The Efficiency of the Market for Bank Accepted Bills*

COLM KEARNEY RONALD MACDONALD JOHN HILLIER school of Economics Dcpartmcnrof~nomics, school of Economics

Univrrsiry of NSW, Uniwrs i ryOfDwldeC Univasity of N W , Sydney, NSW S Y ~ , NSw

l k p e c u h i w ~ of the Sydncy F~lnues~hange ' smarkrr i n b o n k o c c e p ~ b i u r i r ~ b y c o n n ' d c r i n g i f d u f i c ~ p r i c e is an unbiarcdprrdictor of the subsapumt spot price and if other publicly OvoilOMr information can impme on this pndictor. Data JpMnLgthcpCr iod1980(1)~ 1986(S)artunploycd Thcnnclts am crdwnc to the @iency hypothesis in that thejimmprice in some cases is not an unbiadpredictor and &is it an optimal predictor.

I Introduction The period since the late 1970s has witnessed

substantial deregulation of the Australian financial system including the abolition of foreign exchange and most interest rate controls and the floating of the Australian dollar in foreign exchange markets. This new deregulatory environment has, together with the international experience of volatile asset prices, contributed to much financial innovation in terms of products, SCMCCS and markets Indeed, a good example of the latter is to be found in the aggressive introduction of new financial futures markets on the Sydney Futures Exchange. The purpose of this paper is to examine the performance of one of tbe most import?nt of these markets, i.e. that which trades contracts in bank accepted bills Financial futures markets generally perform two fuactions which ought to

Ihic paper iC a miscd version of that which was praented to the conference on 'Australian Moneury Policy Post Cunpbell'. Melbome, August 1987. We arc

to the editor md ref- of this Journal whose comments Id to s u b s t ~ t i d impvements. Remaining wuknesscs arc our rrsponribility. Assiinct from thc Reserve Bank of Australia's Economic and Financial Research Fund EIUNSWI8701 is gratefully acknowledgcd.

gnteful to the puticiprnu for belptul ruggestiw md

be the focus of any assessment of overall performance: that is, they provide facilities for risk management through appropriate hedging behaviow, and they perform a forward pricing function which is potentially beneficial to non- market as well as market padcipanu The sections of this paper which follow are concerned with the latter market function, and the assessment is made using the efficient markets hypothesis (EMH) as the benchmark. This amounts to examining whether the futures price for bank accepted bills cpnstitutes an optimal predictor of the subsequent spot price, and this will be the case if the fuhms price is an unbiased predictor of the subsequent spot price and if no other publicly available information can improve up011 the performance of fututes prices in predicting subsequent spot prices.

Previous studies of the efficiency of the market for bank-accepted bills in Australia have been reported by Sharpe and Weston (1983). Juttner, Luedecke and Tuckwell (1985). and by Tease (1 988). The forma two studies, however. have not examined the performance of the market since the floating of the exchange rate while the latter study focuses on the optimality of the implied forward rate rather than the futures rate as a predictor of subsequent spot rates. The contribution of this

225

226 THE ECONOMIC RECORD SEPTEMBER

paper is to examine the optimality of the futures prices in predicting subsequent spot prices for bank-accepted bills on both pre- and post-floating exchange rate monthly data which span the period 1980( I ) to 1986(5). Tests for unbiasedness are first conducted and these are followed by investigation of the extent to which other publicly available information is orthogonal to the futures price forecasting error. The information set which is examined consists of a large subset of the recently fashionable 'checklist' of monetary policy indicators, and it is found that not all of this information is incorporated into the futures prices for bank-accepted bills.

A brief outline of the paper is as follows. Section I1 outlines the test procedures and presents the results while comparing the findings with those of previous studies at the appropriate junctures. Section 111 summarizes the paper. draws together the conclusions and points to the direction of future related research.

II Test Procedures and Resub The futures price of an asset which is traded

on a frictionless financial market in which transaction costs are negligible is determined by the market's expectation of what the corresponding subsequent spot price will be together with the allowance for the existence of a possible risk premium. In order to operationalize this relationship we must hypothesize how market participants form their expectations, and in what follows we adopt the convention of assuming that they do so in a rational manner without making systematic errors. This of course implies that the market efficiency tests which follow are joint tests of this condition as well as the assumption of rational expectations so that rejection of the tests could result from either source. We can formalize this relationship between spot and futures prices by recourse to equation ( 1 )

F P = El( S,,J + PI where Fpdenotes the c m n t period price of an n-month futures bank accepted bill (BAB) contract, S,, denotes the spot price which prevails in n months time, P, denotes the risk premium and E, (J denotes the rational expectations operator conditional on all information which is cumntly available. The actual realization of S,, will differ from the expected level by a rational forecasting error, U,+,.

S,,, = F:+"- P,+ U,,, (2)

If risk neutral financial market operators form their expectations rationally, the risk premium term (PI) will be equal to zero and equation (2) can be written in regression format as

(23 In this case, market efficiency implies that the coefficients a and /3 should not be significantly different from zero and unity. respectively and the error term should be a white noise process which is orthogonal to the information set.

Equations of the form (23 have been commonly used to test for the efficiency of the forward market for foreign exchange (see Frankel. 1981. 1982) as well as for the Australian market for 90-day BABs (see Juttner, Luedecke and Tuckwell. 1985). Apart from any treatment of risk, these tests suffer from the problem that if spot and forward or futures rates exhibit non-stationary behaviour. the standard inference techniques of linear regression analysis will be invalid. This problem has been overcome, however, by subtracting S, from both sides of equation (2') in order to induce stationarity.

S,,, - S,= a,+ P,(F?"-S,) + Uo,.+ (3)

When we explicitly include risk, the futures-spot price differential (the term in brackets in equation (3)) is decomposable into the expected spot rate change and a risk premium as in equation (I).

F Y - S, = E,(S,,- S> + PI (13 Fama ( 1 984) has enhanced the interpretation of equation (3) by considering the 'complementary' regression equation (4).

While equation (3) is the standard form of market efficiency test which overcomes the stationarity problems encountered by equation (23, equation (4) is 'complementary' to (3) insofar as the left- hand side components of both (3) and (4). sum to the right-hand side, so that the intercepts and slopes sum to zero and unity respectively (a,+ a, - . =O.&+p,= I ) .

It is of interest to note that Fama (1984) has demonstrated that the deviation of Po &om unity indicates a varying risk premium component in the futures price, assuming that the market is efficient and that the expected future spot price is formed rationally. Observing that the left side term of (4) is the random error of the rational forecast plus the risk premium. deviation of/3, from zero is also indicative that the risk premium

1989 BILL MARKET EFFICIENCY 227

component of the futures premium has variation which is reflected in the actual forecast error.

(i) Swnmary Statistics of the Dara The data employed in this study span the period

1980(1)- 1986(5) and are described in detail in the Data Appendix. The full sample of 77 observations was divided into the pre- and post-float sub-periods from 1980(1)-1983(10) and from 19841)-1986 (5) with 46 and 29 observations respectively. Observations on the spot BAB rates were sampled on the Wednesday before the second Friday of each month (which corresponds to the maturity date of BAB contracts) and corresponding observations were sampled for both the one-month and three- month futures contract. The data which were used in the orthogonality tests were sampled at the times of public availability closest to the above- mentioned days each month.

The means, standard deviations and higher moments (skewness and kurtosis) of the futures forecast errors for the one- and thret-month contracts are shown in Table 1 with the same for the corresponding changes in the spot rates and futures premia. The table provides these summary statistics for the N1 data period as well as for both sub-periods and some interesting observations can be made from inspection of the table. To begin with, it is noticeable that the mean forecast errors for both futures contracts are negative during the later sub-period. This undoubtedly reflects the use of interest rates to 'target' on the exchange rate since the decision to float was implemented at the end of 1983. Of perhaps greater significance in the current context. however, is the fact that for the period as a whole as well as both sub-periods. the standard deviations of the forecast errors are smaller than those of the spot rate changes. This tends to imply that the current futures rate is a better predictor of future spot rates than is the current spot rate. It is worth noting that Fama (1 984) obtained the opposite result in a study of foreign exchange markets, but as Sharpe and Weston (1983) point out, this result might not be unexpected in the context of a financial market which is subject to seasonal influences.

The coefficients of skewness statistics in Table 1 give no indication of skewness for any of the one- and three-month spot rate changes. The coefficients of kurtosis indicate few departures from normality. It is interesting to note that this finding contrasts with the findings from foreign exchange markets in which Friedman and

TABLE 1 Summary S&atida of the Fomaa Enor, Forward ptaiwn and Spot kue Changes

Mean Standard Skewness Kurtosis Deviation

FEl 0.002 1.283

FE3 -0.191 1.880

AS1 0.059 1526

AS3 0.265 2.458

FPl 0.061 0:mi

FP3 0.074 1.178

B: Re- Flwr (I 980- I 98J) FEl 0.091 1.,103

FR -0.11 I 1 .764

AS1 0.008 1.684

as3 0.1 1 1 2.549

FPl 0.100 0.677

FP3 0.221 1.533

C: PoJt - tht (I 983-1 986) FEI -0.231 I049

FE3 -0.971 I795

,AS1 0.065 1.176

AS3 0.625 2.135

FPl -0.166 0.650

FP3 -0.346 1.335

0.699 (0.02) 0.288

(0.33) -0.353 (0.23) 0.200

(050) 0504

(0.08) 0.443

(0.13)

0.652 (0.09) 0.364

(0.35) -0.379 (0.33) 0.493

(0.20) 0.766

(0.05) 0.314

(0.4 18)

0568 (0.28) 0.453

(0.38) 0.003

(0.99) -0.732 (0.16) 0.136

(0.79) 0.687

(0.19)

2.141 (0.00)

-0.108 (0.86) 1.253

(0.04) -0.698 (0.25)

-0.025 (0.97)

-0.65 1 (0.28)

2.587 (0.00)

-0.449 (058) - 1.462 (0.07)

-0540 (05 1 ) 0.282

(0.73) -0.935 (0.25)

-0.469 (0.68) 0.007

(0.99) -0.144 (0.90)

-0.302 (0.79)

-0.340 (0.76) 0.022

(0.98)

Notes: FEl and FE3 uc the f- (v - S,+& for the 1- and 3-month contracts, AS1 md AS3 arc spot rate chmge CS,+,- S>, while FPl a d JT3 PTC

the corresponding f o m r d prcmia (y - S?. ?'he figures for Kurtosis have becn adjusted in order to ycld zero for a normal dismbution. Numbers in brackets arc marginal significance levels.

228 THE ECONOMIC .RECORD SEPTEMBER

TABLE 2 Compkmouary Regmuions Tke Change in rhr Spor Rae and he F o m m Error projcrrcd onto du FUI- Rrmiwn

1980(1) 1 .OO5 1.134 -.005 -.I34 .33 .01 .I4 .I4 .72 .72 .46 1986(5) (.03) (6.23) (0.3) (.74)

3 .I47 1.085 -.I47 -.085 .42 .OO .OO .OO .65 .65 62 (.41) (6.25) (.41) (.49)

19891) I -.I39 1.441 .I39 -.441 .34 .05 .I7 . I 7 .26 26 12 I983( 10) (64) (5.09) (.64) (1.56)

3 -.I59 1.221 .I59 -.221 .54 .04 .23 2 3 .I2 . I2 .05 (.46) ( 1 0 (.46) (1.98)

1984(1) I .258 .981 -.258 .019 .33 .02 .76 .76 .25 .25 .93 (1.39) (4.48) (1.53) (.42)

1986(5) 3 .747 .932 -.747 .068 .30 .OO .OO .OO .08 .08 .83 (1.49) (2.95) (1.49) (.22)

Nates S and F are as defined in the text an$ R2 is thecoefficient of de!cnnination, Q is the Ljung-Box test statistic. X i and X: test the ’oint hypotheses that a =O and Bo=I, and that a,=O and /3 = I respectively. while X?, tests the hypothesis thr t j o = I . Both and f l \.we chi-squares distributions. Numbek in the Q and x2 columns are the marginal significance levels whe n u m L r s in parentheses below estimated coefficients arc r ratios which have been calculated using Hanscn’s method of moments (MOM). For n=l , MOM corrects for arbitrpry heteroscedasticity while for n=3. MOM comcts for arbitmy hcteroscedasticity as well as the second-order moving average which is implied by the overlapping nature of the data base.

Vandersteel ( 1982) found strong evidence of lepto- kurtosis. The autocorrelations of these variables also indicate the existence of diminishing seasonal influences since the early 1980s; Kearney, MacDonald and Hillier (1987) discuss this in greater detail.

(u) A n Funvc~ prices Unbiased predictors of SUbseqUmt spot Ricer?

The regression estimates of equations (3) and (4) arc shown in Table 2 for the one- and three- month futures BAB contracts over the full sample period and for both sub-periods. The ‘complementary’ nature of thesc regressions is evidenced by the fact that the constant and slope terms sum to zero and unity respectively. As Fama (1984) demonstrates. the slope coefficients. Do and B,, contain the proportions of the variance in the futures premium, FP- S, which are due to variation in the expected spot rate change, El

(S,+n.-S,), and the risk premium, f, respectively. If nsk-neutral operators trade on frictionless financial markets with negligible transaction costs, the futures prices will be unbiased predictors of subsequent spot prices. so the joint hypothesis of uo= 0 and B0= I will not be refuted and the residuals will be serially uncorrelated. Table 2 shows that this is the case insofar as for all periods and for each contract horizon, the marginal significance level of the chi-square test statistic does not indicate rejection of the. null hypothesis. However, in the case of the three-month contract horizon in the full and later sample periods. the marginal significance levels of the Ljung-Box test statistic indicate that the equation residuals are not ‘white noise’.

It is also of interest to observe that in each case, the risk premium does not seem to be varying, as evidenced by the marginal significance of the chi-square statistic (which tests the hypothesis that P o = I ) .

1989 BILL MARKET EFFICIENCY 229

(iii) Are Futum Prices Optimal Pwdcton of subsequmt spot prices?

In addition to testing for unbiasedness, it is important to examine the extent to which futures prices are optimal predictors of subsequent spot prices. Optimality in this context means that the futures prices contain all available information which could conceivably help to predict the future course of spot prices. If this condition is not met. the market is inefficient insofar as exploitable profit opportunities may exist which have not been arbitraged to zero. The finding of serially correlated errors in the previous tests suggests that the futures prices do not contain all potentially useful information. In the remainder of this section we examine the extent to which this is the case by regressing the forecast error of the two futures contracts on their own and each others lagged values as well as on lagged values of spot BAB rate changes and a set of other macroeconomic variables which is likely to impinge upon domestic rates of interest. Specifically. we estimate the following equation:

FEN, = Q(FEN,-,-,, AS,,, AhTwI,-, IFR,,, IFR*,-,. ( 5 )

where i - -

FEN, =

s = IFR =

IFR* =

CA =

M = R E s =

TWI =

number of lags (in months) required for observability. the forecast error on an n-month ( n = 1.3) BAB futures contract, (F7"- S,,,,), the spot rate on BABs. the implied forward rate from the 90-day and 180-day BAB spot rates, the foreign (US) implied forward rate derived from 90- and 180-day Treasury bill rates adjusted for the implied forward premium on the SA6.U.S. spot exchange rate. the balance of payments on current account, domestic monetary growth, Reserve Bank transactions in foreign exchange reserves. Australian dollar's trade weighted index.

ation criterion and likelihood ratio tests, involve the prior specification of a general lag structure and subsequent 'testing down' to the optimal length. The design of this study which includes splitting the sample into the pre- and post-floating exchange rate sub-periods imposes severe limitations on our specification of the lag structure. We have accordingly restricted the lag length to two months in our orthogonality tests of equation (5 ) .

The results from sequentially estimating equation ( 5 ) for the full sample period as well as for both sub-periods are presented in Tables 3-5. We begin by examining the results for the full sample period which are given in Table 3. The testing strategy involved firstly regressing the one- and three-month forecast errors on twoown-lagged forecast errors ( i t . a .weak-fonn test) and on two cross forecast errors from the market for the other contract (i.e. a semi-strong-form test). The null hypothesis that the ctnfficient on the two lagged values together with the constant term are qua1 to zero is not rejected in any of these cases.

Further semi-strong form tests of market efficiency were performed by adding lagged values of other economic information contained in equation ( 5 ) and testing the joint null hypothesis that the coefficients on these additional terms plus the constant are equal to zero. This null hypothesis is rejected for the one-month contract in system 8. The implication which follows is that the futures prices for these BAH contracts are not optimal predictors of subsequent spot prices insofar as they do not contain all infomation which could be of assistance in reducing the forecast error.

It is interesting to cxamine the extent to which this finding of sub-optimal pricing performance in both futures contrac'ts is robust across the two sample sub-periods u hich span the pre- and post- floating exchange rate regimes. Tables 4 and 5 provide the results. Lmking first at the results for the pre-floating exchange rate period. the null hypothesis that the coefficients or the constant term together with the economic information are equal to zero is accepted in all cases except for system 7 for the one-month contract, and systems 1 and 2 for the three-month contract.

Further details of data sources and the construction of variables are provided in the Data Appendix.

The initial task which must be addressed in performing the orthogonality tests concerns the choice of the optimal lag length. A number of methods which have k e n popularized in studies of market efficiency, such as the Akaike Inform-

When we move to consider the post-floating exchange rate period, the evidence of market inefficiency does not persist for the one-month contract. For the three-month contract, however, the evidence of continued market inefficiency persists insofar as the null hypothesis is rejected for systems 2, 4, 5 and 8 which indicates that the

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0.37

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(1.46)

0.401 0.00 005

(1.43)

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0.791

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(1.71)

(1.8

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(0.76)

-0.099

0.418

-0.1 I9

0.251

-1.5

60

0.01

0.18

(0.47)

(2.15)

(0.17) (0.83)

(0.9

0)

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4 FE

I -0.405

-0.W

9 -0.0002 -0.0001

0.50

I 034

0.J2

2 (2

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(O

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(0.38)

(0.23)

(0.91)

(0.52)

(1.27)

(1 1

5)

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m

-0.1

01

0.273

0001

0.00

1 -1.122

o.m

o.37

5 B # rn

(2

.31)

(0

.35)

(1

.09)

(0

.04)

(0

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(0.22)

(1.9

0)

(0.6

8)

(071)

(0.6

6)

i;i z 6

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-0.297

0.149

-0.o

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0.0008

0.259

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c)

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5)

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0.254

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01

o.oO

06

0.29

9 0.00 0.29

(0.32)

(1.1

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(0.1

5)

(1.02)

(0.9 I )

5 FE

I -0.421

-0.0

48

-0.O

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-0.o

O04

-0.256 0.38 0.374

-000

1 0001

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3 f CII r,

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1989 BLL MARKET f3FlCIENCY 233

cross forecast errors, monetary growth, current account performance and foreign interest rates arc not fully reflected in futures prices.

I l l swnmary and ConCMns The futures market for BAB's in Australia has

become one of the outstanding success stories of the Sydney Funves Exchange. Eariier analyses of this market's experience prior to the floating of the $A indicated the existence of strong seasonality influences coupled with evidence of market inefficiency. This study has re?ssessed these findings in the light of recent experience and found evidence of declining seasonality influences coupled with continuing scope for improved efficiency. More specifically, there is evidence that the

futures markets do not yet fully incorporate all available information which can be of assistance in helping to predict future movements in spot rates Amongst this unexploited infomation is the economy's performance on current account of the balance of payments, the rate of monetq growth and adjusted foreign implied forward rates of interest. Future related research will aim to provide further analysis of the usc of information in the market for BAB's in Australia using data which are less aggregated over time.

DATA APPENDIX

This appendix describes the sources and definitions of data which have been used in the reporcal empirical tests Thc interest rare and exchange nte data were initillly supplied on a daily b u k frvm the Reserve Bank of Australia and tbe monthly database w.s c e from this source. The other macroeconomic vuiabks which are uscd in the orthogonality tats w a e obtained from

observations were publicly a v d a b k at tbc date and time of day which c0mrpoad.s to the hnves contracts obsenations. The following abbreviations rre laed for the sources; ABS = Austrdian of Statittics UESR = Melbounre Institute of Applied Economic and Social Rcseuch, RBAB = Reserve Bank of Austnli. B u U e b RBACP = Resave Bank of Austnlia computer printout database. SFEY = Sydney F u h ~ a Exchange Y m k , and WSJ = Wall S m t Journal. S = Spot Rates for 90-day BABs which arc mid-

points of ntes quoted to the Reserve Bank of trades conducted during the morning by the authoriztd money market dealers. Observations

readily r v d l b l e sounxs lnd oglnized so t h t the

were taken monthly to coincide with maturity dates of fi~hlrrs conmcts. RBACP.

= Futures nttr on 90-day BABs f a one- and three- moatb contracts which mature on the WcQtsdry prior to the second Fridry of u c h month. More h a hdf of the futures prices arc a d rndc prices On days in which no tn&soccumd,tbe average of bid and ask prices were employ& in many cast% tbe between bid and asked prices was lcss than 50 basis poinu

IFR = Implied forward ntes on %day BABs calculated from the 90- and 180-day forward rates for these bills RBACP.

IFR*= Foreign implied f m a r d rate calculated from k- and six-month US Treasury bill daily data adjusted for the implied forwad rate of the SUSlSA exchange ntc hwn three- and six- month forward exchange ntcs RBACP and WSJ.

CA = Balance of paynients on c m n t account., Table KI, RBAR

M = Money supply (M), T i b k A I , RBAB. RES = Tnnsactions movements in foreign exchange

resmes, Table K3, RBAB. Y = Index of industrial production, UESR and RBAB.

F

REFERENCES

Fama, EE. ( 1984). 'Fonwud and Spot Exchange Rates'.

Frmkcl. J.A. (1981). 'Flexible Exchange Rates, Prices and Ihe Role of "News": Lesums from the 1970's',

- (1982), Tests of Rational Expectations in the Foreign Exchange Market', Sovdtan Economic J o d

Friedm~. D. and Vanderzteel. S. (1982). 'Short Run Fluctuations in Fomign Exchrnge Ratcs: Evidence from the Data 1973-79', Journal of Inrrrnorionaf

Juttncr. DJ.. Luedeckc. B.P. lnd Tuckwell. R (1985).

J o d of MonrUVy iicOnomia 14.3 19-38.

J O ~ of Pdidcpl Econont~ 83,325-38.

49,406- 16.

Econanict 13.171-86.

'Arr EX~CCU~~OOS of S ~ ~ ~ ~ - T C I Y I I Interest Rates R a t i d ? ' . AvsPolion EccMomic Pqpas 356-69.

Kurney, C. MacDonlld. R md Hillier. J. (1987). 'The Efficicacy of tbc M e t for Bank Accepted Bills'. Working Paper No. 98. C e a a fa Applied Economic R a c a ~ d ~ , University of New South Wales

shupe. L d Weston, R (1984). 'New Information from New Markets Futures'. in R Weston (d). 1-n in rhr A~stmlim F d Sy- Mclbourm.

Teare. WJ. (1 988),'The Expcctationz Thcg. of the T a m Structure of Interest Rates in Australia'. Economic RcronlM. 120-7.