Efficiency in the Forward Foreign Exchange Market: Weekly Tests of the Australian/US Dollar Exchange Rate

January 1984-March 1987* COLM KEARNEY and RONALD MACDONALD

Departmmr of Economics, Univrrsity of Dundee

school of BI(siRcs and T ~ ~ l o g y , university of wesrmr Sydney

This paper cuunines the rekrtionrlup which exists between the spot and forward AuuaLanlUS D o h crchange rater for om-, k- and &-month contmcts using weekly hta over the penod January

a component due to rid and one which is due to a f o m d g mor, and thir anatysis is suggestive of a time-varying kk premirun

1 9 8 4 - 1 U ~ ~ h 1987. l’k p a ~ r r splits rhc f o w d pnmium into

I Introducbbn Since the move to a system of floating exchange

rates for the major industrialized countries in the early 1970s a great deal of m a r c h attention has been focused upon the efficiency of foreign exchange markets. I In th is paper we examine the efficiency of the Australian fomgn exchange market since the inception of the Australian dollar’s float in December 1983. More specifically, we examine the relationship which exists between the spot and forward AustralianAJS dollar exchange rates for one-. three- and six-month contracts over the period January 1984 to March 1987. Previous work by Sharpe and Weston (1984) and Tease (1986) have investigated this issue 011, mpectively, prc- and post-float Australian data and obtained mixed results. Our study, however, has a number of novel features. First, we test for the unbiasedness

* Assistance from the R e s t m Bank of Australia’s Economic and Financial Rercarch Fund E/UNSW/8701 is gratefuly acknowledged. John Hillier provided excellent research usist?ace. We arc ?Is0 indebted to Rofcssor Alan Woodland and two anonymous refems for their helpful comments on an earlier draft of this paper. The usual disclaimer applies

I Useful surveys of this extensive literature arc provided by Hodrick (1987). MacDonald (1988) and MacDondd and Taylor (1989).

of the forward exchange rate, as a predictor of the future spot rate, using appropriate stationary inducing transformations Second, we use a decomposition developed by Fama (1984) to separate the (ex post) forward premium into a component due to risk and one which is due to a forecasting emor. However, in contrast to Fama, who effectively drops observations to create a non- overlapping data base, we utilize an overlapping data base and an estimation technique which is robust to the serial cornlation imparted by such data and to conditional heteroscedasticity.

The remainder of this paper is organized as follows. In Section II we outlined a framework for testing the efficiency of the forward market for foreign exchange. The data are described in Section Ill where some descriptive statistics are also presented. Our regression based tests of market efficiency arc described in Section IV.

I1 Testing Market E m n c y and the Risk Premium In this section we outline some implications of

the efficient markets hypothesis (EMH) for the behaviour of spot and forward exchange rates. Following Fama (19761, an asset market is said to be efficient if prices fully and instantaneously reflect all available information so that no profit

237

238 THE ECONOMIC RECORD SEPTEMBER

oppomnities are left unexploited. The efficient markets hypothesis (EMH) is a joint hypothesis that agents form their expectations rationally (i.e. they avoid knowable forecasting errors given cumntly available information), while rapidly arbitraging away any deviations ofexpected returns which are consistent with supernormal profits. The latter component of the joint hypothesis requires low transaction costs, but it is equally consistent with either risk neutrality or risk aversion on the part of economic agents.

Let s, be the spot price of the Australian/US dollar exchange rate (hereafter denoted A$) at time r, and letf:be the forward price of an A$ contract at time r for delivery and payment at time r + n. In what follows, lower case letters denote natural logarithms, I denotes the information set upon which market participants base their expectations and E denotes the mathematical conditional expectations opentor. If the joint hypothesis of rational expectations and risk aversion holds, the n period ahead spot price should equal the sum of the n period forward price, a risk premium, A,, and a rational expectations forecast error, u , +

Equation I is normally implemented econo- metrically by assuming risk neutrality (i.e. A, -0). In terms of equation 2, the null hypothesis of risk neutrality and rationality will be validated if a a equals zero, /3 quais unity and the error term is, in the presence of non-overlapping data, white noise and orthogonal to the information set (i.e. E (w, + . I I , ) - 0).

(2) During the early experience of recent floating exchange rates, quations like (2) proved to be the most popular way of testing market efficiency. Subsequent realization that spot and forward rates are non-stationary processes in levels (see e.g. Mecsc and Singleton, 1982). implying that the usual test statistics generated from an estimate of (2) will have non-standard limiting distributions, resulted in equations like (3) being formulated in terms of rates of change by subtracting s, from s,, and f;" to get

s, + . - a + Bf: + w +

where f," - s, has the interpretation of the forward premium and the joint null hypothesis of risk neutrality and rationality again implies a2 - 0 and

Scc MacDonald (1988) for a discussion.,

82- I and, in the presence of non-overlapping data, the error term should be a white noise process.

A large amount of econometric evidence, for a variety of currencies and time periods has now accumulated on equation (3) (see Hodrick, 1987, and MacDonald, 1988, for extensive surveys). The main conclusion to be drawn from this body of research is that the EMH is easily rejected in particular, a number of researchers report estimates of 8 2 in (3) which art significantly different from unity (in fact they are closer to minus one than plus one) and, in the case of non-overlapping data, serially comlated errors. In the exchange rate literature two interpretations have been placed on such findings. Assuming that agents are rational, Fama (1984) and Hodrick and Srivastava (1984) argue that such findings are evidence of time- varying risk premia. Alternatively, Bilson (198 1) and Longworth (1981) assume that agents are risk neutral and therefore rejection is attributable to irrationality.

Here we conduct our tests of (3) under the assumption of rationality (as economists, we find the irrationality interpretation particularly unappealing) and therefore rejection of the joint hypothesis is attributable to the risk adverse behaviour of economic agents. Fama (1984) has usefully provided a novel way of interpreting the risk premium. A, (which, with an appropriate stationary inducing transformation is equal to ( f,"-s,)-(s,+. -sl)). In particular, Fama demonstrates that non-constancy of the risk premium will be reflected in deviations of 8 2 from unity and deviations of 1-82 from zero. In terms of Fama's terminology, the 1-82 term is equal to PI in the complementary equation, (4):

where al=-a2. Furthermore, 1-2b2 (it. Fama's equation 10) indicates the relative size of variances of the risk premium and the expected rate of change in the spot price as a proportion of the variance of the forward premium.

111 Data and swnmary statirtics In this section we consider the main summary

statistics for the variables used in our regression based tests. In order to test equation (3) we utilize weekly data for one-, three- and six-month forward rates along with the corresponding spot rates for the Aush;llian/US dollar exchange rate. "he data were supplied by the Reserve Bank of Australia and are derived from the Reuters screen at 4p.m.

1991 EFFICIENCY IN THE FORWARD FOREIGN EXCHANGE MARKET 239

on a Friday (in cases where Friday was a public holiday. the next working day was used). In computing forward premiums and forecast errors, we have exactly aligned spot and forward rates in order to reflect the actual trading opportunities which are available to market participants. The sample period starts 1 March 1984 for all three forward rates and ends on 19 may 1987 for the One-month contract (177 observations), 24 March 1987 for the three-month contract (169 observations) and 23 December 1986 for the six- month contract (156 observations).

In Table 1 the means and standard deviations of the one-, three- and six-month forward premiums are presented along with the corresponding changes in the spot rates and forward forecast errors. Given the close correlation between contemporary spot and forward exchange rates, we would expect a priori that the variability of the forward premium should be less than that of either the change in the spot rate or the forecast error. This is supported by the evidence in Table 1.

For all maturities the mean forecast error .is less in absolute terms when the forward rate is used to predict the spot rate rather than the spot rate itself. For the full sample period, the forward rate over-predicts the spot rate for all three contracts which may reflect erroneous expectations. or if expectations are correct, a risk premium which acts as an offset (we investigate this hypothesis more fully in the next section). Interestingly. for all forecast horizons the standard deviation of the forecast error is greater than that of the exchange rate changes This suggests that in terms of standard deviations, the cumnt spot rate is a better predictor of the future spot rate than the cumnt forward rate. This finding is supportive of Fama's (1984) results for a selection of OECD currencies It is possible, however, that the comparative advantage of the spot rate in this case could be an implication of the variation in the risk premium which obscures the predictive power of the forward rate-hopefully our estimates of A and the implied 8, can shed further light on this.

In Table 1 we also present correlograms of the raw data series for our sample period. All com- lations for the change in the exchange rate are insignificant (the standard error for our sample is approximately 0.08 apart from that at lag 2 which suggests that the exchange rate series does not

3 The mean changes in the spot rate over the thm- and six-month periods arc, rapcctively, -0.020 and - 0.047 and their standard deviations arc 0.080 and 0.120.

follow a pure random walk process. This is supportive of the assertions made by Mussa (1979). It is well known that even with rational expectations. n-step-ahead forecasts will exhibit autocorrelation of order up to n-1 and this is reflected in the autocorrelation properties of the forecast errors reported in Table 1. Since the forward premium, fp, consists of the expected change in the exchange rate and the risk premium, the autocorrelations reported in Table 1 for fpl, fp3 and@ suggest that the risk premium and/ or the expected change in the exchange rate must vary in an autocorrelated way. The regression based tests which are reported in the next section are designed to shed further light on this issue.

N Regresnon Based Tests In Table 2 we present estimates of equation (3)

for our full sample period and also for a number of sub-samples. For all sample periods the joint hypothesis, a2-O and 82-1. is easily rejected, on the basis of the reported Wald statistics, at the 5 per cent level or better (the exception is the first equation, where the joint hypothesis is rejected at the 8 per cent level).4 Given such rejection, we proceed to examine the estimates of B2 along the lines suggested by Fama (1 984). For the full sample period. the P2 coefficient is negative, although not significantly so, across all three maturities, whilst the implied B I estimates are significantly positive throughout the sample. Given the way B, and B2 are defined by equations ( 5 ) and (6) of Fama (1984), this implies that the covariance between the expected rate of depreciation and the risk premium must be negative and larger in absolute value than the variance of the expected rate of depreciation, given that variances cannot be negative, this, in turn implies that Var(A,) must be larger than Var(€(s,+, - s,)), which can be ilustrated by computing (10) of Fama The estimates of BI-f12 for the one-, three- and six- month forecast horizons are, respectively, 6.83, 7.20 and 1.88; with only that for the three-month horizon being more than two standard errors above zero (the standard errors for B1- /& are twice the common standard error).

The sub-sample results are particularly interesting insofar as they indicate that the full sample estimates conceal a change in the parameter

4 Given the overiapping nature of our data base. we do not present xrial cornlation tests. However, our estimator is robust to such cornlation.

240 THE ECONOMIC RECORD SEPTEMBER

TABLE I

Some Dcscnph Smidcs of C h g a in the Sp01 Rae Forwd pmniwn and F m a h r

VARIABLE: A s Autocodations of Series:

1 .O 1 I962 7 .033876

13 -.OM163 VARIABLE: fpl Autocomlations of Series

1 .970335 7 332548 13 .726625 19 549207 VARIABLE: fe I Autocomlations of Series:

1 357358 7 .190878

13 -.079965 19 -.25 1370 VARIABLE: fp3 Autocomlations of Series

I .977856 7 .850986

13 .744592 19 .644739 VARIABLE: fe3 Autocomlations of Series:

1 ,956548 7 511821

13 -0698 I 1 19 -.246595 VARIABLE: fp6 Autocomlations of Scries:

1 .175275 7 .185232

13 .1868 I3 19 .181784 VARIABLE: fe6 Autocomlations of Series

I 348147 7 661997

13 .3455 15 19 .08925 1

MEAN -0.006

,18611 I -.118 I26 ,050 I27 .07 1324

-. I5078 .060894 MEAN: -0.005

.94 1663 .919375

.8 I2399 .79 I930

.7 14473 .700268

..639 I75 MEAN : 0.00 I

.663888 .453796

.206022 .176637 -. 129540 -.1637 I7 -.235489

MEAN : 0.0 I5

.953256 ,932658

.83 1408 312311

.727705 .7 10092

.628 I35 MEAN: 0.005

.89004 I .825009

.43 1693 .33620 I -. I30605 -.169829 -.247250

MEAN : -0.03 1

.I7 I854 .181148

.I78852 .173991 ,195283 .198852 . I72623

MEAN : 0.0 16

.820850 .799237

.a8697 564141

.302794 .257370

.05430 I

.08598 1

.0693 12 -.046652

.897320 774592 .685623

.290762

. I08942 -.199307

.9 I284 1

.795872

.690679

.758896

.228 132 -.205069

582148 .181 I12 .189425

.821413

.5 18986

.I93179

STANDARD DEVIATION : 0.04 1

.029453 .035082 -.Ol9 164 -.07829 1 -.085249 -. I39392 STANDARD DEVIATION: 0.004

A72946 A5302 I .756732 .740075 .675002 .660353

STANDARD DEVIATION: 0.042

.176942 .168805

.03 I872 -.029920 -.235058 -.256438

STANDARD DEVIATION: 0.010

,892544 .871850 .778264 .761375 .6 7 7 4 7 0 .663089

STANDARD DEVIATION: 0.085

.675586 S87024

. l I9823 .02 1 I45 -.2333 13 -.243468

UANDARD DEVIATION: 0.047

.I67280 .172559

.I98037 .193563

.183087 . I82704

STANDARD DEVIATION : 0.120

.723157 .693153

.463538 .397780

.158196 .122299

Notes: hr denotes the change in h e spot exchange rate;fP denotes a forward prcrniurn;fe denotes a forward forecast e m I , 3 and 6 denote, rtspectively, one-, three- and sixth-month horizons; dl variables arc in natural logarithms.

1991 EFFICIENCY IN THE FORWARD FOREIGN EXCHANGE MARKET 24 1

SamplePeriod n kl A R2 X2

19841) 1 -.022 -2.9 I .06 .08

19841) 3 - 0.67 -3.098 .I4 .05 1987(3) (-1.91) (-1.82) 19841) 6 -.06 I -.440 .04 .o 1 198q 12) (-1.67) (-.97) 19841) I -.oo 1 1 I .627 .30 .oo 198412) (-.20) (4.78) 19841) 3 -.026 12.641 .49 .oo 198412) (-2.05) (4.08) 19841) 6 -.I22 2.217 .02 .oo 198412) (-5.20) (4.1 1) 1985(1) I -.I 12 -15.798 .4 I .oo 1985( 12) (-4.54) (-4.14) 198% 1) 3 -.2 16 -1 1.017 .44 .oo 1983 12) (-3.01) (-3.17) 1983 I ) 6 -.I 14 -3.5 12 .26 .oo I985(12) (-3.70) (-3.36) 1986(1) I -.I31 - 16.262 .26 .oo 1987(5) (-2.18) (-2.45) 1986(1) 3 -376 - 16.208 .39 .oo 1987(3) (-2.44) (-2.77) 1986(1) 6 -.w .126 .oo .oo I986(12) (-.OI) (2.70)

a: The numbers in parenthesis underneath coefficient estimates are r ratios, calculated using Hanscn’s (1982) method of moments procedure (this corrects for both the moving average process implied by the overlapping data and conditional hctemedasticity). R denotes the unadjusted coefficient of determinaton and x2 is the marginal significance level of a Wald statistic which tests u2 - 0 and & - 1.

1987(5) (-1.65) (-1.62)

estimates over time. Thus in the last two sub- samples (1985 and 198617) the & and /& co- efficients differ significantly from unity and zero respectively indicating that both A, and E(s,+.-s,) are time-varying. As in the full sample, the estimates of 1-2/92 indicate that the variance of A, is much greater than the variance of &J,+.-s,), with all the estimates being statistically significant. The coefficient estimates for the first full year of the float, however, differ dramatically from the corresponding estimates for the full sample in that p2 is positive and the implied BI is therefore negative. Thus, on the basis of eadier reasoning,

this implies that the variance of E(s, + “-sf) is greater than the variance of A,. However, since the estimates of /32 are more than two standard errors above unity (and those of 8, arc more than two standard errors less than zero) there is. in common with the findings for the other sub-samples, strong evidence for the existence of a time-varying risk premium.

Summary and Conclusion The purpose of this paper has been to examine

the extent to which the market for foreign exchange

242 THE ECONOMIC RECORD SEPTEMBER

in Australia has operated efficiently since the move to floating exchange rates. More specifically, we have examined the relationship which exists between the spot and forward AustraliadUS dollar exchange rates using weekly data for one-. thrce- and six-month contracts over the period January 1984-March 1987. Our main concern was to employ Fama's (1984) technqiue for separating the forward premium into a risk component and a forecasting error.

A number of results have emerged from this study. We saw in Section UI that, in accordance with the assertions of Mussa (1979), the change in the spot exchange rate does not follow a random walk while the forecast errors also exhibit autocorrelation. While this is consistent with the assumption of rational expectations, it suggests that either the risk premium and/or the expected change in the exchange rate are varying in an auto- correlated way. The regression based tests allowed us to examine this issue more closely, and the results demonstrate the existence of a significant risk premium which does indeed vary over time.5 Future work could usefully model this premium.

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