nternational Monetary Economics
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Topic3PartA2021.pptxExchange Rate Determination in the Short-Run and the Long-Run
Topic 3: Part A
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Learning outcomes
Identify the forces that affect exchange rates
Explain the asset market approach to short run exchange rate determination
Explain the purchasing power parity theory of exchange rates
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The Concept of the Exchange Rate
The exchange rate will be defined as the domestic currency price of a unit of foreign exchange and will be denoted by e. It will be interpreted as the number of units of domestic currency per unit of foreign currency eg A$/US$ denotes the Australian dollar price of one US dollar
e will denote the spot exchange rate, the rate applicable to transactions involving immediate exchange of currencies.
f will denote the forward exchange rate, the exchange rate that is set at one point in time for a transaction involving a purchase or sale of foreign-exchange at future date.
An increase in the exchange rate therefore denotes a decrease in the value of the domestic currency ( and an increase in the value of the foreign currency) e = value of AUD
Be careful to correctly specify a change in e in terms of the value of the domestic currency.
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USD / AUD
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Exchange rate determination e - Price of FX
D = imports and capital outflow
S = exports and capital inflow
What might be the role of interest rates?
Prices – domestic – foreign?
Expectations?
SFX
Dfx
e
Qfx
e
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To be covered in this topic
The Exchange Rate in the Short Run
The Asset Market Model
Covered Interest Parity
Uncovered Interest Parity
Unbiased Expectations Theory
The Exchange Rate in the Long Run
Absolute and Relative Purchasing Power Parity
International Fisher Relationship
Part B – Next week
The Monetary Model
Sticky Price Model and Overshooting
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The asset market model
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Exchange rate determination in the Short run
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Asset market approach to exchange rate determination.
Movements in exchange rates can be explained by looking at the demand and supply of assets denominated in different currencies
Interest rate differentials
Short term real interest rate differentials influence international capital movements
Real interest rate is nominal minus inflation
Low short-term rates lead to less demand for the currency and depreciation
High rates lead to greater demand for the currency and appreciation
Link to Article on Interest trade differentials
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Interest rate differentials
Link to Article on Interest trade differentials
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Covered interest rate parity
If two assets have the same risk then they must have the same return because otherwise no one will hold the asset with the lower return.
Assume that domestic and foreign Government securities can be considered to have the same level of default risk, that being zero
Although the two securities have the same default risk from the point of a domestic individual foreign securities still carry exchange rate risk that domestic securities don’t.
One way to avoid this risk is to use a forward contract that specifies today what the exchange rate will be for you at the future date you want to convert your interest earnings back into domestic currency. Denote this forward rate as f.
If the exchange rate risk can be removed through the forward market then the two securities must yield the same return.
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Covered interest parity (CIP)
(1 + i) is the Australian dollar return from a A$1 investment in Australia.
is the AUD return of a A$1 investment overseas
using the forward market. The return is known with certainty at the beginning of the investment period
This expression is called covered interest parity (CIP) because all exchange rate risk on the foreign currency side has been “covered” by use of the forward contract.
The covered cost (return) of borrowing (lending) in a foreign currency is the same as the domestic cost (return) when it is hedged through the forward market
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Worked example
Australia, US i = 12% i* = 6% e= 1.4 f= 1.4793A/US
An Australian borrows US equivalent of $100A
Borrow US $71.43 US interest costs = US$4.29
At time of borrowing will buy US$ forward.
A$ cost of principal repayment
= US$71.43 (1.4793 A$/US)
=A$105.66
A$ cost of interest repayment =US$4.29 (1.4793 A$/US)
= A$6.34 Total covered cost of borrowing $100A
= A$105.66+A$6.34=A$112
12% covered cost
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What if f unknown ?
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Logic of the CIP condition
If covered interest parity does not initially hold (eg the covered US return is higher than the Australian return),
then market participants would borrow as much as possible in Australia, buy US$ on the spot market, invest in the US and sell US$ forward. This would:
e=?
i and i* = ?
f= ?
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Logic of the CIP condition:
If covered interest parity does not initially hold (eg the covered US return is higher than the Australian return), then market participants would borrow as much as possible in Australia, buy US$ on the spot market, invest in the US and sell US$ forward. This would:
Place upward pressure on e (buy FX)
Place downward pressure on the forward rate (sell FX forward)
Place upward pressure on the domestic rate of interest
(sell bonds – price bonds fall – interest yields rise)
Place downward pressure on the US interest rate (buy bonds – interest yield falls)
until the CIP condition holds
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Barriers to Covered Interest Parity
Imperfect substitutability of assets; eg due to default and political risk
Transaction costs
Limited arbitrage funds
Capital mobility imperfect
Taxes (withholding taxes)
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UNBIASED EXPECTATIONS THEORY
Assume that the market is dominated by risk neutral individuals such that no risk premium is present.
If investors do not care about risk then they have no reason to prefer to avoid risk by using the forward rate, or to accept risk by awaiting the future spot rate.
The forward rate at time 0 for time 1 equals the expected spot rate for time t=1.
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One-year Treasury bills currently earn 3.06 percent. You expected that one year from now, one-year Treasury bill rates will increase to 3.25 percent.
Assume if the unbiased expectations theory is correct, what should the current rate be on two-year Treasury securities?
What is the Current Rate?
1R2 = [(1+0.0306)(1+0.0325)^1/2 - 1
1R2 = (1.0306)(1.0325) = 1.064
1R2 = 1.064^0.5 = 1.0315
1R2 = 1.0315 - 1 = .0315 x 100 --> 3.15%
Current Rate = 3.15%
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UNBIASED EXPECTATIONS THEORY
Assume that E(e)=1.4A/US and f=1.46A/US
The market will sell US $s forward as it can sell it forward at A$1.46 and believes with perfect certainty that it can buy it later on at the ruling spot rate for only A$1.4 giving an expected profit of A$0.06 for every US$ sold forward.
As the forward supply of US $ increases f will fall and will continue to fall until it hits A$1.4.
Individuals will sell US $s forward until they believe that there is no longer any expected profit to be made. The expected profit will be zero once the forward rate is equal to the expected spot rate.
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If E(e) < f
SFX
Dfx
1.46
Qfx
f
The forward supply of US $ increases.
f will fall and will continue to fall until it hits A$1.4. where
E(e) = f
1.4
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UNBIASED EXPECTATIONS THEORY
If the forward exchange rate exceeds the spot rate, a currency is said to be selling at a forward premium. A currency is selling at a forward discount when the forward rate is less than the current spot rate.
Define the forward premium as the proportion by which a country’s forward exchange rate exceeds its spot rate.
If the forward rate equals the expected spot rate, then the expected rate of increase in the value of the foreign currency (between today and the future period) equals the forward premium on the foreign currency (the proportional difference between the forward and spot rates).
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UNCOVERED INTEREST PARITY
When covered interest parity and unbiased expectations hold, the expected return from investing domestically is equal to the expected return from an unhedged investment overseas.
An individual will indifferent between hedging and not hedging.
There are two alternative ways that uncovered interest parity can be interpreted.
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Uncovered Interest Parity 1) In terms of Expected returns
UIP = The return from one period domestic investment equals the expected return from an unhedged one period investment overseas in the same asset.
Any difference in expected returns will be offset by a change in e, resulting in equal returns.
If UIP does not initially hold there will be an arbitrage opportunity. An increase in the uncovered return on foreign currency assets (for example, due to an increase in foreign interest rates) would put upward pressure on e (downward pressure on the exchange value of the domestic currency).
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If US uncovered return is greater than AUD return
<
Borrow in Australia and invest in US – buy USD – push up e
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UNCOVERED INTEREST PARITY: (ii) In terms of Expected Exchange Rate Changes
The expected change in the exchange rate equals the nominal interest differential.
The country that has the currency that is expected to decrease in value will have the higher nominal rate of interest
The intuition is as follows.
Holding domestic currency or foreign currency deposits rewards the investor with domestic currency interest. Holding foreign currency deposits also rewards investors with the loss or gain on the foreign currency equal to the rate of increase in the foreign currency. Thus, for UIP to hold, and for an investor to be indifferent between domestic deposits and foreign deposits, any expected loss (gain) in the form of an decrease (increase) in the value of the foreign currency must be compensated for by an higher (lower) interest rate on the foreign currency side.
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The Effect of Changing Expectations on the Current Spot Exchange Rate
Assume an increase in E(e).
This increases the expected decline in the value of the domestic currency.
This increases the expected AUD return on foreign currency assets.
Market participants would purchase US$ on the spot market, placing upward pressure on e, until uncovered interest parity holds.
Therefore a rise in the expected spot exchange rate causes a rise in the current spot exchange rate.
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Increase in E(e) – increase in expected return of foreign assets – buy Fx – e rises
SFX
Dfx
e
Qfx
e
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Expectations in the market
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THE EXCHANGE RATE IN THE LONG RUN
Purchasing Power Parity
Model of long run exchange rate behaviour that provides the framework that actors in the asset market use to forecast exchange rates.
As the expectations of these agents influence exchange rates immediately, predictions about long run movements in exchange rates are important even in the short run.
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Law of One Price
Pi=Pi*e
Where i denotes commodity i
Identical goods, sold in different locations must sell for the same price when prices are expressed in a common currency.
Based on commodity arbitrage.
Consider the trade in diamonds that takes place between the United States and the Netherlands. If diamonds were more expensive in the United States, economic agents would buy at a low price in the Netherlands and sell at a high price in the United States. If Dutch prices were higher, arbitragers would profit from the reverse trade.
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Absolute Purchasing Power Parity
P=P*e
Assumes the law of one price holds for all goods
P and P* refer to overall price levels, rather than the prices of individual goods.
Implies that the exchange rate at which two currencies trade equals the relative price levels of the two countries.
For example, if a basket of goods costs US$460 in the United States and the same basket costs A$400 in Australia, absolute purchasing power predicts an exchange rate (e) of A$400/US$460 = A$0.87 per US dollar.
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Big Mac Prices and Exchange Rates
In the long, the exchange rate between two countries should move towards the rate that equalises the prices of an identical basket of goods and services in each country when expressed in terms of some currency.
The Economist uses McDonalds Big Mac as its “basket” of goods and services. The Big Mac purchasing power parity index is the exchange rate that would mean hamburgers costs the same in the US as elsewhere, when expressed in the same currency.
Comparing actual exchange rates with purchasing power parity indicates whether a currency is under or over valued.
https://public.tableau.com/views/TheBigMacindex/Main?:showVizHome=no
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2019
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Big Mac Prices and Exchange Rates, October 2010: http://www.economist.com/content/big-mac-index
Big Mac cost US$2.18 in China in October 2010 against US$3.71 in the US. Suggests that the Chinese currency was undervalued (too low) against the US dollar
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Explaining Deviations from the Law of One Price
Existence of non traded goods. These goods may have different prices in different locations. Impossible to engage in arbitrage if the goods cannot be traded. Local inputs such as rent and wages tend to be lower in lower income countries. International variations in the prices of non traded goods could be a source of international differences in price levels between rich and poor country.
Statistical problems in comparing like with like, eg identical baskets between countries where poor countries spend more on food. Even if the two economies have the same goods they are likely to be consumed in different proportions.
Transactions costs, such as transport costs and tariffs (and other trade barriers) reduce profits from arbitrage.
Imperfect competition and price discrimination.This may help to explain why the exchange rate frequently deviates from absolute PPP. Deviations from PPP can be quite persistent. Approximately half of any PPP deviation still remains after four years. PPP is better in explaining long-run rather than short-run movements in the exchange rate.
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Relative Purchasing Power Parity
Relative purchasing predicts a relationship between changes in prices and changes in exchange rate, rather than a relationship between their levels.
The left hand side reflects the expected change in exchange rate. The right hand side is the difference between the expected domestic rate of inflation and expected foreign rate of inflation.
The expected change in the exchange rate is equal to the expected inflation differential
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Fisher Relationship
The Fisher effect illustrates how the nominal interest rate is determined in the long run. It refers to the link between inflation and nominal interest rates under flexible prices.
Recall that according to purchasing power parity:
Recall that according to uncovered interest parity:
Therefore
i – i* = E(p) – E(p*)
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Fisher Relationship
The equation predicts that changes in the expected rate of inflation will be fully incorporated into changes in nominal interest rates.
All else equal, a rise in expected domestic inflation will lead to an equal rise in the domestic nominal interest rate.
Note that because this result depends on an assumption of PPP, it is therefore likely to hold only in the long run.
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PPP and Interest parity- (note)
Notice that interest parity is essentially an extension of relative PPP.
Interest is the price of borrowing, and interest parity arguments (covered interest parity and uncovered interest parity) argue that changes in these special prices will cause adjustments in the exchange rate.
A major difference between interest parity and PPP is that interest parity is related to financial assets whose prices adjust very quickly, and that have substantially lower transactions costs, transportation costs, etc.
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Empirical evidence / notes
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Sport Rate VS Forward rate
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When the economy is dominated by risk neutral individual E(e) = F
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Real Interest rate Differentials
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Deviation from Covered Interest rate Parity
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Between 1970 and 1981 the difference was positive and often large
Traders would have profited from arbitrage by moving money from pound deposits to mark deposits
But capital controls prevented tem from freely doing so.
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Absolute PPP is a Long-Run concept
Large deviations from PPP in the short run
Absolute PPP holds better in the long run
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This graph charts co-movements of inflation in the US and Britain and the dollar: pound exchange rate. Over time, exchange rate and relative price levels do not always move together
Relative PPP would then predict a steady depreciation of the dollar against the DM (a rise in the number of dollars needed to purchase DM). If you look at the endpoints of the graph this seems to be borne out. However, over shorter periods relative PPP does poorly.
-- From 1973-79 and from 1985-1990 the dollar depreciates too fast
-- From 1979-1985, the dollar actually appreciates (relative PPP gets magnitude and direction wrong)
-- After 1990 the exchange rate bounces around independent of inflation.
When does relative PPP work better?
- in the long run
- when inflation differentials are very large, especially in hyper-inflationary countries (US v. German inflation differences are small).
Why does PPP fare poorly in short run?
- variation in price of nontradable goods (60% of US price index)
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-6%-4%-2%0%2%4%6%8%10 year bond rate differential (% per year Versus U.S.)Sourse: FREDUKAUSGermanyFrance
