10/1/2015multinational corporate finance prof. r.a. michelfelder 1 outline 5: purchasing power...

04/19/23 Multinational Corporate Finance Prof. R.A. Michelfelder

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Outline 5: Purchasing Power Parity, Interest Rate Parity, and Exchange Rate Forecasting (Bond

Markets, Good Markets, Interest Rates, and Inflation

5.1 Introduction5.2 Arbitrage and the Law of One Price5.3 Primer on Money Demand, Money Supply, Inflation, and Interest

Rates 5.4 Purchasing Power Parity (PPP)5.5 Fisher Effect5.6 Interest Rate Parity5.7 Relationship Between Future Spot and Forward Rates5.8 Exchange Rate Forecasting


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5.1 Introduction

• Discusses Relationships Among Countries Bond Markets, Goods Markets, Interest Rates, Inflation, and Exchange Rates

– How are goods prices and asset returns linked globally?

– How do we determine the equilibrium value of an exchange rate?

– How are inflation rates, interest rates, and exchange rates linked?

– How does domestic monetary policy affect inflation, interest rates, and exchange rates?

– How are forward and future spot rates linked?

– How can we use these links to forecast exchange rates?


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5.2 Arbitrage and the Law of One Price

• Arbitrage: simultaneous purchase and sale of same asset or goods in different markets to profit from rate of return or price differences

• Law of One Price: exchange-rate-adjusted prices of identical assets or goods are the same globally, except for transactions costs

• Profiteering arbitrageurs prevent large differences in asset returns or goods prices

– They buy low and sell high to the point where there is almost no difference (no profit) between asset returns or good prices across countries

– Buying in the low price/return country increases prices/returns and selling in the high price/returns country reduces prices/returns.

• The key to understanding exchange rates and interest rates is how they adjust to inflation – remember ultimately that all currencies and bonds are assets and

we wish to hold them only for the consumption that they represent.


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5.2 Arbitrage and the Law of One Price

• Arbitrage: simultaneous purchase and sale of same asset or goods in different markets to profit from rate of return or price differences

• Law of One Price: exchange-rate-adjusted prices of identical assets or goods are the same globally, except for transactions costs– That is, the price of an identical good is the same across countries, after

you adjust the exchange rate for differences in inflation.

– The Law of One Price does not hold in the short-run as exchange rates do not equal inflation differences

– If PPP held all of the time, then the Law of One Price would hold and a bottle of Coca Cola would cost you the same in other countries as the US.


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5.3 Primer on Money Demand, Money

Supply, Inflation, and Interest Rates The rate of inflation is dependent upon the level of output and the money supply in an economy:

Md =P (aY – br) (money demand is a “+” function of price level, output and a “– ” function of interest rates)where Y = output, r = nominal interest rate, P = price level, Md and Ms refer to money demand, supply respectively

Ms = Md (always equilibrium in money market)Ms = P (aY – br)Ms = P (aY- b r) if Y cannot respond immediately to a reduction to

interest rates, lower r increase aggregate demand relative to aggregate supply (output), leading to higher inflation, higher future inflation and interest rates turn around and start rising and end up


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5.4 Purchasing Power Parity(PPP)

PPP: exchange rate level that equates prices and price levels worldwide; Absolute Version of PPP is:

EP

Ph

f0

The PPP E0 is the exchange rate that maintains the same price of a good in two currencies (Ph and Pf refer to home and foreign prices indices)


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5.4 Purchasing Power Parity

• E.g. “Big Mac” Index:• Big Mac costs $2.43 in US and /£1.90 in UK, the

PPP dollar price of pound should be:EPPP = $2.43/£1.90 = $1.28 per £

If the actual spot e = $1.61, then the £ is overvalued by:E E

EP P P

P P P

0 6 1 2 8

2 80 2 5 7 8

$ 1. $ 1.

$ 1..


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• The expected future spot rate is $1.28 for the UK pound and the expected depreciation is 25.78% but when will that correction occur– Exchange rates can be away from PPP levels for years

– Refer to Handout Exhibit 4.2, The Big Mac Index for under/overvalued e’s (p.95)

E E

EP P P

P P P

0 6 1 2 8

2 80 2 5 7 8

$ 1. $ 1.

$ 1..


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• Relative PPP:

Where et is future spot rate in time t and ih and if are home and foreign expected inflation rates

• Re-arrange by multiplying both sides by e0:

E

E

i

it h

t

ft

0

1

1

( )

( )

E Ei

ith

t

ft

0

1

1

( )

( )


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• Relative PPP:

Where Et is future spot rate in time t and ih and if are home and foreign expected inflation rates

• Re-arrange:

e EE E

Ei it o

h f

% 0

E Ei

ith

t

ft

0

1

1

( )

( )


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• Relative PPP: the % change in e should be equal to the inflation differences between the two countries in the same time period

%E

ih-if

4%

4%

2%

2%


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• Empirical Evidence:– Holds in the long-run, over many years but not

in the short-run (as we will find out later, capital flows due to interest rate differences across countries cause E’s to be away from equilibrium for years)

– E’s have a tendency to revert to their PPP levels – See Handout Exhibit 8.5 for data evidence


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• E.g. PPP Rate Calculations and Comparisons:

– US $ price of Israeli Shequels 2000 – 2003


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5.5 Fisher Effect

• Fisher Effect (named after Irving Fisher, early 20th century financial economist):– nominal interest rates have two components

• a real rate of return as a price to forgo present consumption for future consumption

• Expected inflation premium to compensate for reduction in purchasing power of loaned funds

(1+r) = (1+rreal)(1+iexp.) or:

r = rreal+ iexp+ rreal iexp

Use as approximation assuming that both are relatively small so that rreal iexp is a small value : r = rreal+ iexp


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5.5 Fisher Effect

r = rreal+ iexp+ rreal iexp

If rreal= 3% and iexp =3%, then the nominal rate will be

.03 + 0.001 + .03 x .001 = 0.03103 or 3.103%

2/20/2009 13 week T-Bill discount rate: 0.3%Current US annual inflation: 0.1% (December 2007 –

December 2008) therefore real interest rate on money market is:

0.3% - 0.1% = 0.2% currently, therefore interest rates are too low to be sustainable


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5.5 Fisher Effect

• The generalized Fisher effect is the result of interest arbitrage whereby investors exploit interest rate differences net of inflation differences:

Or, rh – rf = ih - if

Currencies with high rates of inflation should have higher interest rates than currencies with low inflation rates.

1

1

1

1

r

r

i

ih

f

h

f


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5.5 Fisher Effect

Empirical evidence:

is consistent with the notion that most of the variation of interest rates across countries can be explained by inflation differences.

See Handout Exhibit 4.4 (p.101)


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5.5 Fisher Effect

• Since a rise in home inflation relative to foreign country will cause the PPP value of an exchange rate to rise: E

E

i

it h

t

ft

0

1

1

( )

( )

• Since a rise in home inflation will cause home interest rates to rise relative to foreign country:

1

1

1

1

r

r

i

ih

f

h

f


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5.5 Fisher Effect

• Then we combine the two effects to get the International Fisher Effect:

The single period version is:

( )

( )

1

1 0

r

r

E

Eh

t

ft

t

( )

( )

1

11

0

r

r

E

Eh

f

r rE E

Eh f 1 0

0Re-written:


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5.5 Fisher Effect

This condition shows that currencies with high interest rates are expected to depreciate relative to currencies with low interest rates.

If rh – rf < 0, then e1 is expected to fall, meaning that the future spot rate is expected to be lower than the current spot rate, or, the domestic currency is appreciates due to its low inflation.

r rE E

Eh f 1 0

0


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5.5 Fisher Effect

• The International Fisher Effect is not supported in the short-run by empirical evidence:– Changes in the nominal interest rate can be due to changes in:

• Real interest rate

• Relative inflationary expectations

• These will have opposite effects on currency values:

• Real interest rate rise at home: home currency appreciates

• Rise in relative inflation at home: home currency depreciates

• Therefore, there is no stable relationship between changes in nominal interest rates and exchange rate changes


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5.6 Interest Rate Parity

With interest arbitrage, investors move funds across countries monetary centers to exploit the “+” interest differential with an offsetting forward transaction to cover exchange rate risk.

During the process, the positive interest difference between monetary centers is reduced to the forward premium on the currency.

This is covered interest arbitrage and the result above is also known as “covered” interest parity.

r rF E

Eh f 1 0

0


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• Covered interest arbitrage: capitalizing on the interest rate differential between 2 countries while covering exchange risk– the process where arbitragers move funds from

one country to another for higher interest rates,– leads to the equality of interest rates, after

adjustment for expected depreciation of the foreign currency


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• E.g.:– Invest $800,000– Dollar price of Pound: $1.60– 90-day forward dollar price of pound: $1.60– 90 day interest rate in US: 2% (8% annually)– 90 day interest rate in UK: 4% (16% annually)

• Convert $800k into £500k: 800,000 x 1/$1.60 = £ 500k• Deposit £500k in UK Bank:

– In 90 days you will have £500,000 *1.04= £520,000 – Simultaneously sell £520,000 forward @ $1.60 for $832,000 =

£520,000 x $1.60Interest arbitrage profit is $832k - $816k (2% on $800k)= $16,000


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• Impact of covered interest arbitrage:

Activity Impact

1.Use dollars to buy pounds at spot rate

Upward pressure on the spot rate for the pound

2.Forward contract to sell pounds forward

Downward pressure on forward pound rate

5.Invest funds from US in UK Upward pressure on US interest and downward pressure on UK interest rates


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• Interest rate parity: once market forces cause interest rates & exchange rates so that covered interest arbitrage is no longer profitable, this is interest rate parity.

• At parity, the forward rate differs from the spot rate to offset the interest rate difference between 2 currencies


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5.7 Relationship Between Future Spot

and Forward Rates • Forward rate reflects expectations about the future

spot rate:Ft + risk premium = E(Et)

therefore Ft < E(Et)

Ft = forward rate for time t delivery

E( ) = expected value

Et = future (time t delivery) spot rate for a currency


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5.7 Relationship Between Future Spot

and Forward Rates • Forward rate reflects expectations about the future spot rate:

Ft + risk premium = E(Et)

therefore Ft < E(Et)

The forward rate is the best predictor of the future spot rate but will generally be less than the expected spot rate due to the existence of a risk premium by speculators who accept the risk.


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5.8 Exchange Rate Forecasting

• PPP, forward rates, and long-term interest rates can provide short- and long-term forecasts of exchange rates.

• PPP represents what long-term equilibrium should be.

• Forward rates are the best, yet biased (due to risk premium) predictor of future spot rates

• Forward contract periods are limited but longer-term interest rate differences can be used to provide long-term FX rate forecasts.

10/1/2015multinational corporate finance prof. r.a. michelfelder 1 outline 5: purchasing power...

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