE OF MONEY
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Real money supply equal to the real money demand
M / P  L(i, Y )
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Solving for P:
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Demand for money decreases in i, as people want to hold assets earning higher yields, and increases in Y, as the
demand for transaction money is rising as income is rising
P  M / L(i, Y )
Prices are determined so as to make money supply equal to money demand
Supply and demand for money in a foreign country
P*  M * / L * (i*, Y *)
Monetary Model of Exchange Rates
with Flexible Prices
THE EXCHANGE RATE AND PRICE OF MONEY
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Therefore, the exchange rate is:
S
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M / L(i, Y )
M /M *
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M * / L * (i*, Y *) L(i, Y ) / L * (i*, Y *)
S is price of foreign currency in terms of domestic currency
Rise in foreign supply of money (M*), triggers decline in price of foreign money, i.e. exchange rate (appreciation)
Rise in demand for foreign currency (L*) has the opposite effect (depreciation)
Rise in domestic money supply (M), causes increase in the exchange rate (depreciation)
Rise in domestic money demand (L), causes a decrease in the exchange rate (appreciation)
Exchange rate is directly proportionate to M and indirectly proportionate to M*
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When M rises by 10% relative to M*, prices go up by 10%, so th exchange rate goes up by 10%
Homogeneity of nominal variables
Monetary Model of Exchange Rates
with Flexible Prices
THE EXCHANGE RATE AND PRICE OF MONEY
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Demand for money is proportionate to real incomes and depends also on the interest rates differential:
S
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M /M *
 (i  i*)
Y /Y *
Increase in domestic real income, drives up demand for money, triggering fall in FX rate (appreciation)
Interest rate differential causes FX rate to depreciate
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Quite different to what suggested by the Mundell-Fleming model – MF model would suggest that rise in
income triggers trade deficit and depreciation, while positive i.r. differential triggers capital inflow and
appreciation
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Why is the impact on FX now different?
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Due to price flexibility: perfectly flexible prices imply that output is at potential level, so rise in income is actually rise in
potential output, i.e. it is not consequence of demand shock, but rather the consequence of supply-side factors (e.g.
improvement of national efficiency) – rise in income due to such reasons is sign of strength of the economy, triggering
appreciation of local currency (e.g. Yen in 1970s and 1980s)
Monetary Model of Exchange Rates
with Flexible Prices
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Interest rate effects: Rewrite interest rate differential as uncovered interest parity
S
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M /M *
 (s e )
Y /Y *
Increase in expected rate of depreciation will encourage investors to shift their portfolios out of the domestic
currency, triggering depreciation
Therefore, change in depreciation expectations may have an immediate impact on FX rate
PPP can be expressed in terms of the rates change:
S  p  p *
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Change in FX rate should reflect the differential in inflation rate in domestic and foreign country, in order to prevent the
country’s goods to be overpriced or underpriced in world markets
In that case, investors form their expectations accordingly:
s e  p e  p *e
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…or expressing in interest rate terms (real interest parity)
i  p e  i * p *e
Monetary Model of Exchange Rates
with Flexible Prices
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Now, the exchange rate can be stated as a function of inflation expectations:
S
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M /M *
 (p e  p *e )
Y /Y *
Intuition: if currency is expected to lose future value (i.e. inflation is to be high), investors will strive to shift out of that
currency, causing depreciation
Sudden increase in expected future inflation (eg. appointment of new more expansionary head of central bank)
causes immediate depreciation of the currency
Monetary Model of Exchange Rates
with Flexible Prices
EXPECTATIONS OF MONEY GROWTH
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What determines the expected inflation rate?
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Money supply set exogeneously by the central bank is the main driver
Inflation is in steady state (non-zero and incorporated in interest rate and expectations)
M / P  L(i, Y )
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It follows that given increase in prices presupposes money growth of the same magnitude. If money growth is determined
by the central bank, interest rate adjusts accordingly
If money growth is not fully reflected in the inflation rate, real money supply is rising – LM curve shifts to the right and real
income is rising
To have a steady state, ratio of money supply and prices needs to be constant
What is the impact of money growth (e.g. by 1%) on the exchange rate?
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Inflation rate goes up by 1%, expected depreciation and interest rates are rising by 1% -- demand for currency falls –
causing fall in price of currency (depreciation) instantaneously (FX rate jumps although money supply does not jump
descretely, but rather only its growth rate is increasing)
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Percent change in FX rate can be greater than percent change in money supply, if the money supply is thought to signal a
permanent change in money growth rate
Changes in Money Supply and
Equilibrium Exchange Rate
Monetary Model of Exchange Rates
with Flexible Prices
HYPERINFLATION
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Inflation rate od 29,586 percent per month in Germany (October 1923), depreciation of DEM by 29,957
per month – the real exchange rate had reached a steady state
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However, inflation rate rose considerably faster than the money supply, so real money supply declined to
0.15 of the initial real money supply
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The worse the hyperinflation, the more extreme fall in real money holdings (real demand for money
negatively related to the rate at which it is expected to lose value)
Real Money Holdings in Great Hyperinflations of the
Twentieth Century
Monetary Model of Exchange Rates
with Flexible Prices
WHEN THE MONEY SUPPLY FOLLOWS A RANDOM WALK
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What if money supply growth is a random walk?
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Money supply can go up and down, so the best guess is to expect a zero change in money supply, which means that
expected inflation rate differential, expected depreciation and interest rate differential are zero
1 percent increase in money supply, changes prices and FX rate by 1%, but has no further effects
WHEN THE MONEY IS EXPECTED TO JUMP IN THE FUTURE
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What if politcal party with expansionary policy comes into power? Money supply is to rise in the next four
years
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Forward looking expectations, i.e. rational expectations will enter into motion – using all available information,
investors will adjust their portfolios, which will have a depreciation effects on FX rate
Even if the money supply is to increase in 4 years (just before the next elections), it will make FX rate depreciating
today
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If money supply is to increase in 4 years, investors would shift out of domestic currency in 3 years to avoid capital losses –
it will make the currency deprecating in 3 years – to avoid capital losses they will shift out from the local currency in 2
years…and so on…so at the of the adjustment process, currency will depreciate today
The effects on today’s FX rate are smaller the further into the future is the expected increase in money supply