A Literature Review of the Efficiency of the Foreign Exchange Market

linjy581

lecture2.ppt

Home >Business & Finance homework help >A Literature Review of the Efficiency of the Foreign Exchange Market

lecture2.*

Lecture 2

Chapters 2 & 3

lecture2.*

Lecture 1 revision

lecture2.*

Floating versus Fixed Exchange rate

Pure float: exchange rate at any moment determined by net demand for currency
Fixed exchange rate: monetary authority intervenes by a) buying up excess supply of $ with £ (when £ strong, $ weak) or b) satisfying excess demand for $ by selling $ for £ (when £ weak, $ strong), so as to prevent excess demand /supply affecting rate
a) adds $ to FX reserves, adds to £ in circulation
b) takes $ out of FX reserves, reduces £ in circulation

lecture2.*

1.3 Balance of payments

1. Current account: export receipts as credits, import payments as debits, net = current account balance (goods, services including financial services, interest and dividends, rent, tourism)

2. Capital account: net capital inflows = net purchases of £ by foreigners in order to acquire claims on UK residents less net sales of £ by UK residents in order to acquire claims on foreigners (Long term including securities – equities, bonds etc - real estate etc + short term including bank deposits, short term securities)

Total net underlying demand for £ = 1 + 2 (basic balance) is equated to zero by exchange rate movement, unless Government intervenes to fix exchange rate, in which case:

3. Reserve change = - (1 + 2) to prevent basic balance causing exchange rate to move

lecture2.*

2.4 Purchasing Power Parity

(i = 1, . . ., N) (2.3)

where

- domestic prices of good number i;

- foreign prices of good number i.

(2.4)

where

- home country’s price index,

- foreign country’s price index.

lecture2.*

Chapter 3

Financial Markets in the Open Economy

lecture2.*

Introduction

The exchange rate is key to international finance
Allocation of wealth between assets within an economy is just a matter of risk and return
But Internationally we have to also factor in the exchange rate

The basic relationship is UIP

lecture2.*

3.1 Uncovered Interest Rate Parity

Figure 3.1 Uncovered interest rate parity

lecture2.*

3.1.3 Uncovered Interest Rate Parity

(3.1)

where

r - interest rate in the UK

r* - interest rate in the US

- ratio of the expected exchange rate at the end of the year

to the actual rate at the time of the decision

lecture2.*

3.1.3 UIRP: A Simplification

Redefine as follows:

(3.2)

where

- expected rate of depreciation of the domestic currency.

Rewriting (3.1) using (3.2),

(3.3)

lecture2.*

Unless the rate of currency depreciation is very high, the final term in (3.3) can be ignored, so:

(3.4)

which is the approximate form of the uncovered interest rate parity (UIRP) condition.

Interpretation: in equilibrium, domestic interest rate higher (lower) than the foreign interest rate by the expected rate of depreciation (appreciation) of the domestic currency, so as to compensate holders of the currency for their capital loss (gain) on the exchange rate.

lecture2.*

Risk and expectations

UIRP involves expected rate of depreciation.
If expectations wrong, payoff to depositors in FX greater or smaller than RHS in (3.4)
If investors risk-neutral (indifferent to risk), they carry the risk of expectations error willingly, without requiring compensation
If investors risk-averse (risk avoiders), they only carry the risk of expectations error if offered compensation – a risk premium added to payoff on RHS of (3.4)

lecture2.*

3.2 Covered Interest Rate Parity

Using the forward exchange rate F in place of

(3.5)

Defining f as the forward premium)

(3.8),

and ignoring the final term,

(3.9)

- the normal formulation of the CIRP hypothesis.

lecture2.*

Borrowing and lending

To ensure CIP holds we do not need speculators with lots of assets
If CIP does not hold it would be profitable to borrow in one currency and invest in another
An investor who has a liability in a currency is short in that currency
An investor who has an asset in a currency is long in that currency

lecture2.*

3.4 Covered interest rate parity – the facts

The gap between UK and US interest rates is less than

the transaction cost, c

(3.10)

Otherwise instantaneous arbitrage occurs.

lecture2.*

3.5 Efficient Markets – a first encounter

Efficient market: prices fully reflect all available information, so no unexploited profit opportunities left
Unbiased forward exchange rate equals spot rate expected when forward contract matures, so that:

lecture2.*

3.6 PPP revisited

When inflation expected, risk-neutral domestic depositors require payoff of r to give them real return (real interest rate), R:

Unless expected inflation rate very high, Rdp small, so:

which is the Fisher equation. (Note: r is observable, but dpe is not, so R = r - dpe is unobservable, though instead we often consider R = r – dp, where dp is the most recent inflation rate. The approximation works well if inflation is expected to remain at its current level)

(3.14)

lecture2.*

Ex-post Real Interest Rates
Using 12-month Lagged Inflation Rates* and 10-year Bond Yields

* Based on CPI, except for Australia (PPI)

lecture2.*

3.6.2 PPP and the real exchange rate

Fisher equation for the foreign country

(3.14’)

(3.14) and (3.14)’ imply:

(3.15)

With risk neutrality, the nominal interest rate differential is equal

to the expected rate of depreciation (UIRP), so

(3.16)

lecture2.*

In the absence of barriers to cross border capital movements

Therefore (3.17)

(PPP in expectations), which implies: (3.18)

or: (3.19)

i.e. real exchange rate expected to remain constant (next year’s real exchange rate expected to be same as this year’s) – random walk real exchange rate theory

lecture2.*

3.6.2 PPP and the real exchange rate (continued)

Suppose all economic agents know with absolute accuracy:

- the future price levels in the two countries

- next year’s exchange rate

(3.20)

Using UIRP,

(3.21)

or:

(3.22)

lecture2.*

UIRP, Fisher and PPP

3 parity relationships, but only 2 endogenous variables (“unknowns”): inflation differential, dp-dp*, and interest differential, r – r*, which are therefore overdetermined
Any 2 parity relationships implies the 3rd:

PPP + UIRP  Fisher

Fisher + UIRP  PPP etc etc

Reminder: this presupposes
risk neutral investors,
free movement of goods and capital
no transaction costs

lecture2.*

Chapter 4

Open Economy Macroeconomics

lecture2.*

4.1 IS-LM model of aggregate demand

4.1.1 IS curve

The national income identity in an open economy:

(4.1)

where

Y (real) national income

C expenditure on consumption

I investment

B exports – imports = balance of payments current account

G Net government spending (budget deficit)

lecture2.*

Since saving is simply unspent income:

S = Y - C

(4.1) implies that:

S = Y – C = I + G + B

or: B = S – I – G

or: S - I- B = G (4.3)

So (current account of) balance of payments is simply saving net of investment or net national saving (saving of household sector less dissaving of corporate and government sectors)

lecture2.*

4.1.1 IS curve (continued)

A country’s current account is determined by the real exchange

rate:

where is the price of foreign (US) goods, measured in

pounds (domestic currency).

lecture2.*

4.1.1 IS curve (continued)

Now assume S=by, I=-zr and B=hQ

(4.4)

where b, z, h – behavioural parameters, all positive.

Setting

(4.5)

-relationship between y and r, for given values of G and Q.

lecture2.*

4.1.1 IS curve (continued)

Figure 4.1 The IS curve

lecture2.*

4.1.1 IS curve (continued)

From Figure 4.1

If and ,

(4.5a)

If and ,

(4.5b)

lecture2.*

4.1.2 Money Market

Relationship between the demand for money and national income

(ignoring the opportunity cost)

(4.6)

where

the demand for money

national income, both measured in nominal terms

k positive constant.

lecture2.*

4.1.2 Money Market (continued)

Define nominal national income Y as follows:

where y is real income and P is the price level.

Equation (4.6) is rewritten as follows:

(4.7)

- Cambridge quantity equation

lecture2.*

4.1.2 Money Market (continued)

Dividing both sides of Eq.(4.7) by P leads to

(4.8)

where

left-hand side – the demand for real money balances;

right-hand side – k times the real income generated in the economy.

Modifying Equation (4.8) to take account of the opportunity cost

of holding money:

(4.9)

where l is a positive constant and r is the interest rate.

lecture2.*

Government budget constraint

G-T= the budget deficit

This must be funded by borrowing or printing money

G-T= change in money +change in gov debt

lecture2.*

4.1.2 Money Market: supply of money in an open economy

Balance sheet equation of FX= central Bank reserves LG=Lending to gov, MB=monetary base, MBb=currency plus deposits with central bank, L=loans, D=deposits

1. the central bank (MB):

2. the commercial banks (D):

Adding the two equations:

where is domestic credit (DC) which is total lending of the consolidated banking sector, both to the government and to the private, non-bank sector.

lecture2.*

4.1.2 Money Market (continued)

Figure 4.2 Balance sheet of the banking system

lecture2.*

4.1.2 Money market:
supply of money in an open economy

Using the definition of DC and subtracting

where

Since the money stock is the sum of the total of currency in circulation

and deposits in the banks, i.e.,

(4.10)

Rewrite equation (4.1) in terms of discrete changes:

(4.11)

lecture2.*

Exchange rates and Money

A pure floating exchange rate official financing not used to manipulate the exchange rate. Money stock can be controlled by the government (maybe?)
Fixed exchange rate, foreign reserves used to fix the exchange rate by affecting demand and supply, government looses control of the money supply

lecture2.*

4.1.2 Money market: LM curve

Equation (4.9) means

(4.12)

Given that

(4.13)

which has the same general form as the equation of the IS curve.

Given the LM curve, for the money market to clear,

if the interest is

lecture2.*

4.1.2 Money market: LM curve

Figure 4.3 the LM curve

lecture2.*

IS-LM

We can now put the IS and LM curves together to produce a unique solution for y and r.

And change in things such as G or money will change the equilibrium of the system

lecture2.*

Aggregate Demand

We can now see how the solution to IS-LM would vary as the price level changes

This gives the aggregate demand curve

lecture2.*

4.1.3 Aggregate demand

Figure 4.4 derivation of the aggregate demand curve

lecture2.*

Aggregate supply

We have an aggregate demand curve, if we face this with an aggregate supply curve we can then derive the full solution to the system
Two extreme assumptions
Classical flexible prices

Keynesian fixed prices

lecture2.*

Classical flexible prices

Supply is determined by firms and the production function.
Production is a function of Employment
Employment is determined by the labour market which fixes the real wage to make demand and supply equal.

lecture2.*

Figure 4.5 derivation of the classical aggregate supply curve

lecture2.*

Keynesian fixed nominal wages

The extreme Keynesian assumption is that wages will not respond.
So as prices change the real wage changes and firms change their production levels

lecture2.*

Figure 4.6 derivation of the Keynesian aggregate supply curve

lecture2.*

A compromise case

Stickey prices but which do adjust eventually
Initially real things adjust as in the keynesian case but over time wages adjust and eventually we get to the classical case of no change in real things, only prices

lecture2.*

4.2.3 A compromise: sticky prices

Figure 4.7 the sticky price aggregate supply curve

lecture2.*

Conclusion

We have seen the effects of interest rates on exchange rates (UIP) and efficient markets
The IS-LM analysis with an open economy effect from the exchange rate on exports and imports
The effect of exchange regimes on the money stock

)

(

)

(

)

)(

(

)

(

)

(

)

(

)

(

)

(

)

(

)

)(

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

kPy

)

(

)

(