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dealers will tend to quote a forward rate that is equal to s r* - r . Use of t
rate eliminates risk from future exchange rate changes as the forward rate is ag
even though the transaction takes place in (say) one year™s time.

Uncovered Interest Parity (UIP)
We can repeat the above scenario but this time assuming the UK corporat
is willing to take a guess on the exchange rate that will prevail in one year™s
when he converts his dollar investment back into sterling. If the corporate treas
neutral, he is concerned only with the expected return from the two alternative i
and he will continue to invest in the US rather than the UK until expected
equalised
+
S ; + i / S t = (1 rr)/(l+ r:>
or approximately:
- st = rr - r;

where sf+1= In S,+l. above relationship is the condition for equilibrium on
The
account under the assumption of risk neutrality. The UK corporate treasurer
he is taking a risk because the value of the exchange rate in one year™s time is
however, he ignores this risk when undertaking his portfolio allocation decisi
We could of course relax the risk neutrality assumption by invoking the C
the UK treasurer the risk-free rate is r and the expected return on the ˜round
investment in the US capital market is



The CAPM then predicts



where pi is the beta of the foreign investment (which depends on the covarian
the market portfolio and the US portfolio) and E&“+, is the expected return on
portfolio of assets held in all the different currencies and assets. The RHS o
a measure of the risk premium as given by the CAPM. Loosely speaking, re
like (11.7) are known as the International CAPM (or ICAPM) and this ˜glob
is looked at briefly in Chapter 18. For the moment notice that in the context
the CAPM, if we assume pj = 0 then (11.7) reduces to UIP.
by risk neutral speculators and that neither risk averse ˜rational speculators
traders have a perceptible influence on market prices.


11.2 PURCHASING POWER PARITY (PPP)
PPP is an equilibrium condition in the market for tradeable goods and for
building block for several models of the exchange rate based on economic fun
It is a ˜goods arbitrage™ relationship. For example, if applied solely to th
economy it implies that a ˜Lincoln Continental™ should sell for the same pr
York City as in Washington DC (ignoring transport costs between the two citie
are lower in New York then demand would be relatively high in New York
Washington DC. This would cause prices to rise in New York and fall in Wash
hence equalising prices. In fact the threat of switch in demand would be su
well-informed traders to make sure that prices in the two cities were equal. P
the same arbitrage argument across countries, the only difference being tha
convert one of the prices to a ˜common currency™ for comparative purposes.
If domestic tradeable goods are perfect substitutes for foreign goods and
market is ˜perfect™ (i.e. there are low transactions costs, perfect information
flexible prices, no artificial or government restrictions on trading, etc.), then ˜m
or arbitrageurs will act to ensure that the price is equalised in a common cu
PPP view of price determination assumes that domestic (tradeable) goods pri
subject to arbitrage and will therefore equal the price in domestic currency
foreign goods. If the foreign currency price is P* dollars and the exchange rat
as the domestic currency per unit of foreign currency (say sterling per dollar) is
price of a foreign import in domestic currency (sterling) is (SP*). Domestic p
a close (perfect) substitutes for the foreign good and arbitrageurs in the market
that domestic (sterling) prices P equal the import price in the domestic curren

P = SP* (strong form)

or
p=s+p*
+ P*
P =S (weak form)

or
Ap=As+Ap*

where lower case letters indicate logarithms (i.e. p = lnP, etc). If domestic
higher than P*S, then domestic producers would be priced out of the market. Al
if they sold at a price lower than SP* they would be losing profits since they b
can sell all they can produce. This is the usual perfect competition assum
applied to domestic and foreign firms.
imports) to domestically produced substitutes (or vice versa).
The real exchange rate is a measure of the price competitiveness or th
domestic relative to foreign goods. The price of imports into the domestic ec
the UK, is P*S in the domestic currency (sterling). This can be compared wit
of goods produced domestically in the UK, P, to give the real exchange rate
S = P*S/P
'
A similar argument applies had we considered the price of exportsfrom the U
of the foreign currency PIS and compared this with the price of competing g
US, P*. It follows from the definition of the real exchange rate that if PPP hol
real exchange rate or price competitiveness remains constant.
If goods arbitrage were the only factor influencing the exchange rate then th
rate would have to obey PPP:
s=p-p*
or
AS = A p - A p *
Hence movements in the exchange rate would immediately reflect different
inflation and the latter is often found to be the case in countries suffering f
inflation (e.g. some Latin American countries, economies in transition in East
and Russia around 1990). In contrast, one might expect goods arbitrage to w
imperfectly in moderate inflationary periods in complex industrial economies w
variety of heterogeneous tradeable goods. Hence PPP may hold only in the ve
in such economies.
There have been a vast number of empirical tests of PPP with only the
using the statistical technique of cointegration (see Chapter 20). Time does n
examination of these studies in detail and the reader is referred to a recent com
study by Ardeni and Lubian (1991) who examine PPP for a wide range of
of industrialised nations (e.g. USA, Canada, UK, France, Italy). They find n
that relative prices and the exchange rate are 'linked' when using monthly da
post-1945 period. However, for annual data over the longer time span of 1878
do find that PPP holds although deviations from PPP (i.e. changes in the rea
rate) can persist for a considerable time. Hence if we were to plot the PPP ex
denoted Sp where:
sp = P / P *
against the actual exchange rate S,then although there is some evidence from co
analysis that S, and Sp move together in the long run, we find that they can a
substantially from each other over a run of years. It follows that the real exc
is far from constant (see Figures 11.1 and 11.2).
The evidence found by Ardeni and Lubian reflects the difficulties in testin
run equilibrium relationships in aggregate economic time series even with a
span of data. Given measurement problems in forming a representative index o
! lM-O
0
$ 100.0
?
t
s
= 80.0
B
60.O



73 74 75 76 77 78 79 80 8 82 83 04 85 86 87 88 89 90 91
1
Year

and Real (+ + +
Figure 11.1 The Evolution of the Dollar-Pound Nominal ( -
)
Rate, 1973- 1991. Source: Pilbeam (1992). Reproduced by permission of Macmillan P

120.0

110.0

100.0

fa 90.0
-
g 80.0

5 70.0

60.0

50.0

40.0
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91
Year

and Real (+ + +) Ex
Figure 11.2 The Evolution of the Yen-Dollar Nominal (
-)
1973- 1991. Source: Pilbeam (1992). Reproduced by permission of Macmillan Press L


goods, it is unlikely that we will be able to get more definitive results in the
One's view might therefore be that the forces tending to produce PPP are r
although in the very long term there is some tendency for PPP to hold (see
Kaminsky (1991) and Fisher and Park (1991)). The very long run here could
years. Hence in the models of exchange rate determination discussed in Chap
is often taken as a Zong-run equilibrium condition.
resulting equation which explains domestic prices is



where y - 7= deviation of output from its natural rate, f = ˜wage push™ fa
exogenous growth in real wages, X p = growth in labour productivity. It follow
will hold if
++
f a2(y - 7) 0
bl(XW - X p ) =
Hence PPP holds either when output is at its natural rate or ˜wage push™ facto
or real wages grow at the rate of labour productivity. One can see that the
(11.15) involve rather complex, slowly varying long-term economic and so
forces and this may account for the difficulty in empirically establishing PPP
very long span of data.


11.3 INTERRELATIONSHIPS BETWEEN CIP, UIP AN
Forward Rate Unbiasedness and Real Interest Parity
If CIP and UIP hold simultaneously then this implies that the forward rate is a
predictor of the future spot rate (see Table 11.1). The latter condition is referr
forward rate unbiasedness (FRU) property:


Note that unbiasedness holds regardless of the expectations formation process
(i.e. one need not assume rational expectations) but it does require risk neutra

Table 11.1 Relationship between CIP, UIP, FRU, RIP and PPP
Forward Rate Unb
Covered Interest Parity (CIP)

fi - sI = ( r - r*)f fi = $;+I
Uncovered Interest Parity (UIP)
sF+, - st = ( r - r*),

Purchasing Power
Real Interest Rate Parity (RIP)
(Fisher Hypothesis)
r, - Ap: = r: - Apt *e




Real Exchange Rate
Cf = PI - p: - Sf

(i) As:+, = Efs,+1 - s,.
We could have started with FRU. Under risk neutrality, if (11.16) did not
would be (risky) profitable opportunities available by speculating in the forward
an efficient market (with risk neutrality) such profits should be instantaneously
so that (1 1.16) holds at all times. Whether (1 1.16) holds because there is active
in the forward market or because CIP holds and all speculation occurs in the s
so that UIP holds doesn™t matter for the EMH. The key feature is that th
unexploited profitable opportunities.
If UIP holds and there is perfect goods arbitrage in tradeable goods
periods then:




It follows that
r, - Ap;+l = r; - Ap;Tl
and hence
+ UIP jReal Interest Rate Parity (RIP)
PPP
Again, it is easily seen from Table 11.1 that if any two conditions from the
PPP and RIP are true then the third is also true.


11.4 SUMMARY
In the real world one would accept that CIP holds as here arbitrage is riskless.
tentatively accept that UIP could hold in all time periods since financial capit
mobile and speculators (i.e. FOREX dealers in large banks) may act as if th
neutral (after all it™s not their money they are gambling with, but the bank
one would then expect FRU to hold in all periods. In contrast, given rela
information and adjustment costs in goods markets one might expect PPP to
over a relatively long time period (say, 5-10 years). Indeed in the short run
in the real exchange rate are substantial. Hence even under risk neutrality (i.e.
one might take the view that expected real interest rate parity would only h
rather long horizon. Note that it is expected real interest rates that are equalised
if over a run of years agents are assumed not to make systematic errors when
price and exchange rate changes then, on average, real interest rates would b
in actual ex-post data.
The RIP condition also goes under the name of the international Fisher
It may be considered as an arbitrage relationship based on the view that ˜c
investment funds) will flow between countries to equalise the expected real ret
country. One assumes that a representative basket of goods (with prices p and
country gives equal utility to the international investor (e.g. a ˜Harrods™ ham
UK is perceived as equivalent to a ˜Sak™s hamper™ in New York). Internationa
then switch funds via purchases of financial assets or by direct investment to
he will have to exchange sterling for dollars at the end of the investment period
if PPP holds over his investment horizon then he can obtain the same purcha
(or set of goods) in the US as he can in the UK.
From what has been said above and one™s own casual empiricism about the
it would seem highly likely that CIP holds at most, if not at all, times. Ag
FOREX market are unlikely to ˜miss™ any riskfess arbitrage opportunities. O
might accept that it is the best approximation one can get of behaviour in
market™: FOREX dealers do take quite large open speculative positions, at
main currencies, almost minute by minute. FOREX dealers who are ˜on t
and actively making the market may mimic risk neutral behaviour. Provided
available (i.e. no credit limits) one might then expect UIP to hold in acti
FOREX markets. However, since information processing is costly one might
and even CIP to hold only in actively traded markets. In ˜thin™ markets (e.g. fo
rupee) CIP and UIP may not hold at all times. Because ˜goods™ are heterog
because here information and search costs are relatively high, then PPP is lik
at best, in the very long run. Hence so will RIP.
It is worth emphasising that all the relationships given in Table 11.1 are arb
librium conditions. There is no direction of causality implicit in any of these re
They are merely ˜no profit™ conditions under the assumption of risk neutrali
the case of UIP it cannot be said that interest differentials ˜cause™ expectations
in the exchange rate (or vice versa). Of course our model can be expanded
other equations where we explicitly assume some causal chain. For example,
assert (on the basis of economic theory and evidence about government beha
exogenous changes in the money supply by the central bank ˜cause™ changes
interest rates. Then, given the UIP condition, the money supply also ˜cause
in the expected rate of appreciation or depreciation in the exchange rate. The
change in the money supply influences both domestic interest rates and th
change in the exchange rate. Here ˜money™ is causal (by assumption) and th
in the UIP relationship are jointly and simultaneously determined.
In principle when testing the validity of the three relationships UIP, CIP
or the three conditions UIP, PPP and RIP we need only test any two (ou
since if any two hold, the third will also hold. However, because of data avai
the different quality of data for the alternative variables (e.g. Fr is observabl
frequently, but P and P are available only infrequently and may be subje
t :
number measurement problems) evidence on all three relationships in each se
investigated by researchers.


APPENDIX 11.1 PPP AND THE WAGE-PRICE SPIR
In the wages version of the expectations augmented Phillips curve, wage inflation, W,i
by price inflation, p , and excess demand (y - 7).To this we can add the possibility
may push for a particular growth in real wages xw based on their perceptions of their
There may also be other forces f (e.g. minimum wage laws, socio-economic forces
influence wages. It is often assumed that prices are determined by a mark-up on uni
A dot over a variable indicates a percentage change and x,, is the trend growth ra
productivity. Imports are assumed to be predominantly homogeneous tradeable goo
cultural produce, oil, iron ore, coal) or imported capital goods. Their foreign price is
markets and translated into domestic prices by the following (identity):

+s
P, = P*

Substituting (1) into (2) we obtain



Equation (3) is the price expectations augmented Phillips curve (PEAPC) which
inflation to excess demand ( y - 7 )and other variables. If we make the reasonable assu
in the long run there is no money illusion (al = 1, that is a vertical long run PEAPC)
homogeneity with respect to total costs ( b l + b2 = 1) then (3) becomes

P=---- bt [ f + bdxw - X,) + a2(y - ,)I + (P* + $)
1-61
If we assume that in the long run the terms in square brackets are zero then the long
influences on domestic prices are P* and S, and PPP will hold, that is:

P=i)*+$

A rise in foreign prices P* or a depreciation of the domestic currency (S rises) leads
domestic prices (via equation (2)) which in turn leads to higher wage inflation (via e
The strength of the wage-price feedback as wage rises lead to further price rises, etc.
the size of a and b l . Under the homogeneity assumptions a1= 1 and bl + 6 2 = 1, th
1
the feedback is such that PPP holds in the long run. That is to say, a 1 percent deprec
domestic currency (or rise in foreign prices) eventually leads to a 1 percent rise in th
domestic price index, ceterisparibus. Of course, PPP will usually not hold in the shor
model either because of money illusion a < 1 or less than full mark up of costs bl
1
because of the influence of the terms in square brackets in equation (4).
12
I
1
Testing CIP, UIP and FRU

In this chapter we discuss the methods used to test covered and uncovered int
and the forward rate unbiasedness proposition, and find that there is stron
in favour of covered interest parity for most maturities and time periods st
evidence in favour of uncovered interest parity is somewhat mixed although the
of making supernormal profits from speculation in the spot market seems remo
the unbiasedness of the forward rate generally find against the hypothesis and
some tests using survey data to ascertain whether this is due to a failure of ris
or RE. Since only two out of the three conditions CIP, UIP and FRU are indep
the simultaneous finding of a failure of both FRU and UIP is logically cons
tests discussed in this chapter may be viewed as 'single equation tests'. Mo
tests of UIP and FRU are possible in a multivariate (VAR) framework whic
account of the non-stationarity in the data. The latter test procedures are d
Part 5.


12.1 COVERED INTEREST ARBITRAGE
Let us consider whether it is possible, in practice, to earn riskless profits v
interest arbitrage. In the real world the distinction between bid and offer rat
interest rates and for forward and spot rates is important when assessing pot
opportunities. In the strictest definition an arbitrage transaction requires no
agent borrows the funds. Consider a UK investor who borrows U in the E
market at an offer rate rfo. At the end of the period the amount owing will be




where A = amount of borrowed (Es), C = amount owed at end of period (Es)
rate (proportionate) on Eurosterling loan and D = number of days funds are
Now consider the following set of transactions. The investor takes his U and
sterling for dollars at the bid rate Sb in the spot market. He invests these d
Eurodollar deposit which pays the bid rate r:. He simultaneously switches th
into sterling at the forward rate Fo (on the offer side). All these transactions
instantaneously, The amount of sterling he will receive with certainty at the en
Note that the convention in the USA and followed in (12.2) is to define ˜one y
days when reducing annual interest rates to their daily equivalent. The percen
return ER to investing &A in US assets and switching back into sterling on
market is therefore given by

[;:[ - [I+&]]
E R ( f + $) = 100 - = 100 - 1 + r ; -O
;]

which is independent of A. Looking at the covered arbitrage transaction from
view of a US resident we can consider the covered arbitrage return from mo
$s into sterling assets at the spot rate, investing in the UK and switching back
at the current forward rate. This must be compared with the rate of return he
by investing in dollar denominated assets in the US. A similar formula to th
(12.3) ensues and is given by

[S[ 3 [l+rGi]l
3 -
f ) = 100 - 1 + r ; -
ER($ +.



Given riskless arbitrage one would expect that ER(f + $) and ER($ + E) ar
.
Covered arbitrage involves no ˜price risk™, the only risk is credit risk due to
the counterparty to provide either the interest income or deliver the forward

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