Chapter 5 International Parity

Relationships and Forecasting FX Rates

Management 3460 Institutions and Practices in

International Finance

Fall 2003Greg Flanagan

Oct 9-14, 2003 2

Chapter Objectives The student will be able to:

Define Interest Rate Parity

State and apply the IRP equation

Explain and calculate covered Interest Arbitrage

Give reasons for Deviations from IRP

Explain the adjustment process when IRP does not hold that brings it to equilibrium.

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Chapter Objectives The student will be able to:

Define Purchasing Power Parity (PPP)

Explain why there are PPP Deviations and the Real Exchange Rate

Discuss the Evidence for Purchasing Power Parity

Explain the Fisher Effect

Oct 9-14, 2003 4

Chapter Objectives The student will be able to:

Explain the different approaches to forecasting exchange rates:Efficient MarketFundamentalTechnical

Discuss the performance of forecasters.

Oct 9-14, 2003 5

Interest Rate Parity (IRP) Definition: IRP is the situation where the forward

FX premium (discount) of one currency just offsets the higher (lower) interest rate in another country. It is an arbitrage equilibrium condition.

If IRP did not hold, then it would be possible for a trader to make a profit exploiting the arbitrage opportunity.

persistent arbitrage conditions rarely exist suggesting that we can assume that IRP holds.

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Interest Rate Parity (IRP)Return in country j = ij

Covered interest return

(1 + ik) F(j/k)

S(j/k)

or: (1 + ik)(F/S)

IRP equilibrium:

(1 + ij) = (F/S)(1 + ik)

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Interest Rate Parity Example

Suppose you have $100,000 to invest for one year.

You can either

1. invest in the U.S. at i$. Future value = $100,000(1 + i$)

or

2. trade your dollars for pounds at the spot rate, invest in UK at i£ and hedge your exchange rate risk by selling the future value of the British investment forward. The future value = $100,000(F/S)(1 + i£)

Since both of these investments have the same risk, they must have the same future value—otherwise an arbitrage would exist, therefore (F/S)(1 + i£) = (1 + i$)

j = US k =UK

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Interest Rate Parity

$100,000 $100,000(1 + i$)

$100,000(F/S)(1 + i£) 1. Trade $100,000 for £ at S

2. Invest £100,000 at i£ S

3. One year later, trade £ for $ at F

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Interest Rate Parity

(F/S)(1 + ik ) = (1 + ij)

IRP is sometimes approximated as

1 + ik

1 + ij =SF

ij – ik =S

F – S

or

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IRP and Covered Interest Arbitrage

If IRP failed to hold, an arbitrage would exist.

Example:

Spot exchange rate S($/£) = $1.25/£

360-day forward rate F360($/£) = $1.20/£

U.S. discount rate i$ = 7.10%

British discount rate i£ = 11.56%

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IRP and Covered Interest Arbitrage

trader with $1,000 to invest could invest in the U.S., in one year his investment will be worth $1,071 = $1,000(1+ i$) = $1,000(1.071)

Alternatively, this trader could exchange $1,000 for £800 at the prevailing spot rate, (note that £800 = $1,000÷$1.25/£) invest £800 at i£ = 11.56% for one year to achieve £892.48.

Translate £892.48 back into dollars at F360($/£) = $1.20/£, the £892.48 will be exactly $1,071.

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IRP & Exchange Rate Determination

According to IRP only one 360-day forward rate, F360($/£), can exist. It must be the case that F360($/£) = $1.20/£

Why?

If F360($/£) $1.20/£, an astute trader could make money with one of the following strategies:

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Arbitrage Strategy IIf F360($/£) > $1.20/£

i. Borrow $1,000 at t = 0 at i$ = 7.1%.

ii. Exchange $1,000 for £800 at the prevailing spot rate, (note that £800 = $1,000÷$1.25/£) invest £800 at 11.56% (i£) for one year to achieve £892.48

iii. Translate £892.48 back into dollars, if

F360($/£) > $1.20/£ , £892.48 will be more than enough to repay your dollar obligation of $1,071.

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Arbitrage Strategy IIIf F360($/£) < $1.20/£

i. Borrow £800 at t = 0 at i£= 11.56% .

ii. Exchange £800 for $1,000 at the prevailing spot rate, invest $1,000 at 7.1% for one year to achieve $1,071.

iii. Translate $1,071 back into pounds, if

F360($/£) < $1.20/£ , $1,071 will be more than enough to repay your £ obligation of £892.48.

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IRP adjustment process

If the covered interest return was greater in another country, then

(F/S)(1 + ik ) > (1 + iCdn$)

A trader will borrow locally and invest in the foreign country and pocket the difference without risk.

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IRP adjustment process

The interest rate in Canada ij

interest rate in the other country ik will

Sk

Fk

i.e. arbitrage will occur as interest rates approach and Forward and Spot markets differences decrease.

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(F-S)/S(%)

IRP line

1

2

3

4

-4

-3

-2

-1

1 2 3 4 5-5 -4 -3 -2 -1

(ij)- ik(%)The difference in interest rates falls

The difference in forward and spot rates rises

A combination of both changes occur

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Uncovered IRP

Expectations play a considerable role in Exchange rates

The expected rate of change in the exchange rate is approximately equal to the difference in the interest rates between two countries.

E(e) = ij- ik

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Reasons for Deviations from IRP

Transactions CostsThe interest rate available to an arbitrageur for

borrowing, ib, may exceed the rate he can lend at, il.

There may be bid-ask spreads to overcome, Fb/Sa < F/S

Thus (Fb/Sa)(1 + iJl) (1 + iJ

b) 0

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(F-S)/S(%)

IRP line

1

2

3

4

-4

-3

-2

-1

1 2 3 4 5-5 -4 -3 -2 -1

(ij)- ik(%)

Transaction Costs

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Reasons for Deviations from IRP

Capital Controls

Governments sometimes restrict import and export of money through taxes or outright bans.

Political Risks

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Purchasing Power Parity The exchange rate between two

currencies should equal the ratio of the countries’ price levels:

S(j/k) = Pk

Pj

i.e. Prices after exchange transactions should be the same—the absolute version of PPP

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Purchasing Power Parity For example, if an ounce of gold costs

$300 in the U.S. and £150 in the U.K., then the price of one pound in terms of dollars should be:

S($/£) = P£

P$

£150

$300= = $2/£

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Purchasing Power Parity

Relative PPP states that the rate of change in the exchange rate (e) is equal to the differences in the rates of inflation ():

e = (1 + £ )

($ – £) ≈ $ – £

If Cdn inflation is 5% and U.K. inflation is 8%, the pound should depreciate by 2.78% or around 3%.

Oct 9-14, 2003 25

PPP Deviations and the Real Exchange Rate

The real exchange rate (q) is:q =

(1 + e)(1+ £)

(1 + $)

If PPP holds, (1 + e) = (1 + £ )

(1 + $ ) then q = 1.

If q < 1 competitiveness of domestic country improves with currency depreciations.If q > 1 competitiveness of domestic country deteriorates with currency depreciations.

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Evidence on PPP PPP doesn’t hold precisely in the real world for a

variety of reasons:Labour: Haircuts cost 10 times as much in the

developed world as in the developing world.Standards: Film, on the other hand, is a highly

standardized commodity that is actively traded across borders.

Shipping costs, tariffs, and quotas can lead to deviations from PPP.

Capital investment differences.

PPP-determined exchange rates still provide a valuable benchmark.

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Oct 9-14, 2003 28

The Fisher EffectsAn increase (decrease) in the expected

rate of inflation will cause a proportionate increase (decrease) in the interest rate in the country.

$ is the equilibrium expected “real” interest rate

E[$] is the expected rate of inflation

i$ is the equilibrium expected nominal interest rate

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Expected InflationThe Fisher effect implies that the expected

inflation rate is approximated as the difference between the nominal and real interest rates in each country, i.e.

E[$] = (1 + $)

(i$ – $) ≈ i$ – $

i$ = $ + (1 + $)E[$] ≈ $ + E[$]

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International Fisher EffectIf the Fisher effect holds in the U.S.

i$ = (1+ $)(1 + E[$]) ≈ $ + E[$]

and the Fisher effect holds in Japan,

i¥ = (1+ ¥ )(1 + E[¥]) ≈ ¥ + E[¥]

and if the real rates are the same in each country (i.e. $ = ¥ ), then we get the International Fisher Effect

E(e) = (1 + i¥)

(i$ – i¥) ≈ i$ – i¥

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International Fisher EffectIf the International Fisher Effect holds:

then forward parity holds.

E(e) = (1 + i¥)

(i$ – i¥)

and if IRP also holds

= (1 + i¥)

(i$ – i¥)

S

F – S

S

F – SE(e) =

Oct 9-14, 2003 32

≈ Forward PPP

≈ Fisher Effect

≈ Forward Expectation

s Parity

≈ International Fisher Effect

Approximate Equilibrium Exchange Rate Relationships

E($ – ¥)

≈ IRP≈ PPP

S

F – S

E(e)

(i$ – i¥))

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Foreign Exchange Forecasting

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Efficient Markets ApproachFinancial Markets are efficient if prices

reflect all available and relevant information. If this is so, exchange rates will only change

when new information arrives, thus:

St = E[St+1]

and Ft = E[St+1| It]

Predicting exchange rates using the is affordable and is hard to beat.

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Fundamental Approach Involves econometrics to develop models that

use a variety of explanatory variables. This involves three steps:step 1: Estimate the structural model.step 2: Estimate future parameter values.step 3: Use the model to develop forecasts.

The downside is that fundamental models do not work any better than the forward rate model or the random walk model.

Oct 9-14, 2003 36

Technical Approach

Technical analysis looks for patterns in the past behavior of exchange rates.

Clearly it is based upon the premise that history repeats itself.

Thus it is at odds with the Efficient Markets

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At A the short-term moving average exchange rate is rising above the long –term moving average appreciation of the £

At D the short-term moving average exchange rate is falling below the long –term moving average depreciation of the £

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Levich Analysis MAE(S) Mean Average forecast Error

of a forecasting Service.

MAE(F) Mean Average forecast Error of the Forward exchange rate predictor.

R = MAE(S)/MAE(F)

If the forecast service is more accurate R< 1.

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Only 25 out of 104 are < 1!

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Performance of the ForecastersForecasting is difficult, especially with

regard to the future.

As a whole, forecasters cannot do a better job of forecasting future exchange rates than the forward rate.

The founder of Forbes Magazine once said:

“You can make more money selling financial advice than following it.”