ñòð. 30 
â€˜dealingâ€™ quotes on the spot and forward rates and the two interest rates. There
many studies looking at possible profitable opportunities due to covered intere
but not all use simultaneous dealing rates. However, Taylor (1987, 1989a) ha
the CIP relationship in periods of â€˜tranquillityâ€™ and â€˜turbulenceâ€™ in the foreig
market and he uses simultaneous quotes provided by foreign exchange and mo
brokers. We will therefore focus on this study. The rates used by Taylor rep
offers to buy and sell and as such they ought to represent the best rates (h
lowest offer) available in the market, at any point in time. In contrast, rates
the Reuters screen are normally â€˜for information onlyâ€™ and may not be act
rates. Taylor uses Eurocurrency rates and these have very little credit counte
and therefore differ only in respect of their currency of denomination.
Taylor also considers brokerage fees and recalculates the above returns
assumption that brokerage fees on Eurocurrency transactions represent abou
1 percent. For example, the interest cost in borrowing Eurodollars taking
brokerage charges is
ri + 1/50
While the rate earned on any Eurodollar deposits is reduced by a similar amo
ri  1/50
Taylor estimates that brokerage fees on spot and forward transactions are so
they can be ignored. In his 1987 study Taylor looked at data collected every
reexamined the same covered interest arbitrage relationships but this time in
â€˜market turbulenceâ€™ in the FOREX market. The historic periods chosen wer
devaluation of sterling in November of that year, the 1972 flotation of sterling
that year as well as some periods around the General Elections in both the U
US in the 1980s. The covered interest arbitrage returns were calculated for m
1, 2, 3, 6 and 12 months. The general thrust of the results are as follows:
In periods of â€˜turbulenceâ€™ there were some profitable opportunities to be m
0
The size of the profits tend to be smaller in the floating rate period than
0
rate period of the 1960s and became smaller as participants gained exp
floating rates, post 1972.
The frequency, size and persistence over successive time periods of profitab
0
opportunities increases as the time to maturity of the contract is lengthened
say there tended to be larger and more frequent profit opportunities when co
12month arbitrage transaction than when considering a onemonth covere
transaction.
Let us take a specific example. In November 1967, Elm arbitraged into do
have produced only E473 profit, however just after the devaluation of sterling (i
of turbulence) there were sizeable riskless returns of about E4000 and E8000
arbitrage at the threemonth and sixmonth maturities, respectively. Capital c
UK sterling outflows) which were in force in the 1960s cannot account for th
since Eurosterling deposits/loans were not subject to such controls. Clearly th
not always perfectly efficient in that riskless profitable opportunities are not im
arbitraged away. In periods of turbulence, returns are relatively large and
persist over a number of days at the long end of the maturity spectrum, while
end of the maturity spectrum profits are much smaller.
The reason for small yet persistent returns over a onemonth horizon may w
to the fact that the opportunity cost of tradersâ€™ time is positive. There may not
traders in the market who think it is worth their time and effort to take advant
small profitable opportunities. Given the constraint of how much time they ca
one particular segment of the market they may prefer to investigate and exe
with larger expected returns, even if the latter are risky (e.g. speculation on
spot rate by taking positions in specific currencies). It may even be more wor
them to fill in their dealersâ€™ pads and communicate with other traders rathe
advantage of very small profitable opportunities.
The riskless returns available at the longer end of the market are quite
represent a clear violation of market efficiency. Taylor puts forward several hy
to why this may occur, all of which are basically due to limitations on the cred
dealers can take in the foreign exchange market.
Marketmakers are generally not free to deal in any amount with any c
that they choose. Usually the management of a bank will stipulate which o
it is willing to trade with (i.e. engage in credit risk), together with the max
preference for covered arbitrage at the short end of the market since funds are
relatively frequently.
Banks are also often unwilling to allow their foreign exchange dealers
substantial amounts from other banks at long maturities (e.g. one year). Fo
consider a UK foreign exchange dealer who borrows a large amount of doll
New York bank for covered arbitrage transactions over an annual period. If th
wants dollar loans from this same New York bank for its business customers
thwarted from doing so because it has reached its credit limits with the New Yo
so, foreign exchange dealers will retain a certain degree of slackness in their c
with other banks and this may limit covered arbitrage at the longer end of th
spectrum.
Another reason for selfimposed credit limits on dealers is that Central B
require periodic financial statements from banks and the Central Bank may c
shortterm gearing position of the commercial bank when assessing its â€˜sou
foreign exchange dealers have borrowed a large amount of funds for covere
transactions, this will show up in higher shortterm gearing. Taylor also notes
of the larger banks are willing to pay up to 1/16th of 1 percent above the mar
Eurodollar deposits as long as these are in blocks of over $loom. They do so
order to save on the â€˜transactions costsâ€™ of the time and effort of bank staff. He
recognises that there may be some mismeasurement in the Eurodollar rates h
hence profitable opportunities may be more or less than found in his study.
Taylor finds relatively large covered arbitrage returns in the fixed exchange
of the 1960s, however in the floating exchange rate period these were far le
and much smaller. For example, in Table 12.1 we see that in 1987 there were
no profitable opportunities in the onemonth maturities from sterling to dollars
at the oneyear maturity there are riskless arbitrage opportunities from dollars in
on both the Monday and Tuesday. Here $ l m would yield a profit of around $1
oneyear maturity.
Taylorâ€™s study does not take account of any differential taxation on intere
from domestic and foreign investments and this may also account for the ex
persistent profitable covered arbitrage at maturities of one year. It is unlikely t
participants are influenced by the perceived relative risks of default between sa
ling and Eurodollar investments and hence this is unlikely to account for arbitr
even at the oneyear maturities. Note that one cannot adequately test CIP betw
Table 12.1 Covered Arbitrage: Percentage Excess Returns (1987)
1 month 6 month 1
(E + $) $1
+ f) + $)
Monday 8/6/87 ($ (& ($ + f) (f +
(12 noon) 0.043 0.016 0.097 0.035 0.117
Tuesday 9/6/87 0.075 0.064 0.247 +0.032 0.192
(12 noon)
Source: Taylor (1989), Table 3.
arbitrage that ensures CIP. This is in part reflected in the fact that if one
bank for a forward quote it calculates the forward rate it will offer by usin
relationship. That is to say it checks on the values of rf, r,$ and S, and then qu
F , calculated as
where the bidoffer distinction has been ignored. Looking at potentially profit
using data on which marketmakers may have undertaken actual trades is clear
way of testing CIP. However, many early studies of CIP used the logarithm
mation and ran a regression:
The null of CIP is
Ho:a=O, b = l
and if there are transactions costs these may show up as a # 0. Since (r$  rf)r
nous then 2SLS or IV rather than OLS should be used when estimating (12.8)
these regression tests of CIP have a number of acute problems. The regression
do not distinguish between bid and offer rates and do not explicitly (or care
account of transactions costs. Also if the logarithmic form is used then (12.8)
approximation. In early studies the rates used are not sampled contemporane
these reasons these regression tests are not reported (see Cuthbertson and Ta
and MacDonald (1988) for details).
1 . UNCOVERED INTEREST PARITY AND FORWARD
22
UNBIASEDNESS
With perfect capital mobility (i.e. foreign and domestic assets are perfect
instantaneous market clearing, zero transactions costs) and a zero risk premiu
neutrality) then the uncovered speculative return is zero:
 S,1  d,l =0
s;
where d,l = r,1  r:l, the uncovered interest differential and s, = In S,. Equa
holds if the spot market is â€˜efficientâ€™ and hence eliminates knowable oppor
supernormal profit (providing there is a zero risk premium). Assuming RE, s
hence:
+ +
S, = st1 d,1 U,
Equation (12.10) has the testable implication that the current spot rate depend
previous periodâ€™s spot rate and the uncovered interest differential, with a unit
on each variable. The orthogonality property of RE implies that no other varia
at time t  1 or earlier should influence sf (other than sfl and d,l).
effective rate (July 1972February 1980) found that the interest rate coeffic
included as independent variables, have unit coefficients; but lagged values of
in the exchange rate and a measure of credit expansion are also significant.
RE forecast error ur is not independent of all information at time t  1 or ear
joint hypothesis of zero risk premium and the EMH fails; similar results we
for the E/$ rate. Cumby and Obstfeld (1981) using weekly data (July 1974Jun
six major currencies against the dollar found that lagged values of the depende
(sf  stl  d f  l ) of up to 16 weeks are statistically significant for all six
The RE forecast error is therefore serially correlated, contrary to part of the
hypothesis.
+
Our interim conclusions concerning the validity of UIP RE is that not all
the maintained hypothesis hold and this may be due either to a (variable) risk
or a failure of RE or risk neutrality.
Testing FRU
First some stylised facts. A graph of the 30day forward rate F and the actu
led by 30 days Sr+l for the $/DM(using weekly data) is shown in Figure
obvious that the broad trends in the $/DMactualfiture spot rate are picked
current forward rate. This is the case for most currencies since the root m
of the prediction error, Sr+l  F f , is of the order of 22.5 percent against
.4907
1
WDM

.3128
24 February 19
5 January 1973
Figure 12.1 Forward Rate (30 Days) and Spot Rate (Led Four Weeks): DollarDe
Source: Frankel (1980). Reproduced by permission of the Southern Economic Journal
by Fo
l/aFD dEGZ7
 
n
n
Deutschmark 2.10 2.12
1.
French franc
2. 2.21 2.09 11
Pound sterling 2.18 2.23
3.
Italian lira 2.53
4. 2.76 1
Swiss franc
5. 2.5 1 2.61
1
Dutch guilder 2.10 2.0
6.
Japanese yen
7. 1.84 1.84
Source: Frankel (1980), Southern Economic Journal, April.
Date Period: weekly data 5 July 19744 April 1978 (193 data points).
for the currencies shown in Table 12.2. This is particularly true for those cur
experience a trend in the exchange rate (e.g. Japan and the UK). The fourweek
in the spot rate in column 2 of Table 12.2 is about 22.5 per cent for most
The forward market does not predict changes in the spot rate at all accurately
For example, only 2 percent of the changes in the $/DMrate are predic
forward rate (column 3). In some cases this percentage is negative indicati
forward rate is a worse predictor than the contemporaneous spot rate. The la
these prediction errors does not necessarily imply a failure of market efficien
alternative predictors of S t + l , given information at time t , may give even larg
errors.
It is clear from Figure 12.1 that a regression of St+l on F , will produce
serially correlated residuals since F , provides a run of under and overpredicti
If the $/DMfuture spot rate S,+l is lagged one period, the solid line would
right and would nearly coincide with F , . Hence the current forward rate ap
more highly correlated with the current spot rate than with the future spo
suggests that variables or news that influence S , also impinge upon F , .
If the forward market conforms to the EMH and speculators are risk neutr
forward rate is an unbiased predictor of the (logarithm of the) expected futur
sp, 1 If we incorporate an additive risk premium rp, and invoke RE then
*
+k+l
= $+I
Sf+1
Risk neutrality implies r p , = 0. The risk premium is the expected profit ma
speculator and may also capture any transactions costs (e.g. manpower costs)
with the forward contract. RE implies:
Er(ut+l IQ) = 0
which includes the assumption that u,+l is serially uncorrelated. The simplest
to make concerning the risk premium is that it consists of a positive consta
â€˜white noiseâ€™ random element v,:
+
r p , = a vt
of the form:
+ Bft + v A + Er+l
=a ˜
sr+l
where At is a subset of the complete information set available at time t. If t
true we expect a < 0, /3 = 1, y = 0 and Er to be serially uncorrelated. 121 may
relevant economic variables including values of the lagged dependent variab
or lagged forecast errors ( S t  ft1). A slightly weaker test of the EMH assu
+
+
and tests for p = 1 in the regression st+l = a Bfr E r , which excludes A,.
There is an important econometric point to be made here. E t + l in the
equation (12.18) is equal to uf+l  vr, but vr influences the risk premium rp,
equation (12.13). Hence Er+l and f, in equation (12.18) are correlated, and OL
inconsistent estimator. This is the socalled â€˜errors in variablesâ€™ problem in eco
â€˜Correctâ€™ (i.e. asymptotically unbiased) estimates may be obtained using an in
variables technique such as 2SLS. (A correction to the covariance matrix an
dard errors because of the presence of heteroscedasticity can be made usin
estimator.)
Alternative formulations of the unbiasedness property to equation (12.18)
times used. For example, unbiasedness also implies that the forward premiu
(f  s) is an unbiased predictor of the future change in the spot rate. Subtract
both sides of (12.13) and using (12.14):
B = 1 and that
A test of unbiasedness is then a test of a = y1 = 0, is whi
Er
the regression:
+ Y1Ar + Er+1
+ B(f  s)r
Asr+l = a
Some early studies used the â€˜levels versionâ€™ (12.18) of the unbiasedness
However, if sf+l and fr are 1(1) the usual test statistics in (12.18) are invalid.

equation (12.20) we see that if (s, f ) are 1(1) but st+l and fr are cointegrated
+
tegration parameter (1, l), that is st+l = fr Et+l with Er+l I ( 0 ) then the v
(12.19) are I ( 0 ) . The latter carries over to (12.20) if the variables in At are eith
I(1) but cointegrate among themselves or if y1 = 0. In general (12.20) is to b
to (12.18) under the assumption of cointegration between s and f , since the er
stationary and hence the usual test statistics are valid,
Early Tests
Frankel (1982a) reports a regression of the change in the spot rate Asr+l on t
premium/discount (f  s)t and other variables known at time t (e.g. Asr). He
to reject the null hypothesis that a = y1 = 0, @ = 1 and E t is not serially corr
equation (11.27)). However, the â€˜powerâ€™ of this test is rather low since on
accept the joint hypothesis a = y1 = B = 0. The latter result should come as
since we noted that the forward premium/discount explains little of the change
for the set of currencies will be contemporaneously correlated (i.e. E(Eif,E j t ) #
Zellnerâ€™s (1971) seemingly unrelated regression procedure (SURE) yields mo
estimates of the standard errors of the parameters a and j?. For example, M
using a SURE estimator, finds that for quarterly data over the period 1972(1)
six major currencies against the dollar only sterling and the Canadian dollar pa
hypothesis that a = 0, B = 1. Rejection of the null hypothesis appears to be
to a # 0 rather than /?# 1, and is more severe when Zellnerâ€™s estimation meth
compared with the more favourable results in his OLS regressions. However
does not address econometric problems associated with the nonstationarity o
Notwithstanding the above empirical results, the balance of the evidence
single equation studies is that there is a strong negative correlation between t
premium and the subsequent change in the exchange rate (e.g. Fama (1984)
and Roghoff (1983)). In fact the coefficient on the forward premium fp, =
often nearer 1 than the â€˜unbiasedness valueâ€™ of +l. This could be due to a
rational expectations or of risk neutrality. Following Fama (1984) we now m
assumption of RE while relaxing the assumption of risk neutrality to see if the
be the cause of the â€˜failureâ€™ of FRU.
12.3 FORWARD RATE: RISK AVERSION AND RATIO
EXPECTATIONS
Risk averse speculators in the forward market will require compensation
premium payment) for holding a net forward position in foreign exchange. H
fr = rpr + $+I
 sr, fpr = fr  s t , and rpr is an adhoc a
where = Ersr+l, As;+1 =
premium which may be time varying. Under RE equation (12.22) becomes:
fr  S t + l = r p ,  Er+l
where Er+l = st+l  s:+l is the RE forecast error. Suppose we now assume a v
â€˜modelâ€™ for the risk premium, namely that it depends (linearly) only on t
premium fpr:
rpt = 81 + BlfPr
Under the null of RE but with a time varying risk premium given by (12.24
substituting (12.24) in (12.23) (Fama, 1984):
If the risk premium depends on the forward premium then we expect /?I
however, that equation (12.25) embodies a rather restricted form of the ris
+ B2fPr +
 st = 82 &t+1
St+l
We expect /32 = 1 for unbiasedness and a time invariant risk premium im
constant. After some tedious algebra (see Appendix 12.1) Fama (1984) is ab
that the difference between B1 and 82 is given by:
>I/ var<fpt>
 8 2 = [var(rpt> var(As;+,
B1
 var (expectations)]/ var( f p f )
= [var (risk premium)
A positive value for (/I1  82) indicates that the variance of the risk premium
than the variance of expectations about s;+˜. However, it can be seen from (12
rp, is highly variable then the forward premium will be a poor predictor of th
change in the spot rate and this is what we find in the usual â€˜unbiasedness sing
regressionâ€™ (12.26). Therefore 81  82 provides a quantitative guide to the rela
tance of the time variation in the risk premium under the maintained hypo
RE holds.
Studies of the above type (e.g. Fama 1984) which estimate equations (
(12.26) usually find that 8  8 2 is positive. The latter usually arises becau
1
cally 8 2 is less than zero while is usually positive. Fama (1984) finds
 82 of 1.6 (for Japanese yen) to 4.2 (for Belgian francs). Famaâ€™s result
indicates that variations in the forward premium cause variations in the ris
(see equations (12.22), (12.24) and (12.25)) while 8 2 < 0 implies that unbiase
not hold (see equation (12.26)). Thus the overall conclusion from this work is
the null of RE, the FRU proposition fails because the (linear additive) risk
â€˜highlyâ€™ time varying.
It is worth repeating that a limitation of the above analysis is that the poten
varying risk premium r p , is assumed to depend only on the time varying forwar
fpr. Also the risk premium is an adhoc linear addition in equation (12.13)
based on any wellfounded economic theory.
The weakness of the above analysis is that it assumes that RE holds s
violation of the null hypothesis is attributed to a time varying risk premium
require is a method which allows the failure of FRU to be apportioned between
of RE and variations in the risk premium.
Forward Rate: The Separation of RE and Risk Using Survey Data
+
As we have seen the joint null of â€˜FRU R E + risk neutralityâ€™ is rejected
number of empirical studies (using a variety of regression techniques). By us
data on agentsâ€™ expectations of the future spot rate, Frankel and Froot (1986)
one can apportion the rejection of the null between that due to a failure of R
due to a failure of risk neutrality. Consider the usual forward premium regres
+ Bfpt + E f + l
Ast+1 = a
It is easy to show that
P = 1  BRE SRN
where
ñòð. 30 