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5 Efficient markets – a first encounter

5 Efficient markets – a first encounter

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The international setting

consider the important link between uncovered and covered interest parity, which involves

the concept of market efficiency.

Recall that, in introducing the idea of hedging in the forward market in Section 3.2,

the assumption was made that the forward rate on 1 January was equal to the spot rate

expected to prevail on 31 December. In order to illustrate what was meant by covered arbitrage, some value for the forward rate had to be assumed, and the expected spot rate was

certainly convenient, since it allowed us to use the same numerical examples in both cases.

Look back at the formal analysis in Equations 3.5–3.8. Nothing there required us to have

f = Δse (or F = Se). Covered interest parity could therefore still apply, even if we did not have

the forward rate equal to the expected spot rate.

None the less, it is obvious from comparing Equations 3.4 and 3.9 that the condition

f = Δse is far from arbitrary. In fact, since Equations 3.4 and 3.9 together imply that f = Δse,

it is obvious that covered and uncovered parity cannot both apply unless we also have

equality between the forward rate and the expected spot rate. Putting the matter differently, as long as we continue to assume risk neutrality, if the forward rate is not equal to the

expected spot rate, then either covered or uncovered parity has broken down, or both.

Now consider for a moment the situation of an individual market agent who, on

1 January, confidently expects the spot rate at the end of the year to be at a level different

from the one currently obtaining for forward foreign currency. Suppose, for example, that

the 12-month forward rate is \$1.00 = £0.50, and the agent is quite convinced that the rate

at the end of the year will be \$1.00 = £0.60.

If he is confident in his judgement, he will see himself as having the opportunity to profit

by a simple transaction in the forward market. All he need do is buy dollars forward, in

other words sign a contract to buy dollars at the end of the year at the current forward price

of £0.50 each, which he is so convinced will seem a bargain price on 31 December. If he is

correct in his forecast, then 12 months later, when he fulfils his promise under the terms of

the forward contract to buy the dollars at £0.50 each,15 he will be in a position to resell them

immediately at the end-of-year price prevailing in the spot market, £0.60 each – a profit of

£0.10, or 20% per dollar bought.

Of course, this strategy is risky, so if the investor is not risk-neutral he will require a risk

premium to persuade him to undertake the transaction, and £0.10 per dollar may not be

sufficient. However, if we maintain the fiction that investors are risk-neutral, we can say

that anyone who expects the spot exchange rate at some future period to be different from

the forward rate currently quoted for that period can profit by backing his judgement – that

is, by speculating.

If we can generalise the argument to the market as a whole, or, in other words, if we can

treat the market as if it were a single individual, then it follows that equilibrium will entail

a forward rate equal to the consensus view of the future spot rate. Otherwise, there will be

a net excess demand or supply of forward exchange, which will itself tend to move the rate

towards its equilibrium level. We shall henceforth make use of the following definition to

describe this situation:

Unbiasedness applies when the (3-, 6- or 12-) month forward rate is equal to the

spot rate that the market expects to see prevailing when the contract in question

matures.16

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Financial markets in the open economy

What we are talking about here is a particular example of a very general concept indeed:

market efficiency.17 For the moment, we shall take the opportunity to introduce the

following definition:

Efficient markets are ones where prices fully reflect all the available information.

There are, therefore, no unexploited opportunities for profit.

The definition seems a little vague, and, in a sense, so it should. What are we to understand by ‘fully reflect’ all information? That depends on the model of the market in question,

and its properties. By contrast, unbiasedness is a very clearly defined state and is in that

sense a special case of market efficiency. Unbiasedness implicitly assumes a particular market model, where the following conditions apply:

There are an adequate number of well-funded and well-informed agents in the currency

are well-defined.

There are no barriers to trade in the markets (that is, no exchange controls) and no costs

to dealing (no transaction costs).

Investors are risk neutral.

Unbiasedness and efficiency led to different conclusions about the potential for profiting

from arbitrage. If a market is efficient, investors cannot systematically make any profit over

and above their required compensation for bearing risk, whereas if it is unbiased they cannot even earn a risk premium. In the particular case of UIRP with no risk premium, it implies

that cross-country arbitrage will on average yield no profit.

What about the facts? Do they suggest that it is impossible to profit by interest arbitrage?

In the next section, we deal with this question.

3.6

We take an agnostic approach and address the straightforward question: has it been possible in practice to profit from (uncovered) interest rate arbitrage? In other words, looking

back in time, has there been a way of reliably making money by moving money around the

world?

This is not quite the same thing as asking the question: does UIRP fit the facts? In order

to interpret it as a test of UIRP, we would have to add some kind of assumption about how

expectations are formed and what information was available to investors at any point in

time, and these are matters we defer until Chapter 11.

Instead, we want simply to know whether it was possible to profit from the strategy

widely followed by investors in recent years of borrowing in low interest rate currencies and

converting the proceeds into high interest rate currencies in the hope that the exchange rate

would either remain unchanged or at least not move sufficiently to neutralise their gain on

the interest differential. This sort of strategy is known in the international financial markets

as a carry trade. For example, for many years the major global financial institutions, hedge

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The international setting

Figures 3.2 (a–f)  Exchange rate depreciation and lagged interest differential (US as

foreign country)

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Financial markets in the open economy

Figure 3.2  (continued)

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The international setting

funds etc. would target the Asian carry trade, raising large loans in yen and sometimes in

Hong Kong dollars and redepositing the funds in US dollars and pounds, which offered far

higher interest rates.

How well did it work?

Remember that UIRP implies that interest rates only differ because investors expect

the exchange rate to change, as we saw in Equation 3.4, so if, on average, investors’

forecasts are correct, this strategy will be unsuccessful, yielding a loss as often as a profit.

Yet the facts suggest otherwise, as we can see from Table 3.7 and Figure 3.2, which shows

exchange rate changes plotted against lagged interest rate differentials (annual averages

in each case).19

A number of points are clear from this data:

Exchange rates are far more volatile than interest rates. In fact, interest rates move only

slowly, and when they do move, there tends to be a high degree of international synchronisation.20 In fact, the standard deviation21 of annual exchange rate changes over the

years 1976 to 2011 is surprisingly uniform, varying from 9% for the yen to 11% for the

Canadian dollar, while for interest differentials the comparable figures are in the range

11/2 % to 3%. So on the face of it, whether or not forecasts based on interest rate differentials were right on average, it looks as though they were highly inaccurate, capturing very

little of the currency depreciation that actually occurred.

The carry trade was profitable to varying degrees for all six currencies considered here.

In the average year it earned an amazing 6% in New Zealand dollars, over 2% in pounds

and between 1% and 2% for the other currencies.

As Table 3.7 shows, these returns were very risky, however. They were associated with a

standard deviation of between 9% and 12% in every case except the Canadian dollar,

and as can be seen from columns (3) and (4), the ‘bad’ years generated extremely large

losses, sometimes larger in absolute terms than the returns in the best years. This raises

the question of whether the excess returns from this sort of arbitrage were in fact simply

a risk premium. In other words, it may be that UIRP fails to fit the facts because investors

Table 3.7  Returns to carry trade (in percent) 1975  –2012

AUSTRALIA

JAPAN

NZ

SWITZERLAND

UK

(1)

MEAN

(2)

S.D.

(3)

MIN

(4)

MAX

(5)

>0

(6)

AVGE (> 0)

(7)

AVGE (< 0)

(8)

CUMULATIVE

1.8

1.6

1.1

6.0

1.0

2.2

9.8

5.1

11.4

11.1

11.7

9.2

−21.3

− 6.1

−30.7

−18.6

−27.8

−16.4

19.1

12.4

20.6

26.7

22.3

17.4

59

57

57

68

59

62

4.8

2.9

5.1

8.2

5.1

5.0

−3.1

−1.2

− 4.1

−2.1

− 4.2

−2.9

1.3

1.5

0.4

5.5

0.3

1.8

Notes

Cols (1), (2), (3) and (4): mean, standard deviation, minimum and maximum annual carry trade return

Col (5): percentage of years when carry trade return was positive

Cols (6), (7): mean return in years when return was positive, negative

Col (8): annualised cumulative return over data period

Source: Thomson Reuters Datastream

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Financial markets in the open economy

are not risk neutral, as the theory assumes, but in fact risk averse, in which case we

need to ask whether the risk premium was of the right magnitude. As we shall see in

Chapter 13, the answer is controversial since it depends on how we think risk is priced

in the currency markets.

Ultimately, the carry trade was profitable over the last 35 years because there were

substantially more good years than bad years (column (5)) and because, in spite of the

catastrophic years, the average return in good years outweighed those in bad (compare

columns (6) and (7)). The net effect for a hypothetical investor who each year took either

a short or long position in his chosen currency, depending on whether it paid a higher or

lower interest rate than the dollar, was a cumulative annual return of between 0.4% on

the yen and 5.5% on New Zealand dollars.

Allowing for higher frequency trading, resetting the arbitrage at monthly or quarterly

horizons, and permitting our hypothetical investor to choose whichever currency pair had

the widest interest rate differential would generate even greater profits than these. In fact,

an important recent paper estimated the excess returns to the carry trade at over 5% even

after carefully allowing for transaction costs.

These anomalous results explain why the carry trade has been the subject of so much

research as well as lively controversy. We shall return to it at various points in subsequent

chapters.

By Anthony Fensom

18 June 2013

For years, the so-called ‘Mrs Watanabe’ and her brigade of Japanese households sold the

low-rate yen to buy higher interest-rate currencies, such as the Australian dollar. But with the

US Federal Reserve moving to end its easy money policy and ‘commodity currencies’ such

as the Aussie under pressure from lower rates and resource prices, the days of the carry

trade could be drawing to a close.

‘That [carry] trade works until it doesn’t. And the Fed has basically just said that’s not

going to work anymore,’ Goldman Sachs Asset Management partner Michael Swell told the

Australian Financial Review.

Prior to the global financial crisis, yield-seeking Japanese investors sought currencies

ranging from Brazilian real to New Zealand dollars to gain higher returns. With total savings

of 1,500 trillion yen (\$15.8 trillion) earning ultra-low returns at Japanese banks, Japanese

households have been keen buyers of ‘uridashi’ foreign currency bonds issued in Japan,

with emerging markets such as Turkey receiving some \$3.5 billion in uridashi flows in 2012.

The popularity of the yen carry trade among overseas investors led to an estimated US\$1

trillion being invested by early 2007. The Fed’s zero interest rate policy fostered the carry

trade, with hedge funds profiting from borrowing at low interest rates and speculating on

higher-yield investments, including corporate bonds and emerging market debt.

Yet signs that the party is over for the carry trade have sparked fears of massive unwinding by global investors.

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The international setting

The Australian dollar climbed as high as US\$1.10 in July 2011 partly as a result of the

carry trade, but has recently fallen to as low as US\$0.94 on the back of weakening commodity prices and interest rate cuts by the Reserve Bank of Australia.

Meanwhile, the Bank of Japan’s move to unleash aggressive monetary stimulus as part

of Japanese Prime Minister Shinzo Abe’s reflationary Abenomics policies has sparked

increased volatility for both the yen and Japanese bonds. Recent yen appreciation reportedly

forced a scramble by Japanese investors to unwind the carry trade, with the effects felt

around the world.

‘Margin call’

According to UBS’ Art Cashin, the yen’s strength and recent dive into bear-market territory

for the Nikkei Stock Average sparked major losses for US hedge funds, as noted by the

Wall Street Journal:

‘A couple of months back, when Mr Abe announced Abenomics (aggressive QE, purposeful increase in inflation, etc.), hedge fund wizards around the world flocked to what they saw

as a ‘no-brainer’ carry trade – short the yen (which QE should push lower) and buy the Nikkei

(which would benefit from higher inflation and more trade from the lower yen). Scores of

hedge fund managers reached for this too easy brass ring.

‘Those are just one (most popular) of the carry trades. There are many others. And, when

the yen spikes, it is like a margin call on each of those trades. We all painfully remember

[what] forced liquidations looked like and felt like in late ’08 and early ’09. That’s what

markets fear – possible random liquidations.’

Yet US hedge funds have not been the only ones to feel the pain. Recent volatility in the

‘commodity currencies’ of Australia, Brazil and South Africa has been blamed on investors

exiting their investments in such emerging markets, forcing spikes in bond yields.

‘I am finding how much leverage the hedge fund community has. Everyone seems to be

up to their earlobes in Mexican government debt,’ Loomis Sayles co-head of fixed income,

David Rolley, told the Australian Financial Review.

As the spread between higher and lower yield currencies has shrunk, leveraged traders

have been squeezed on both sides amid the Fed’s threatened ‘tapering’ of quantitative

easing.

‘With commodity prices under pressure and with growth slowing globally, there’s

concern about the higher-yielding commodity currencies. The [carry trade’s] best days are

behind it and it’s going to be much more of a trading market,’ said Pierpont Securities

strategist Robert Sinche.

3.7

We can now take the opportunity to tie up a loose end from the previous chapter relating to

the link between IRP and PPP. However, since the link is via another parity relationship, we

need first to deal with the analysis of how inflation impinges on interest rates in the domestic

economy.

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Financial markets in the open economy

3.7.1 Real interest rates and the Fisher equation

We start with an apparent digression on the mechanism underlying individual savings

decisions. Our initial standpoint is that of an individual economic agent in the setting

of his domestic market making a choice, again involving two periods – the present and

next year. In this stylised market, claims22 to future consumption baskets are exchanged

for an identical basket for immediate consumption, in a ratio that reflects demand and

supply at each date, now (period 0) and next year (period 1). The question we consider

is: how much should the individual consume this period, and how much consumption

should he be willing to defer to next year? In other words, what determines the willingness

to save?

In its most basic form, this simple question in applied consumer choice theory was settled

by Irving Fisher in the early twentieth century. The analysis shows that, subject to the standard assumptions of elementary choice theory,23 and in particular assuming that prices are

constant, the consumer will select a consumption-savings pattern that is determined, other

things being equal, by the rate at which the market allows him to exchange consumption

between the two periods. Other things being equal, the greater the future sacrifice required

per unit of present consumption, the less he will choose to consume this period and the

more next. The critical ratio24 is the number of units of future consumption offered in the

market in exchange for a unit of current consumption, which will be denoted by (1 + R).

For example, if at some point in time R is 5%, market conditions mean consumers have to

sacrifice 1.05 units of consumption next year, in period 1, in order to secure an extra unit

for immediate consumption. R is therefore the market premium current consumption commands over future consumption. (Notice that we can be more or less certain that R is always

positive.)

By now, it should be clear that R is actually an interest rate – in fact, the real interest rate.

It is real precisely because it is measured in units of consumption.

To appreciate the importance of inflation, or its absence, consider how R is determined.

Plainly, as usual in these models, the market price is the outcome of aggregating the choices

of consumers as a whole.25 If R is 5%, then it follows that it is possible to satisfy borrowers

in aggregate only if savers are offered the reward of a standard of living 5% higher next year

to compensate for the sacrifice required of them this year. If R were lower than 5%, then

there would be insufficient goods available for current consumption, i.e. unsatisfied

borrowers, because of an inadequate flow of savings. If R were higher than 5%, then there

would be too great a supply of sacrifice i.e. an excess demand for future consumption and

excess supply of current consumption by unsatisfied savers only too happy to defer satisfaction until next year.

Now consider how this constant-price scenario would be affected by inflation at the

rate of, say, 3% per annum. The answer is not entirely straightforward, because there can

be no inflation without money, and so far there has been no money in the analysis. Inflation

is by definition a rise in the price of goods relative to money, whereas the only price that

matters in this model is the price of period 0 goods in terms of period 1 goods. (Since the

whole analysis is in terms of physical units of consumption, it is often described as a barter

model.)

However, since R is determined by the preferences of individuals, there is no reason to

expect it to change simply because prices rise (or fall) – unless preferences are actually

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The international setting

affected in some way by the money units in which consumption is measured. We shall

assume here that people are immune to this particular form of irrationality, known as

money-illusion. In other words, we take for granted that agents are ultimately concerned

only with their access to real goods and services, and not with the number or denomination

of the banknotes involved in transactions.26

In order to cope with the introduction of inflation, imagine that what changes hands

between borrowers and savers in the market is not consumption goods directly, but claims

on goods – in other words, some form of money e.g. pounds. The sum of money, £P0, buys

a unit of current consumption, while £P1 buys a unit of consumption one year from today,

at period 1. How much of a premium per pound will savers need to be promised at period 1

in order to persuade them to sacrifice sufficient current consumption to satisfy borrowers?

In other words, how many more pounds will they need to be offered in order to keep their

behaviour unchanged? In physical terms, the answer remains the same: 5% more consumption, because, as has been explained already, there is no reason for the ‘exchange rate’

between current and future goods to have moved up or down. But the key point is that,

however many pounds were required to buy 1.05 units of consumption next year when we

were assuming zero inflation, the number of pounds required in the presence of inflation

will be greater by 3%. This is the case because, if P1 is 3% greater than P0, equilibrium

requires an exchange ratio of 1.05 × 1.03 = 1.0815. In other words, the premium on current

consumption in money terms, known as the nominal interest rate, must be the product of

1 plus the real rate and 1 plus the inflation rate:

1 + r = (1 + R)(1 + dp)

(3.12)

where dp denotes the inflation rate27 over the year: (P1 − P0)/P0. Again, unless the inflation

rate is extremely high,28 we can simplify the relationship to:

r = R + dp

(3.13)

which means that in the numerical example, the equilibrium nominal interest rate is

approximately 5% + 3% = 8%.

There is, however, one important modification needed to make the hypothesis realistic.

In the light of what has been said in the earlier sections of this chapter, the reader should

not need convincing that the inflation rate in Equation 3.13 ought to be replaced by the

expected inflation rate, since in practice the future price level, P1, is unknown and unknowable in the current period when the consumption-saving decision has to be made. So the

Fisher equation, as it is known to economists, can be written:

r = R + dpe

(3.14)

which says that the nominal interest rate – the only one we actually observe directly – is the

sum of the real interest rate and the market consensus expected inflation rate.

In fact, economics has seen decades of debate on the correct formulation and interpretation of the Fisher equation. We ignore most of these issues here, except to note that, once

again, the explanation given here ignores the risk premium. Once we allow for the fact that

the choice between consuming now and consuming in the future depends on expected

rather than actual inflation, there is always the risk that the decision-maker’s forecast may

turn out to be wrong. If the representative consumer is risk-averse, the Fisher equation will

have to incorporate a premium as a reward for bearing this risk. For present purposes, we

stick with the simple formulation in Equation 3.14, in other words we assume risk neutrality.

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Financial markets in the open economy

Notice that although the Fisher equation is supported by an undeniable logic, its

empirical validity is impossible to ascertain, because attempts to test it against the facts

run headlong into the joint hypothesis problem in its most acute form. Both the right-hand

side variables in Equation 3.14 are usually unobservable. Survey data have on occasion

been used as a measure of expected inflation, though they are often unsatisfactory for the

purpose,29 and there are few direct measures of the real rate.30 None the less, and perhaps

because, unlike PPP, it is so difficult to refute, the Fisher equation tends to be accepted by

default in economics.

3.7.2 Purchasing power parity and the real exchange rate

This brings the digression to an end. To see why it was worthwhile, suppose Equation 3.14

applies to the domestic economy, while a similar Fisher equation applies to the foreign

country:

r* = R* + dp*e

(3.14′)

Notice we are allowing for the possibility that any or all of the variables are different in the

foreign country. Clearly Equations 3.14 and 3.14′ imply that the interest rate differential is

given by:

r − r* = (R − R*) + (dpe − dp*e)

(3.15)

But unless there is something to prevent arbitrage between the securities markets of the two

countries, we know from UIRP in Equation 3.4 that, with risk neutrality, the observed or

nominal interest rate differential on the left-hand side of Equation 3.15 is equal to the

expected rate of depreciation. It follows that:

dse = (R − R*) + (dpe − dp*e)

(3.16)

which tells us that the rate of depreciation of, say, the dollar against the pound over any

time period (e.g. one year) is the sum of the difference between UK and US real interest

rates for one-year loans and the difference between UK and US expected inflation rates

during the 12 months.

Now consider the real interest differential. Suppose, given my (and the market’s) expecta­

tions with regard to inflation rates in the UK and USA, I believe the real interest rate to be

higher in America. If I can possibly capture the higher real rate in the USA by lending to

American borrowers (buying US securities etc.), I will do so. The opposite will be the case

if I believe that real rates are higher in Britain, i.e. if R > R*. These statements can be made

with confidence because, as we have seen, for risk-neutral agents real rates are the ultimate

determinants of savings behaviour, since they measure the reward for saving in the ultimate

currency: real consumption units or standard of living.

This argument can lead to only one conclusion. In the absence of barriers to cross-border

capital movements, real rates should be the same in both countries, so that R = R* and we

are left with the proposition that:

dse = dpe – dp*e

(3.17)

This is sometimes called PPP in expectations. Its implications are straightforward. It

says that PPP applies not to actual exchange rates and relative inflation rates but to the

market’s expectations of these variables. According to this view, PPP is a relationship

between unobservables, rather than observables, so that any apparent failure to fit the

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The international setting

facts can always be interpreted as the outcome of using the wrong measure (or model) of

the expected rate of depreciation on the one hand or the expected inflation differential on

the other.

Note that we can rewrite Equation 3.17 in terms of the (log of the) expected real

exchange rate. By definition, since d(log Q) = dq = ds + dp* − dp, Equation 3.17 implies

dqe = 0

(3.18)

so that the change in the expected real exchange rate is zero, or q is expected to remain

constant. In time series terms, Equation 3.18 obviously means that:31

e

qt+1

= qt

(3.19)

so the typical agent in the market expects tomorrow’s real exchange rate to be the same as

today’s. This conclusion is more dramatic than it might look at first glance.32

In terms of time series statistics, there is a whole class of models consistent with Equa­

tion 3.19, in particular the so-called random walk process mentioned in Section 2.7. This

argument persuaded a number of researchers that the apparently random nature of the

real exchange rate movements they observed was not such a gloomy conclusion after all,

but simply a consequence of UIRP on the one hand and real interest rate parity on the other.

An alternative rationalisation of Equations 3.17 and 3.19 would be to say that if trade in

goods takes time, then arbitrageurs will operate not on the basis of actual price differentials

but on the basis of their forecasts of price differentials when they complete their trades.

There are two apparent weaknesses in this argument. First, deviations from PPP have far

too long a life to be rationalised in this way. As we have seen, recent research suggests a

half-life of three or four years, which is long even by the standards of physical capital, let

alone consumption goods. Second, for reasons too far removed from the subject of this book

to be covered here, real interest rates are likely to be determined by more than simply consumer tastes, such as the return on capital in each country, and all the many factors that

affect it.33 The process by which real interest rates are equated is therefore likely to be more

complex than is suggested here, and almost certainly anything but instantaneous. In fact, it

is not at all obvious that it will be any faster in practice than the process of arbitrage in the

goods market, and it may be substantially slower.

Finally, it is to be hoped that by this stage the relationship between IRP, PPP and the

Fisher equation is clear in one respect at least. Suppose, as a benchmark case, all economic

agents know the future price levels in the two countries and next year’s exchange rate with

absolute accuracy. Then, in this unlikely scenario, the two Fisher equations mean we can

replace Equation 3.15 with:

r − r* = (R − R*) + (dp − dp*)

(3.20)

and using UIRP (for this reason often called the open Fisher equation) gives, in place of

Equation 3.16:

ds = (R − R*) + (dp − dp*)

(3.21)

dq = R − R*

(3.22)

or:

from which we can see that movements in the real exchange rate reflect changes in the real

interest rate differential. If we are happy to rely on real interest rates being driven into

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