Understanding Exchange Rates: A Comprehensive Guide

Posted on Aug 15, 2024 in Economy

Exchange Rate

The exchange rate is the price of one currency expressed in another currency. Exchange rates are crucial in international trade, enabling comparisons of goods and services prices across different countries.

Changes in Exchange Rates

Fluctuations in exchange rates are categorized as depreciations or appreciations.

• Appreciation: An appreciation of a country’s currency makes its goods more expensive for foreigners, all else being equal.
• Depreciation: A depreciation of a country’s currency makes its goods cheaper for foreigners, all else being equal.

Factors Influencing Exchange Rates

Today’s exchange rate between two currencies is influenced by expectations about the future values of assets denominated in those currencies. These expectations are shaped by various factors, including:

• Inflation
• Business cycle
• Current account
• Changes in interest rates

The Foreign Exchange Market

The foreign exchange market is where international currency trading occurs. Participants include banks, financial institutions, firms, individuals, and central banks. Exchange rates are determined by the forces of supply and demand.

Demand for Foreign Currency Assets

The demand for assets denominated in foreign currencies is influenced by:

• Expected Return: The percentage difference between the expected future value of the asset and its price today.
• Risk: The variability an asset adds to a saver’s wealth.
• Liquidity: The ease with which an asset can be sold or exchanged for goods.

Comparing Returns on Deposits

To compare returns on deposits in different currencies, two key pieces of information are needed:

1. Interest Rate: The amount of interest earned by lending one unit of currency for a year.
2. Expected Change in Exchange Rate: This allows for the translation of returns measured in different currencies into comparable terms.

Calculating Dollar Return on Euro Deposits

A simplified rule can be used to calculate the dollar return on euro deposits. First, define the rate of depreciation of the dollar against the euro as the percentage increase in the dollar/euro exchange rate over a year. Then, apply the following rule:

The dollar rate of return on euro deposits is approximately the euro interest rate plus the rate of depreciation of the dollar against the euro.

Mathematically:

R_$/Euro = R_Euro + (E^e_$/Euro – E_$/Euro) / E_$/Euro

Interest Rate Parity

The foreign exchange market is in equilibrium when deposits of all currencies offer the same expected rate of return (when measured in the same currency). This condition is known as interest rate parity.

Mathematically:

R_$/Euro = R_Euro + (E^e_$/Euro – E_$/Euro) / E_$/Euro

The equilibrium exchange rate ensures that no market participant has an incentive to switch to a deposit in another currency. The foreign exchange market is in equilibrium when there is no excess demand or supply for any currency, which occurs when the interest parity condition holds.

Impact of Exchange Rate Changes on Returns

• If the return on euro deposits is lower than on dollar deposits, there will be excess demand for dollars and excess supply of euros, causing the euro to depreciate and the dollar to appreciate.
• Conversely, if the return on euro deposits is higher than on dollar deposits, there will be excess demand for euros and excess supply of dollars, causing the euro to appreciate and the dollar to depreciate.

Exchange Rate Reactions to Expectations and Interest Rates

• An increase in the interest rate on a currency generally causes that currency to appreciate against foreign currencies, while a decrease in the interest rate leads to depreciation.
• A rise in the expected future exchange rate typically causes a rise in the current exchange rate, and vice versa.

The Law of One Price

In competitive markets without transaction costs, identical goods sold in different markets must have the same price when expressed in the same currency.

Mathematically:

P^US_i = E_$/€ * P^E_i à E_$/€ = P^US_i / P^E_i

Purchasing Power Parity (PPP)

Purchasing Power Parity (PPP) states that the exchange rate between two currencies equals the ratio of the countries’ price levels. It suggests that changes in a currency’s domestic purchasing power will be reflected in proportional changes in its exchange rate.

• Absolute PPP: States that exchange rates equal relative price levels.
• Relative PPP: States that the percentage change in the exchange rate between two currencies over a period equals the difference between the percentage changes in national price levels.

Mathematically:

(E_{$/€, t} – E_{$/€, t-1}) / E_{$/€, t-1} = π_{US, t} – π_{E, t}

where π represents the inflation rate.

Deviations from PPP

Empirical evidence suggests significant deviations from PPP in the short run due to factors like price stickiness, slow price adjustments, and changes in demand and supply. However, in the long run, PPP tends to hold better, although deviations can still occur due to factors such as:

• Transport costs and trade restrictions
• Monopolistic or oligopolistic market structures
• Differences in goods baskets used to calculate inflation rates

Part 2: Money Market and Exchange Rates

Money Demand

Aggregate money demand, the sum of individual money demands, is influenced by:

1. Interest Rate: Higher interest rates decrease money demand (negative effect).
2. Price Level: Higher price levels increase money demand (positive effect).
3. Real Gross National Income (GNI): Higher GNI increases liquidity demand (positive effect).

Mathematically:

M^d = P * L(Y, R) à M^d / P = L(R, Y)

where L(Y, R) represents aggregate real money demand.

Money Supply

Nominal money supply (M^s) is exogenous, determined by the central bank, and not affected by the interest rate. It is represented as a vertical line in a graph of real money supply (Q) against the interest rate (R).

Mathematically:

Q = M^s / P

Money Market Equilibrium

The money market is in equilibrium when the money supply equals aggregate money demand.

Mathematically:

M^s = M^d à M^s / P = L(R, Y)

At given price levels (P) and GNI (Y), the interest rate is determined by the intersection of money supply and demand.

Changes in the Money Market

• Increasing Money Supply: Leads to lower interest rates and higher real liquidity holdings.
• Increase in Output: Shifts the aggregate real money demand curve to the right, increasing the interest rate.

Money Supply and Exchange Rates in the Short Run

An increase in a country’s money supply generally causes its currency to depreciate in the foreign exchange market, while a decrease in the money supply leads to appreciation. This occurs because changes in the money supply affect interest rates, which in turn influence exchange rates through interest rate parity.

Exchange Rate Expectations and the Long Run

To understand long-run exchange rate movements, we need to consider exchange rate expectations. One approach is to use the Purchasing Power Parity (PPP) theory.

Monetary Approach to Exchange Rate Determination

This approach makes the following assumptions:

• Purchasing power parity holds: E_$/Euro = P^US / P^EU
• Prices are perfectly flexible: P^US = M^s_US / L(R_$, Y^US) and P^EU = M^s_EU / L(R_€, Y^EU)
• Interest rates and income/output affect the exchange rate only through money demand.

In this framework, the long-run exchange rate is determined by the relative supply and demand for monies.

Inflation, Interest Rate Parity, and PPP

Combining the Fisher effect (which links interest rates and expected inflation) with interest rate parity and relative PPP leads to the following relationship:

R_$ – R_€ = π^e_US – π^e_E

This equation suggests that the interest rate differential between two currencies should equal the expected inflation differential.

The Fisher Effect

is behind the seemingly paradoxical monetary approach prediction that a currency depreciates in the foreign exchange market when its interest rate rises relative to foreign currency interest rates.

Real interest rate is unchangedà Pure monetary changes do not have long run effects on real

Variables.

Consequences of different assumptions on Price adjustments:

With sticky prices:

·Decreasing money supply requires increase in interest rate for money market equilibrium

·Price level fix, but downward pressure

·Increase in interest rate comes with lower inflation expectations and expectation of a long run exchange rate appreciationàExpectation of an appreciation yields an immediate appreciation

With flexible prices:

·Accelerated increase in money supply yields an increase in interest rates

·Increase in interest rate comes with higher inflation expectations and expectation of a long run Exchange rate depreciationà Immediate depreciation follows

The Real Exchange Rate:

The real exchange rate between two countries’ currencies is a broad summary measure of the prices of one country’s goods and services relative to the other country’s.

Q$/Euro =  E$/Euro* (PEU/ PUS)

The price levels must not be defined over the same basket, in other words, Basket in the USA includes goods and services, which are consumed and produced there, whereas basket in Europe includes goods and services that are consumed and produced here.

Real Depreciation of the Dollar against the Euro:A rise in the real dollar/euro exchange rate (which we call a real depreciation of the dollar against the euro) produce fall in the purchasing power of a dollar within Europe’s borders relative to its purchasing power within the United States. This change in relative purchasing power occurs because the dollar prices of European goods (E$/€ * PE) rise relative to those of U.S. goods (PUS ). à Hypothetical purchasing power of American goods falls relative to European goods

Real Appreciation of the dollar against the Euro: is a fall in q$/€. This fall indicates a decrease in the relative price of products purchased in Europe, or a rise in the dollar’s European purchasing power compared with that in the United States.

In the EMU there is no nominal exchange rate à The real exchange rate between any two EMU countries simplify to                                          qL-Euro/Oe-Euro  = Poe/PL

Demand, supply and the long run real exchange rate:

Long run real exchange rate is a relative price, which is determined by the price ratios of two baskets:

·Every price index is determined by good’s market demand and supply

·The real exchange rate is therefore determined by demand and supply in both countries

We focus instead on two specific cases for explaining why the long-run values of real exchange rates can change:

·A change in world relative demand for American products. Imagine that total world spending on American goods and services rises relative to total world spending on European goods and services.à An increase in world relative demand for U.S. output causes a long-run real appreciation of the dollar against the euro (a fall in ). Similarly, a decrease in world relative demand for U.S. output causes a long-run real depreciation of the dollar against the euro (a rise in q$/€).

·A change in relative output supply. Suppose that the productive efficiency of U.S. labour and capital risesà A relative expansion of U.S. output causes a long-run real depreciation of the dollar against the euro (q$/€ rises).  A relative expansion of European output causes a long-run real appreciation of the dollar against the euro (q$/€ falls).

Nominal and real exchange rates in equilibrium:

Nominal changes in exchange rates can be split in a monetary and a real component:

·Changes in money supply and demand in a country yield in the long run to the proportional change in the exchange rate that is predicted by the relative PPP

·Shifts in (goods) supply and demand, in contrast, yield changes in the nominal exchange rate that oppose the PPP

E$/Euro =  q$/Euro * ( PUS/ PE )

At a given Dollar/Euro exchange rate, changes in money supply and demand in the US or in Europe have the same effects as predicted by the monetary theory. Changes in the real exchange rate do also affect the

long run exchange rate.

Determinants of changes in the long run nominal Exchange rate.

1.  A change in relative money supply level

·Ex: one-time permanent increase in US money supply level

·No effect on relative price and outputà no effect on the real exchange rate

·Proportional increase of PUS with MUS according to PEU = MsEU /L( R€,YEU)

·Change in the nominal exchange rate according to E$/Euro =  q$/Euro * ( PUS/ PE )

·All explained by the monetary approach and PPP

2.  An increase in the growth rate of relative money supply

·Raises long run inflation rate and through the Fisher-effect the Dollar interest rate relative to the Euro interest rate

·Real money demand in the USA fallsàaccording to PEU = MsEU /L( R€,YEU) Price level PUS  increases

·No change in the real exchange rate

3.  A change in relative demand for goods

·No dealt with in the monetary approach

·Changes in the nominal exchange rate only driven by the real exchange rate

·Increase in relative demand for US goods yield Dollar appreciation

4.  A change in the relative supply of goods

·Relative expansion of US-output yields real depreciation

·Increase in output raises demand for liquidity (shift of the L-curve)

·According to PEU = MsEU /L( R€,YEU), US price level falls

·q$=Euro  up, PUS  downà  ambiguous effect on E$=Euro

Determinants of changes in the long run nominal Exchange rate: Summary

·If deviations from the equilibrium have exclusively monetary sources, long run nominal exchange rate follows the relative PPP

·Monetary changes affect purchasing power of the currency for domestic and foreign goods alike

·If deviations from the equilibrium result from deviations on goods and service markets, the exchange rate is unlikely to obey the PPP even in the long run

·This exchange rate model is integrated in a broader framework with endogenous output/income in the next part