A Literature Review of the Efficiency of the Foreign Exchange Market
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lecture6.pptxLecture 6
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Revision
Currency Substitution
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Figure 9.1 Long-run equilibrium in the currency substitution model
9.1 The model
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Figure 9.2 Monetary acceleration in the currency substitution model
9.1.4 Change in monetary policy
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Chapter 11
Optimum currency areas
and
monetary union
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Single Currency Zone (Monetary Union)
Region with a single currency or with multiple currencies linked by exchange rate fixed (at 1:1) forever
Examples: USA, UK, Eurozone have a number of different banks issuing money, but freely exchangeable 1 for 1. A number of countries use dollars as national currency.
Currency union as limiting case of fixed exchange rate regime
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Figure 11.1 Exchange rate regimes
The Spectrum of Exchange Rate Regimes
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Benefits of Monetary Union
Microeconomic: lower transaction costs
Fewer exchange rates: union of N countries eliminates N-1 exchange rates against $ and N(N-1)/2 cross rates
For Europe: possibly around 0.25-0.5% of EU GDP
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Other Cost Savings
Uncertainty costs: currency exposure for international trade/investment – but savings not likely to be large since pre-union:
Only net exposure relevant
Managed by firms as one type of risk exposure (alongside exposure to interest rates, commodity prices etc etc)
Largely hedgeable by use of forwards or money market hedges (costless) or options
Unit of account: single currency reduces number of prices needed
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Costs of Monetary Union (MU)
Macroeconomic: adjustment to shocks under permanently fixed (versus floating) exchange rate
Price/wage flexibility critical
Labour: either wage or employment varies after shock.
With floating rates, fall in demand causes depreciation and price level rise, reducing real wage, as required to reinstate equilibrium (“full employment”), without need for reduction in money wage
With fixed rates, if money wages not fully flexible, real wage fails to adjust, so result is unemployment
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Mundell: Optimal Currency Area (OCA)
OCA defined by labour mobility e.g. fall in demand for labour in one US region causes migration to high-demand region, so migration even if wages inflexible (contrast with Europe)
Conclusion: optimal currency zone is area small enough for labour to be mobile
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McKinnon: OCA
Devaluation ineffective if labour suppliers respond to price level rise by raising money wage
In large country with relatively small open sector, imports have small weight in price index, so workers barely notice price rise caused by devaluation
OCA should be big enough for labour suppliers to behave as if in a closed economy (USA, Europe, China?)
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Political Economy of Monetary Union Fixed Exchange Rate versus Single Currency
Mundell: asymmetry, since fixed exchange rate system has inbuilt deflationary bias, MU has inflationary bias
Reason: fixed exchange rates force deficit countries to restrain demand, single currency forces policymakers to equalize demand at level of lowest-unemployment country
Evidence: mixed e.g. under Bretton Woods, deficit countries deflated, but USA exempt
Importance of automatic fiscal stabilisers
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Is Fiscal Sovereignty Compatible with MU?
In MU, national budget deficits funded by borrowing in common “foreign” currency, so greatly increased risk of insolvency of overspending governments
In EMU, overspending supposed to be banned (subject to fine!) by Stability Pact, and bailout ruled out by earlier treaties establishing EMU
Fiscal indiscipline likely to be contagious, leading to repeated bailouts and monetary indiscipline
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Credibility and MU
Fixing exchange rate means surrendering monetary sovereignty – which may be desirable for country with history of inflation
Tying exchange rate to country with credible monetary policy may permit high-inflation low-credibility country to reduce inflation with less need to demonstrate commitment to lower monetary growth rate
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Costs of Transition
The costs of joining will depend crucially on how similar the economies are before the start
Micro cost of changing the currency (and benefits e.g. reduce fraud)
Need for convergence
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11.3.4 Costs of Transition
| Table 11.1 EMU convergence criteria | |
| Fiscal Policy | |
| Budget deficit | < 3% of GDP |
| Government debt | < 60% of GDP |
| Monetary Policy | |
| Inflation (RPI) | < 1.5% above 3 best performing countries |
| Long-term interest rates | < 2% above 3 best performing countries |
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Common Currency and common market
everyone (virtually) agrees that more trade and removing barriers is good
But this does not in itself imply a single currency
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Currency Boards
Half way between fixed exchange rate and a single currency
Domestic money is backed by a foreign currency one for one. So if necessary could buy back the whole domestic money stock.
The Gold standard is a special type of currency board
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Conclusion
The arguments for and against a monetary union range beyond positive economics
The book does not like EMU
Ultimately it depends on a question of federation and forming one political entity
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Chapter 12
Market Efficiency and Rational Expectations
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Introduction
An efficient market is where prices fully reflect all available information
An efficient market exploits all profit opportunities
The problem of assessing market efficiency is that it is closely linked to expectations formation
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Mathematical expectation
The mathematical operator E(x) gives the expected value of x, it is the weighted average of all possible outcomes for x where the weights are the probability of each outcome occurring.
In a normal distribution it is the mean of the distribution
The conditional expectation is the expectation conditioned on some information
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12.2 Rational Expectations Hypothesis (REH)
Problem: agents’ expectations are key to financial market behaviour. But how does trader/investor forecast?
Let xt be the value at the current time, t, of the variable/asset/security in question (e.g. an exchange rate, share price, retail price index..)
At t , xt is known, but xt+1 is still unknown. Write xt+1e as the agent’s expectation of the future value, xt+1.
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Q. How is xt+1e formed?
REH answer: a rational economic agent uses all information available at t in best possible way, so:
LHS is agent’s subjective expectation
RHS is (statistical) expectation of xt+1 conditional on information set, It.
We often use abbreviated notation:
where Et means expectation conditional on information at t.
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Q. What defines relevant information? How should it be rationally used?
REH answer: depends on model. Rational expectation is consistent with structure of the model it appears in. REH views any other expectation as irrational, hence arbitrary
Note:
since RE is optimal, it is unique i.e. all rational investors share same expectation
RE is NOT the same as perfect foresight:
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RE versus Perfect Foresight
Perfect foresight implies:
RE implies:
Where, by the definition of a mathematical expectation, ut is a zero-mean process Etut+1 = 0 .
So, whereas perfect foresight implies investors always right, REH implies they may make mistakes (possibly large, possibly frequent), but their average error is zero – if they were systematically consistently wrong, they would be failing to make full use of the information.
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Exchange rates under RE Why we use logs
Since 1/S is the FX price of domestic currency, we would like it to be true that:
But this is not generally true under RE, since:
because 1/x is a nonlinear relationship.
Solution: use logs, so log of inverse exchange rate is –s which is linear
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12.3 Forward Market Efficiency
The relationship between the forward and spot markets under the
assumptions of RE, adequate arbitrage funds, free movement of funds and negligible transactions costs:
(12.2)
which is efficient market equilibrium as the forward rate reflects
- publicly available information summarised in the RE, ;
- market’s attitude to risk, as embodied in the risk premium, .
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12.3 Market Efficiency (continued)
Rewrite Equation (12.2) by subtracting from both sides:
(12.3)
Equation (12.3) implies:
(12.4)
Alternatively, stepping back one period:
(12.4’)
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A weakly efficient market is one which reflects all the information in its own past history
A strongly efficient market reflects all publicly available information
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12.4 Unbiasedness
When the forward market is efficient and investors are risk neutral:
▪ forward rate = expectation of the spot rate at the time contract matures
▪ spot rate = forward rate set in the previous period, plus or minus a random error
(12.5)
Rewriting (12.5) in terms of rate of depreciation:
(12.5’)
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12.5 Random Walk Model
Random walk
Change in time series from one period to next is purely random:
(12.6)
Alternatively:
(12.6’)
where is completely random (no pattern over time).
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12.5 Random walk model (continued)
Random walk with drift d
Change in time series from one period to next is equal to drift factor
plus purely random component:
(12.7)
Alternatively:
(12.7’)
where is completely random (no pattern over time).
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12.5 Market Efficiency and the Random Walk Model
The random walk model is compatible with RE, efficiency and unbiasedness.
However, efficiency does NOT require that the spot rate follow a random walk. Deviation from a random walk may be due to a risk premium or a nonzero expected return (depreciation).
The first term on the RHS could be explained by a risk premium (possibly nonconstant). Even in the absence of a risk premium (i.e. risk-neutrality), we could well have (st+1 – st)>0 if there is long run anticipated depreciation – compensated by the interest rate differential.
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12.5 Random Walk Model (continued)
If spot rate follows a RW with drift:
(12.8)
Taking expectations in (12.8) conditional on
(12.9)
(Note Et-1ut= Etut+1=0 because the residual is zero-mean by definition,
and Et-1st-1= E(st-1|It-1)=st-1 because st-1 is in It-1
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12.5 Random Walk Model (continued)
If spot rate does not follow a RW with drift: for example,
(12.10)
RE forecast of the next period’s spot rate:
(12.11)
Forward market efficiency for a RW:
(12.12)
Subtracting equation (12.11) from (12.10):
(12.13)
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Testing for efficiency, a problem
Neither RE nor market efficiency is usually testable on its own.
We almost always test a joint hypothesis, market efficiency AND rational expectation
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12.7 spot and forward rates:Facts
Using the sterling dollar as a representative example
The two track each other very closely
But this is mostly an effect of forward rates being close to the current rate
There is very little predictive power
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12.8 Results
To test for unbiasedness, fit equations of the following form:
(12.15)
1. estimate of the intercept a
- insignificantly different from zero?
2. estimate of the slope coefficient b
- insignificantly different from unity?
3. serially uncorrelated?
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12.8 Results (continued)
If RE is assumed, then UIRP implies:
(12.16)
Since by definition:
Then a test of RE + UIRP would involve testing:
(12.17)
Alternatively, if we have direct (survey) information on expectations, we can test:
(12.18)
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Broad conclusion of empirical research
Evidence seems to be mounting agains unbiasedness
In favour of time varying risk premia
Surveys of expectations have been tried but this is costly and does not work too well
But this also suggest lack of rationality
However bias need to be large enough to overcome transaction costs and make profits
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Conclusion
Market efficiency and RE are key concepts underlying finance
Evidence seems to suggest that even in sophisticated markets there are clear profit opportunities and inefficiencies
Developing markets are often wide open
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Figure 12.1 The Spot and Lagged Forward Rate
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Year
$ per £
Lagged Forward rate (£/$)
Spot rate (£/$)
Figure 12.2 The Spot Rate and the Lagged Forward Premium
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$ US
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