2011 EXAMINATION QUESTION & ANSWERS (2)

2011 EXAMINATION (2)

Question 2(a) In what ways do the roles played by arbitrageurs, hedgers and speculators in the foreign exchange market differ from one another and yet have similar outcomes?

ANSWERS (a)

Arbitrageurs seek to earn risk-free profits by taking advantage of differences in exchange rates and/or interest rates among countries.

Hedgers, mostly multinational firms, engage in forward contracts to protect the home currency value of various foreign currency-denominated assets and liabilities on their balance sheets.

Speculators expose themselves to risks associated with exchange rate changes, buying and selling in the spot and forward markets.

However, the outcomes are similar in the sense that their activities tend to move the exchange rates towards equilibrium

2011 EXAMINATION (2)

Question 2 (b) Suppose that the euro (EUR) is offered at

USD 1.3714 and GBP is sold at EUR 1.1737 in London, while the pound sterling (GBP) is bid at USD 1.6115 in New York. Do you see an arbitrage incentive here? If an arbitrageur were to convert USD 1 million into euro in Frankfurt, sell the euro for sterling in London and then re-sell sterling for the dollar in New York, what would be the profit in this example? How will this arbitrage affect the exchange rates in the three markets?

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ANSWERS (b)

Step 1: USD 1 million is converted into EUR 729,181.86 in Frankfurt

Step 2: EUR 729,181.86 is converted into GBP 621,296.67 in London

Step 3: GBP 629,296.67 is converted into USD 1,001,728.42 in New York

PROFIT: USD 1,728.42

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ANSWERS (b)

EUR strengthens against USD in Frankfurt

GBP strengthens against EUR in LondonUSD strengthens against GBP in New

York

No arbitrage incentive if : EUR 1 = USD 1.3724 GBP 1 = EUR 1.1749 GBP 1 = USD 1.6126

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Parity Conditions in International

Finance

Lecture 5INTERNATIONAL FINANCE

(FN6053/5053)

PARITY CONDITIONS IN INTERNATIONAL FINANCE

If markets are not impeded, there is a set of equilibrium relationships that should apply to product prices, interest rates and spot and forward exchange rates.

There are 5 theoretical economic relationships :Purchasing power parity (PPP)Fisher effect (FE) International Fisher effect (IFE) Interest rate parity (IRP)Unbiased forward rate (UFR)

These relationships are known as parity conditions.

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PARITY CONDITIONS INTER. FINANCE (cont’d)

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Forward Exchange

Rate

Spot Exchange

Rate

Nominal Interest Rate

Inflation Rate

IRPFE

UFR PPPIF

F


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In competitive markets, with numerous buyers & sellers, rational participants, low-cost information, exchange-adjusted prices of identical tradable goods and financial assets must be within transactions costs of equality worldwide – i.e. equal prices after adjusting for exchange rates.

Otherwise, there is opportunity for arbitrage. Similarly, risk-adjusted expected returns on financial assets

in different markets should be equal. The common denominator of these parity conditions is the

adjustment of the various rates and prices to inflation i.e. inflation effects

PPP : relationship between inflation and nominal exchange rates

An important concept underlying these parity conditions is the law of one price.

FE : relationship between inflation and interest ratesIFE : relationship between interest rates and exchange

rates


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According to modern monetary theory, inflation is the logical outcome of an expansion of money SS in excess of the growth in real output.

A further link in the chain relation of money SS growth, interest rates and exchange rates, is the notion that money is neutral. That is money should have no impact on real variables.

E.g. a 10% in money SS, relative to DD for money should lead to a price increase of 10%.

So, though in quantity of money should lead to in prices and exchange rate (in nominal, not real, terms), the terms of trade (Px/Pm) shouldn’t . i.e. domestic goods for foreign goods: both numerator and denominator affected evenly).

This is the idea behind PPP, IFE and FE.


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If international arbitrage enforces the law of one price, then the “exchange-rate” between home currency and domestic goods must equal the exchange rate between home currency and foreign goods.

In other words, a unit of HC should have the same purchasing power worldwide. If it gains (loses) purchasing power at home, it will gain (lose) purchasing power abroad too.

This is the idea behind PPP. first stated by Gustav Cassel in 1918.

Since, then PPP is widely used as one indicator of equilibrium exchange rate by Central Banks.

At a corporate financial management level, PPP is often used for a whole range of purposes from forecasting exchange rates, deciding which currency to borrow in or lend in to plant locations.


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PPP

2 versio

ns

Absolute Version

Relative Version

Ignores transportation costs, tariffs, quotas etc (product differentiation thus less relevant).More relevant


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The relative version of PPP states that the exchange rate between the HC and any FC will adjust to reflect in the price levels of the 2 countries.E.g. if inflation in Japan = 2% Inflation in US = 6%

Then according to PPP, Yen should appreciate against US$ by approximately 4%.

Mathematically if ih = home inflation

if = foreign inflation

e0 current exchange rate : et exchange rate at time in future.

then: tf

tht

i

i

e

e

)1(

)1(

0

…………………..(1)


e.g. if US inflation (h) = 5%, German inflation (f) = 3%

e0 is = $ 0.75 per DM then, the exchange rate 3 years from now is:

The one-period version of equation (1) above is commonly stated as:

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7945.0$)03.105.1(75.0 33 e

f

h

i

i

e

e

1

1

0

1……………………… (2)


By subtracting 1 from both sides of the above equation, and if if is relatively small then we get:

This means that the in exchange rate during a period should equal the inflation differential for that same period.

In effect, PPP says that currencies of countries with higher inflation should devalue/depreciate against currencies of countries with relatively lower inflation.

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fh iie

ee

0

01 ……………………(3)


Graphically, PPP can be shown as :

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% in HC value of F.C.

PPP Parity line

Home has 3% higher inflation so FC value by 3% i.e. HC depreciates

% Inflation differential of home country to foreign country.

5

4

3

2

1

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

-1

-2

-3

-4

-5

PPP: THE PARITY LINE IMPLICATIONS

Every point on the parity line represents a certain real exchange rate (RER)

In other words, RER remains unchanged as one moves up or down the parity line: depreciation offset by inflation

Above the parity line (i.e. to the left) HC is undervalued, as HC depreciation is excessive relative to inflation differential

Below the parity line (i.e. to the right) HC is overvalued, as depreciation is insufficient to wash off the inflation effect

Along the parity line, no change in competitiveness Above the parity line, gain in competitivenessBelow the parity line, loss of competitiveness

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Should the % in exchange rate not equal the % inflation difference then there’s possible arbitrage opportunity in a world where PPP holds.

PPP Exchange rate s should cancel out in the foreign price level relative to domestic prices.

*These offsetting movements should have no effect

on the relative competitive positions of domestic or foreign firms.

**Thus, changes in the nominal exchange rate may

be of little or no significance in determining the true effects of currency on a firm and a nation.

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in competitiveness will depend on the real exchange rate.

E.g. if you had higher inflation of 5%, and as a result your currency by 5%, you shouldn’t be anymore competitive as a result of the devaluation why should you? The real exchange rate hasn’t .

If PPP holds perfectly, then real exchange rates do not , (holding other things constant).

The real exchange rate is the nominal exchange rate adjusted for inflation.

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The real exchange rate e1 at time t is :

If PPP holds perfectly:

Equals e0 or current real exchange rate same as before since PPP ensures that all inflation differential is washed off.

*When PPP doesn’t hold or there’s deviation from PPP then real exchange rate s Thus, the competitive position changes.

**E.g. if your inflation is 5% higher but your currency only depreciates 3%, then ceterus paribus your currency is overvalued, and you lose competitiveness.

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tf

th

tt i

iee

)1(

)1(1

tf

th

t i

iee

)1(

)1(0


Empirical Evidence of PPP The strictest from of PPP that there’s one price for all

goods everywhere obviously fails empirical tests. However, there is very clear evidence of a relationship

between relative inflation rates and s in nominal exchange rates.

The general conclusion from empirical studies is that PPP holds up well in the long run but not as well over shorter time periods.

Adjustment to PPP occurs but usually with a lag. One difficulty in empirical studies of PPP is that the price

indices CPI, WPI etc. are often constructed and measured differently in different countries.

Still, there are dangers in attributing too much importance to a deviation from PPP, because PPP is not a complete theory of exchange rate determination there are other things – like (IRP, GNP growth expectations, uncertainties etc).

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A GENERALIZED VERSION OF PPP

A major problem of PPP is that it suggests that PPP should hold for all types of goods.

A generalized version of PPP differentiates between traded & non-traded goals.

Goods

While traded goods are susceptible to international competition, non-traded goods like haircuts (services), houses (products) are not.

*Thus, PPP is more likely to hold for tradeables than non-tradeables.

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Traded Tradeables

Non Traded

A GENERALIZED VERSION OF PPP

Since PPP only holds for tradeables, the proportion of tradeables to non-tradeables can affect PPP as a determinant of exch. rates.

For example, if there is increased productivity in the non-tradeables sector, then the relative price of tradeable is lower, implying a PPP appreciation in exchange rate.

Suppose labour (non tradeable) becomes more productive, the amount of tradeable goods (say cars) increases since SS while DD is the same, price of cars , so less inflation HC appreciates.

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TESTING PPP: MEASUREMENT PROBLEMS

In using indices like WPI etc., it is mostly tradeables that get captured , non–tradeables often are not.

Weights differ even within CPI between products and between countries

Quality differences among similar prods. across countries.

Base period of index differ between countries

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EMPIRICAL EVIDENCE ON PPP

Frenkel (1981) shows that PPP tends to perform better for countries that are geographically close to one another and where trade linkages are high. E.g. countries within EC. (transport costs low, less impediment, similar products – thus the strong PPP).

*Still, prolonged deviations from PPP does happen.Exchange rates have been more volatile than PPP

dictates.PPP tends to hold better in the long run than short run.High inflation countries like Brazil, Argentina, Israel etc.

– saw rapidly declining currencies implying PPP is a major determinant of exchange rates.

Overall, PPP tends to hold better for tradeables than non-tradeables.

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THE FISHER EFFECT

According to Irwin Fisher, market interest rates fully adj. to in inflation since, lenders would want to be compensated for loss of purchasing power.

i.e. the nominal interest rate is made up of the real interest rate and the inflation rate:

or

**The generalized version of the Fisher effect asserts that real returns are equalized across countries thru arbitrage i.e. real r1

h = real r1f .

**Currencies with higher rates of inflation should bear higher interest rates than currencies of lower inflation rates.

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raterealnom ii .inf111 …………………….. (1)

1.inf11 raterealNom ii

THE FISHER EFFECT

If real returns were higher in one currency than another, capital would flow from the lower to higher currency. In the absence of govt. intervention, the arbitrage will continue until expected real returns are equalized.

Thus, in equilibrium, it should follow that the nominal interest rate differential will approximately equal the inflation rate differential or

if rf and rh are relatively small, then this exact relationship can be approximate by

Nom rh – nom rf = infl.h – infl.f ……………………..(3)

dif. in nom int = dif. in infl. rates

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h

h

f

h l

rnom

rnom

.inf1

.inf1

.1

.1

……………………….(2)

THE FISHER EFFECT

Generalized Version: Currencies with high rates of inflation should bear higher interest rates than currencies with lower rates of inflation

Example: Given 4% inflation in US and 7% inflation in UK, Fisher effect says nominal interest rates should be 3% higher in UK than in US

If nominal interest rate differential is less than 3% in UK, funds would flow from UK to US

If nominal interest rate differential is more than 3%, funds would flow from US to UK

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THE FISHER EFFECT

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Parity Line using Equation (3) above

Since, HC has 2% higher inflation than FC, it has 2% interest

% Inflation differential, home relative to foreign country.

% Interest differential in favour of Home Country

5

3

2

1

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

-1

-2

-3

-4

-5

FISHER EFFECT IMPLICATIONS

Every point on the parity line represents equality between inflation differential and interest rate differential: no reason for to funds to move from one country to the other, as interest differential is offset by inflation differential

Above the parity line (i.e. to the left), interest rate differential exceeds inflation differential: funds would flow into the home country

Below that parity line (i.e. to the right), interest differential is less than inflation differential: funds would move out of the home country

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THE FISHER EFFECT

Empirical studies of FE appear to show evidence consistent with the hypothesis that most of the variation in nominal interest rates across countries can be attributed to differences in inflationary trends.

In today’s world of integrated financial markets, it is unlikely that significant real interest differentials could last for long especially due to “HOT MONEY”.

In an integrated capital market (integrated with other international markets) the domestic real interest rate depends on both what is happening within and outside the country.

It also means that, as a result, real interest rates in other countries like US and Japan could also , if there is an in worldwide DD for funds.

Capital market integration has homogenized markets around the world, eroding much - if not all- of the real interest rate differentials between comparable domestic and off-shore securities.

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THE FISHER EFFECT So what could account for the real interest rate differentials

that still exist for some currencies:a) Can’t be totally attributed to currency risk, since this type

of risk is unsystematic and can therefore be diversified away.

So, more likelyb) Differences in tax policies, (difference in taxation rates on

savings etc) and / or imposition of regulatory barriers to capital flows and consciously presenting varying risks to would-be investors e.g. CB may stop domestic banks paying interest on hot money meant for currency speculation

c) Political risks e.g. currency controls, expropriations etc. Given reason (b) and (c) one could explain why real interest rates in

developing countries can exceed those in developed countries and still not be arbitrageable.

**Finally, when comparing / analyzing currencies for int. dif. be careful to use “appropriate” comparison since there are many quoted interest rates.

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THE INTERNATIONAL FISHER EFFECT (IFE)

IFE is really the result you get when you combine the results of PPP and FE.

Recall that

So IFE is essentially

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tf

th

i

i

e

ePPP

)1(

)1(

0

1

t

f

th

tf

th

i

i

r

rFE

)1(

)1(

1

1

)1(

)1(

0 f

ht

r

r

e

e t


Again, if rf is relatively small, then equation (4) can be rewritten as;

Graphically, the IFE can be shown as;

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00

ee

err fh

Expected in HC value of FC

Interest* dif. in favor of HC

4

4-4

-4

•Since, HC has 4% inflation, that means, it would have 4% higher nominal interest rate (FE), thus, according to IFE, the HC depreciates 4% against FC (since FC in HC value by 4%)

•IFE also implies that interest dif. bet. 2 currencies is also an unbiased predictor of future exchange rates.

*Thus IFE combines all we know from PPP, FE and UFR too.

IFE& CAPITAL MOVEMENTS

Every point on the parity line represents equilibrium where interest rate differential is just offset by currency depreciation: no arbitrage incentive to shift funds

Above the parity line (i.e. to the left), expected currency depreciation (forward discount) exceeds interest rate differential: there is arbitrage incentive for funds to move from home to foreign country

Below the parity line (i.e. to the right), expected currency depreciation (forward premium) is less than interest rate differential: there is arbitrage incentive for funds to move from foreign to home country

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The implication of IFE is that the expected return from investing at home (1+rn), should equal the expected return

from investing abroad Example:

Invest at home => (1+rn)

Invest abroad

Suppose: US infl. =4%,nom. r = 8%

UK infl. =8%, nom. r =12% Invest at home in US = 8% return

Invest in UK

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of eer /)1( 1

(1+rƒ)

∆ in each rate

12% interest earned

-4% exch. loss

Total Ret = 8

In effect, IFE states that currencies with low interest rates should appreciate relative to currencies with high interest rates.

INTERNATIONAL FISHER EFFECT (IFE)

Equilibrium position: interest differential in favour of home country (say 4%) is just offset by anticipated depreciation of the home currency (i.e. 4%)

If home currency is expected to depreciate by only 3%, then funds will flow from foreign to home country

Conversely, if home currency is expected to depreciate by >4%, then funds will flow from home to foreign country

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EMPIRICAL EVIDENCE

There is clear evidence that currencies with high interest rates tend to depreciate and those with low interest rates tend to appreciate.

Empirical studies have also found evidence that interest differentials do anticipate currency s; especially a long-run tendency for these interest differentials to offset exchange rate s.

Thus, at any point in time, currencies bearing higher interest rates can reasonably be expected to depreciate relative to currency with lower interest rates.

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INTEREST RATE PARITY (IRP)

The movement of funds across countries is an “arbitrating” (equalizing) factor in exchange rates.

According to IRP, the currency of country with a lower interest rate should be at a forward premium in terms of a currency with higher interest rate.

So, IRP really connects the forward rate to spot rate.

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In efficient markets the % forward premium or discount should equal the % interest differential. IRP

Where f, is the forward rate, e0 is spot. IRP ensures that the return on a “hedged” or

“covered” foreign investment will equal the return from a domestic investment of similar risk.

In effect, IRP states that high interest rates from a currency are offset by forward discount and that low interest rates are offset by forward premiums.

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0

1

)1(

)1(

e

f

r

r

f

n


Start with USD 1 million in New YorkConvert USD 1 million to euros at EUR 0.740 per

USD (or USD 1.351 per EUR) into EUR 740,000Invest EUR 740,000 in Frankfurt at 1.5% for 90

days, yielding EUR 751,000 in 90 daysAt the same time sell EUR 751,000 forward at a

rate of EUR 0.73637/USD (USD 1.358 per EUR) for delivery in 90 days (EUR at premium)

Receive USD 1,020,000 after 90 days [gain = USD 20,000]

Alternatively: Invest USD 1 million New York, for 90 days at 2% and receive USD 1,020,000 in 90 days

PARITY EXISTS, SO NO ARBITRAGE OPPORTUNITY!

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IMPLICATIONS OF IRP

Currencies with low relative nominal interest rates would have forward premium.

Currencies with high relative nominal interest rates would face forward discounts.

Forward premium or discount = nominal interest differential at equilibrium when parity is established

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COVERED INTEREST ARBITRAGE: EXAMPLE

Suppose £ interest in London 12% $ interest in New York 7% £/$ spot rate = $1.75 per £ And 1 year forward £/$= $1.68 per

£These mean the forward discount on £ in $

terms is 4%

So, investing in £ would give net return of 8% 12% - 4% = 8% higher than domestic return of 7%

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1.75 - 1.68 x 100 = 4.166%

1.75

COVERED INTEREST ARBITRAGE

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Action CFO CF/yr

1. Borrow $ 1 mil in NY @7% +$1,000,000 -1,070,000

2. Immediately convert $1mil to £ @ spot rate = $1.75 per £

-$1,000,000+£

571,428.57

3. Invest the amt (£) in London at 12% i

-£ 571,428.57

+£640,000

4. Simultaneously sell £ forward for £640,000 @ $1.68 (forward rate)

-£ 640,000+

$1,075,200

5. Profit by delivering on forward and repaying initial $ borrowing.

0 $5,200

COVERED INTEREST ARBITRAGE

As more and more of this type of arbitrage takes place, as £ are bought spot and sold forward, the spot-forward differential will widen until it meets/equals the interest differential.

As funds move from US to UK, nominal interest rate will rise in US and fall in UK, narrowing the US-UK interest rate differential until it meets/equals the sterling-dollar spot-forward differential.

IRP holds when there is no more arbitrage incentive or opportunity for covered – interest arbitrage.

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THE CARRY TRADEBorrowing a currency bearing low interest rate

and investing in a currency bearing high interest rate.

Example: borrowing yen in Japan at rates close to zero and selling the yen to invest in high-yielding assets such as US treasury or European bonds (in trillion dollars a year).

Danger is that small, steady returns (say, 1% int. rate on yen loan and 5% int. earned in dollar investments: spread of 4%) may be more than offset by sudden, large dollar depreciation against yen: “picking up nickels in front of a steamroller”!

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THE CARRY TRADE & THE INTERNATIONAL FISHER EFFECT

According to the IFE, carry trades should not yield a predictable profit, because the interest rate differential between two currencies should equal the rate at which investors expect the low-interest rate currency to appreciate against the high-interest currency.

But, the opposite may happen with low-interest yen depreciating (large capital outflows) and high-interest dollar appreciating (large capital inflows), providing more incentives for carry trades (interest rate spread plus exchange rate gains)

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RELATIONSHIP BETWEEN FORWARD RATE AND FUTURE SPOT RATE

Given econ. fundamentals (e.g. interest rates etc.), if a currency is expected to devalue, then it is only logical that the forward rate would be falling faster than the spot.

So, here the forward currency rate will be at a discount to the current spot rate.

The forward rate will be lower by the % of expected devaluation.

Why is the forward rate at a discount to current spot rate? Because the future spot rate is expected to be lower. i.e.

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11 ef which means that the current forward rate is an unbiased estimator of the future spot rate.


Suppose 90-dayforward rate for DM is DM1 = $0.40. This means the expected spot rate 90 days from now would be 1 DM = $0.40

The above equation can be converted into % as follows: minus one on both sides

Which really means the forward differential equals the expected change in the exchange rate.

It should be noted that market efficiency requires that people process information and form reasonable expectations, it does not require that f1 = e1

Only that f1 is an unbiased estimator of e1

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0

0

0

0

1

e

eee

e

f


e1 could end up being higher or lower, but not systematically higher or lower.

If f1 = e1 where’s the risk premium is associated with making a commitment today by taking a position in forward f1. Note: f1 = e1 , risk prem. = 0.

The argument for an expected risk premium of zero has to do with fact that currency risk is diversifiable, and

therefore not a systematic risk that needs to be compensated.

Whether the risk prem. is 0 is an empirical not theoretical question.

Most empirical studies show, that the risk premium is about 0 i.e. forwards are indeed unbiased estimators.

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TAKEAWAYSPPP is about the theoretical relationship between

relative price levels (inflation rate differential) and spot exchange rates

FE points to the connection between interest differential and inflation differential

IFE combines PPP and FE so as to underscore the relationship between interest rate differential and exchange rates

IRP relates to relationship between interest differential and the forward spread (forward premium or forwad discount)

UFR links future spot rates to current forward rates where the latter serve as an indictor of the direction in which spot rates are likely to move in the future

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TAKAWAYS (cont’d)

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The absolute version of PPP states that price levels should equal worldwide when expressed in common currency; in other words, absolute PPP and the law of one price hold

The relative version of PPP states that ER between home currency and foreign currency will adjust to reflect changes in the price level of the two countries

According to PPP, a 3% higher domestic inflation relative to another country (inflation differential) is just offset by a 3% appreciation of the foreign currency

The nominal exchange rate (NRE) refers to the rate at which one currency is exchanged for another in the spot market

TAKEAWAYS (cont’d)

The real exchange rates (RER) is NER adjusted for changes in the relative purchasing power of each country since some base period

RER remains unchanged if changes in NER are fully offset by changes in the relative price levels between 2 countries

The distinction between NER and RER has important implications for forex risk measurement and management

The Fisher equation suggests that if the required real return is 3% and expected inflation is 6%, then the nominal interest rate will be 9%

the Fisher Effect asserts that the nominal interest rate differential will roughly equal the inflation differential

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According to the Fisher effect, currencies with high rates of inflation should bear higher interest rates than currencies with lower rates of inflation

The international Fisher effect states that currencies with low interest rates are expected to appreciate relative to currencies with high interest rates (high interest rates imply high inflation rates)

Interest rate parity theory posits that the currency of the country with a lower interest rate should be at a forward premium vis-à-vis the currency of the country with higher rate (likewise, higher interest rate implies forward discount for the currency)

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Funds flow from one country to another to take advantage of higher returns abroad after adjusting for forex risk through forward market transactions (meaning that interest differential is greater than the forward discount)

Funds also flow from high-interest country to lower interest country, if the forward premium on the currency exceeds the interest differential

International capital movements will go on until the forward spread equals the interest differential

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Spot rates and forward rates tend to move in tandem, with the link between them based on interest differentials

Pressure from the forward market is transmitted to the spot market, and vice versa

The current forward rates may well become future spot rates

Forward rates serve as unbiased predictors / estimators of future spot rates

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2011 EXAMINATION (Q 3)

Question 3:(a)Show diagrammatically with explanations how inflation

affects nominal exchange rate, leaving real exchange rate unchanged, in the framework of the purchasing power parity (PPP) theory. [6 marks]

(b)Explain the direction in which funds would move between New York and London if: (i) the return on a GBP instrument is 11% in London and that on a comparable USD instrument in New York is 7%, given a 3% forward discount on GBP, (ii) the return on a GBP instrument is 10% in London and that on a comparable USD instrument in New York is 6%, given a 4% forward discount on GBP, and (iii) the return on a GBP instrument in 6% in London and that on a comparable USD instrument in New York in 7%, given a 2% premium on GBP. [6 marks]

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END OF LECTURE 5

THINK OUT OF THE BOX!59

2011 EXAMINATION QUESTION & ANSWERS (2)

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