RATIONALITY AND THE RISK PREMIUM ON THE AUSTRALIAN DOLLAR. BRUCE S. FELMINGHAM* University of Tasmania. PETER MANSFIELD University of Tasmania

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1 INTERNATIONAL ECONOMIC JOURNAL 47 Volume 11, Number 3, Autumn 1997 RATIONALITY AND THE RISK PREMIUM ON THE AUSTRALIAN DOLLAR BRUCE S. FELMINGHAM* University of Tasmania PETER MANSFIELD University of Tasmania A model of the forward rate error of the USD/AUD spot exchange rate is fitted to daily data for the period 15th December 1983 to 31st December This provides a data set of 2034 daily trading observations. Explanations of the forecast error include a risk premium represented by a constant plus the conditional variance generated from a GARCH (1,1)-M analysis of the error process and information variables in the form of lagged forward rate errors. The following conclusions are drawn from estimates for the full sample: the USD/AUD spot rate is subject to a constant premium; there is little evidence to support a time varying component and the market is influenced by lagged forward errors. Sub period estimation confirms these results, although a time varying premium is evident prior to the february 1985 depreciation. The economic implications of these findings are discussed. [F31] 1. INTRODUCTION In an earlier analysis, Felmingham and Buchanan (1993) found that international transactors required a risk premium if they were to hold the Australian currency (AUD). A risk premium appeared in the 30 day forward following the deep and sudden depreciation of the spot USD/AUD rate in February The problem for foreign exchange (forex) market participants during this period was to determine how far the value of the AUD might fall against the USD and they required a premium to hold the AUD in these circumstances. Felmingham and Buchanan discovered additionally that the risk premium shifted discretely with changes in domestic policies and substantial changes in market conditions. This study was based on a daily data set which terminated in July 1985, however, many events have taken place since this date. These include: Federal elections, two down-gradings of Australia s country credit rating, and monthly announcements about bad current account balance *The authors are indebted to Dr. Jon Kendall for the provision of the computer program for research assistance. This research was supported from funds provided by the Australian Research Council - small grants scheme and University of Tasmania, Faculty of Business Research Fund.

2 48 B. S. FELMINGHAM AND P. MANSFIELD outcomes. These events can impact the size of the risk premium or constitute news or information which prevent forward rates from providing unbiased predictions of spot rates. It is of interest to determine if Felmingham and Buchanan s findings in the Australian 30 day market hold across a more recent time series, one incorporating the foreign exchange market consequences of the events referred to above. The authors cited confined their analysis to discrete changes in the risk premium. However, over a longer time series and with modifications to the author s original model it is possible to test for the continuous variation of the 30 day forward risk premium on the AUD. The comparison between discrete and continuous variation of the risk premium has to do with the degree of volatility confronting foreign exchange market transactors who are likely to place greater trust in more reliable market signals. Discrete variation, which is predictable in terms of policy changes or market disturbances, is likely to be less destabilising in comparison with unpredictable continuous variations. Why should a continuously varying risk premium matter in an economic context? There are two compelling answers to this question. First, the risk premium drives a wedge between the expected value of the spot rate and the known current forward rate k periods ahead. A continuously varying premium impairs the effectiveness of forward market facilities in providing cover from the risk associated with forward trading. Foreign exchange transactors may make less use of forward market facilities as a consequence. The second aspect concerns the attitudes of the monetary authorities towards market intervention. For them, the presence of a volatile risk premium separating forward and spot rates distorts the foreign exchange market and may encourage the authorities to intervene. A model which allows for the continuous variation of the risk premium on the AUD is developed in the following section. We take up the suggestion of Kearney and McDonald (1991) to apply GARCH techniques to test for a time varying risk premium on Australian data. These researchers find some evidence of a time varying risk premium on weekly Australian data over the period January 1984 to March Our preference for daily data is governed by the consensus prevailing now in the literature that volatility diminishes over longer sample periods. The GARCH framework allows examination of the continuous variation of the risk premium. However, it will not detect structural breaks in the behaviour of the premium. To accommodate this issue, we identify structural breaks by first looking for clusters of outlying observations of the forward forecast error. The model of the risk premium is then estimated in the resulting sub periods. 2. THE RISK PREMIUM AND RATIONAL EXPECTATIONS The theoretical foundations for analyses of risk premia on national currencies is provided in the international capital asset pricing literature by authors such as Lucas (1978, 1982). These theories give rise to a set of equilibrium conditions which apply to investment in international assets generally.

3 RISK PREMIUM ON AUSTRALIAN DOLLAR 49 The application of these models depends on further statistical assumptions including some specification about the behaviour of the information set relevant to agents expectations. The normal basis of attempts to describe currency risk premia involves the expected value of the forward forecast error: E t (s t+k ) - f t,k (1) This is represented as the difference between the conditional expectation of the logarithm of the spot rate in the future period t + k (E t (s t+k )) and the logarithm of the current forward rate for delivery in period k (f t,k ). The risk premium on an individual currency drives a wedge between these, so most econometric research about the premium is focussed on explanations of (1). Two general problems are associated with tests for the existence of a premium. The first relates to the fact that E t (s t+k ) is not in general observable. This problem is often resolved by assuming that agents hold rational expectations. Then the conditional expectation E t (s t + k ) may be proxied by the e x p o s t realised value (s t + k ). Therefore, following Hansen and Hodrick (1980, p.831), it is not appropriate to infer that the difference between the expected value of the spot and the relevant forward rate is a risk premium unless the currency market is efficient according to Bilson s (1981) definition of efficiency. Here we recognise the joint nature of tests for market efficiency and for the presence of a risk premium. Frankel and Foot (1993) indicate that researchers often assume either that expectations are rational and test for the presence of a risk premium, or assume no risk premium and test for rational expectations. Our approach is to preserve the joint nature of our hypothesis testing. Consider equation (2) below. The risk premium (R P t ) is defined in equation (3), while we argue that the lagged forecast errors y t and y t-1 in (2) are extraneous information. If either of the coefficients b 1 o r b 2 is significantly different from zero our rationality assumption is not justified in estimates of (2). The specified objective in this paper requires a joint test for market efficiency (rationality) and for the presence of a risk premium. Rational expectations are assumed so that E t (s t + k ) is proxied by the expost realised spot rate (s t + k ) and the veracity of this assumption is then tested. This is achieved by applying Fama s (1984) decomposition of the observable forward rate error into a risk premium, RP t, lagged forward rate errors y t and y t-1 which provide a direct test of the rational expectations assumption, and a forecast error. The econometric formulation emerging from these arguments takes the following form: y t+k = RP t + 1 by t + 2 by t-1 + (1 - γ 1 Lγ 2 L 2 - γ k L k )ε t+k (2)

4 50 B. S. FELMINGHAM AND P. MANSFIELD y t+k = s t+k - f t,k : the forward rate error for period t+k y t = s t - f t-k,k : the forward rate error for period t y t-1 = s t-1 - f t-k-1,k : the forward rate error t-1. This formulation provides a straightforward test of the rational expectations hypothesis in the 30-day market for the $US/Australian dollar rate. Rational expectations hold provided b 1 and b 2 turn out to be zero in estimates of (2). The formulation of the risk premium follows Domowitz and Hakkio (1985) and the many authors who have followed them since: 1 RP t = a 0 + a 1 h 2 t+k (3) Here in (3) h t + k is the conditional component of the variance of the error term ε t + k. So the risk premium has a constant component (a 0 ) and a time varying 1 component, which is the standard deviation of the conditional variance (h 2 t+k ). If estimates of (2) reveal that a 0 = a 1 = 0, then there is no risk premium. If a 0 0 b u t a 1 = 0 there is a constant premium and a significant time varying component applies provided a 1 0. The final feature of (2) is the moving average error process MA(k) which corrects the equation (2) for serial correlation. This is required in the chosen estimation framework because the forecast horizon (k = 19) is longer than the sample frequency which occurs daily. The GARCH-M framework has been chosen because it represents an established way of measuring volatility, in this case in the form of a time varying risk premium. This approach is preferred to alternative methodologies which correct the estimates for autocorrelation due to the presence of overlapping observations. The generalised method of moments (GMM) represents an alternative treatment. The preference for ML methods is discussed presently. 3. DATA This study is based on a daily time series spanning the period 15th December 1983 to the 31st December 1991: a total of 2034 observations. This interval was chosen for the following reasons: the 15th December 1983 is the first trading day following the Australian government s decision to deregulate the foreign exchange market on the 12th December The terminating date of 31st December 1991 was chosen to provide a time series long enough to accommodate the major events influencing

5 RISK PREMIUM ON AUSTRALIAN DOLLAR 51 Australia s foreign exchange market. These included the sudden, sharp depreciation of the AUD/USD spot exchange rate in February 1985, and the Australian Treasurer s reference to Australia s burgeoning foreign debt as an aspect of a banana republic. This statement was made on the 14th May 1986 and is claimed to have had a profound effect on the financial markets and the timing of the two announcements by Moody s International credit rating agency about their rating of Australian government securities. Moody s downgraded this rating from AAA to AA1 in September 1986 and to AA2 in October The calendar years 1985 to 1986 were periods of greatest instability in Australia s foreign exchange market and these are incorporated in the data set. Further, the period selected includes the events studied by Felmingham and Buchanan (1993) and Kearney and McDonald (1991). The following analysis is based on a forward forecast error in the thirty day forward market. Tease (1988) has established that the markets for 15,90 and 180 days forward are efficient and not influenced by a risk p r e m i u m. Data relating to the spot USD/AUD exchange rate was sourced from the Reserve Bank of Australia which provided both the buy and sell spot rates. Daily observations on the USD/AUD rate were calculated as the simple average of these. A daily time series of the 30 day USD/AUD forward rate was obtained from the Commonwealth Bank of Australia s 4.00 pm Reuter s Monitor Service. These raw data were subject to a logarithmic transformation before the difference between the logarithm of the spot and equivalent 30 day forward rate was obtained. The task of matching the spot and forward rates is complicated by the effects of non trading days on the length of the forecast interval (k). Clearly, a forecast interval of 30 calendar days must be adjusted for the effects of weekends and public holidays. The convention in studies using daily time series is to discount each 30 day period by 8 weekend days making k = 22. However, 2 months in each 7 contains an extra weekend and there is also the effect of public holidays. This last issue is subject to a peculiarly Australian problem: public holidays are not synchronised across the Australian States. So one or both of the major markets in Sydney or Melbourne are closed for business on 18 public holidays. Felmingham and Buchanan (1993) find that both markets are open for 19.5 days each month of their sample period and they find that a forecast interval of k = 19 days is appropriate in the Australian case. The same approach is adopted here and k = 19. Preliminary tests of the data set reveal that observations on y t + k which also constitute y t and y t-1 with appropriate lags are kurtotic. So the forward forecast error data set is no different from daily financial price time series in general. The data set is characterised by having a comparatively fat tailed distribution. 1 1 The standard normal test statistics for excess kurtosis (17.78) and skewness (3.79) are above the customary critical values associated with the normal distribution. Further the Jarque- Bera (1980) test for normality, distributed as x 2 (2) indicates a test statistic of (206.3) well above accepted critical values.

6 52 B. S. FELMINGHAM AND P. MANSFIELD This problem is accommodated partially be assuming that the forecast error in (1), namely, ε t+k is conditionally, normally distributed: ε t+k N Φ t ~ (0,h t+k ) (4) In (3) the forecast error ε t+k conditional on the information set φ t has zero mean and is subject to the conditional variance h t+k. However, the unconditional component of the error variance is leptokurtic. The data set for y t+k is stationary. This is to be expected because y t + k is the difference between the logarithms of spot and forward rates. 2 The final issue surrounding the data set relates to the generation of observations for the conditional variance h t + k. This can be observed daily now that y t + k i s observable, but the question of how this variable is generated remains. the argument is that h t+k is generated by the familiar GARCH (p,q) model. The form preferred is simply p = q = 1 as follows: 3 2 h t+k = α 0 + α 1 ε t+k-1 + α 2 h t+k-1 (5) Our preliminary examination of the data set indicates that there is no obvious day of the week effect. This comes as no surprise given that the foreword forecast error is comprised of two market prices: the spot and forward exchange rates. If a particular day of the week is associated with thin trading, for example, in the spot market, then it is possible that the same applies in the forward market. Thin trading in the forward market may balance thin trading in the spot market and no day of the week effect is apparent in relation to the forward forecast error. 4. IDENTIFICATION OF SUB PERIODS OF INTEREST Our preference for the GARCH methodology is driven by the need to test for a continuously varying risk premium. However, the GARCH framework does not accommodate structural shifts in the behaviour of the premium through time. We accommodate this problem by fitting our GARCH model to selected sub periods in 2 We have confirmed the stationarity of y t + k through the application of the augmented Dickey-Fuller test for unit roots. 3 The full model (equations (6), (7) and (8) below) was estimated jointly with GARCH (1,2), GARCH (2,1) and GARCH (2,2) trialed. No lag s exceeding p = q = 1 were found to be significant.

7 RISK PREMIUM ON AUSTRALIAN DOLLAR 53 addition to estimation based on the entire sample period 15th December 1983 to 31st December We apply a formal approach to the identification of these sub periods. first, we identify those periods of greatest turbulence in the forecast error; turbulence which nay be reflected in a structural break in market attitudes to the Australian dollar and to the behaviour of the risk premium which reflects this change in transactors perceptions. Second, we attempt to find explanations for these structural breaks by examining market conditions at these times. To formalise the first step, we plot the distribution of forward forecast error (ffe s) and calculate its mean and standard deviation. From this, we identify the outlying observations of the ffe as those observed ffe s which are at least three standard deviations from the mean. Turbulent periods are defined as a sequence of three or more days of outlying observations of the ffe. The results of this analysis reveal substantial turbulence in two periods: the first of these begins on the 25th January 1985 and ends 15 days later on the 10th February So each successive observation of the ffe in this period is an outlier as we have defined the term. This period is easy to identify because it is also identified by Tease (1988) and Felmingham and Buchanan (1993) as turbulence associated with the sudden depreciation of the Australian dollar in the spot markets and the appearance of a constant risk premium. It is appropriate to estimate our model before and after this depreciation. So sub period I dates from the 12th December 1983 to the 15th January 1985, while sub period 2 begins on the 12th February Sub period 2 extends to the beginning of the next turbulent period which we find begins on 3 February Examination of market conditions on that day show that a record current account deficit was announced. From this date through to the 8th February 1989, observations of the ffe were all identified as outliers. Again, this period saw the rapid depreciation of the Australian dollar and so it is a period in which market perceptions and the risk premium may have altered once more. So sub period 2 terminates on the 31st January This leaves sub period 3 dating from the 10th February 1989 to the end of the sample period. The details of sample periods are provided in Table 1. Table 1. Estimation Periods Period Dates Observations Full Sample (S) 12 Dec 1983 to 31 Dec Sub Period (SP1) 12 Dec 1983 to 15 Jan Sub Period 2 (SP2) 12 Feb 1985 to 31 Jan Sub Period 3 (SP3) 10 Feb 1989 to 2 Dec

8 54 B. S. FELMINGHAM AND P. MANSFIELD Note that other episodes are not associated with at least 3 successive outlying observations of the ffe. These are not interpreted as periods of turbulence. An interesting example of this is the Australian Treasurer s Banana Republic statement made on the 15th May This referred to Australia s burgeoning foreign indebtedness and current account deficits. The market reacted instantaneously to this announcement: the Australian dollar depreciated by 5 percent (3 cents) on that day. However, this sudden drop followed a month of gradual gain, and no outlier in the ffe is observed during this period. So this episode does not qualify as a period of sustained turbulence. Similar comments apply to the Moody s downgradings of Australia s credit rating in late 1986 and Although there are instances of occasional single outliers in the ffe in our 12 year data set, there are no other clusters of 3 (or even 2) outliers together. 5. ESTIMATION METHOD AND RESULTS The equations (2) and (5) are to be jointly estimated noting the definition of the risk premium in (2) and the assumption of conditional normality in (4). There are two candidates for the estimation of (2) and (5). The approach adopted frequently is the maximum likelihood (ML) algorithm developed by Berndt, Hall, Hall and Hausman (1974) or the generalised method of moments (GMM) which is proposed by Rich, Raymond and Butler (1991) in the context of ARCH models. These authors suggest that ML methods may yield inconsistent parameter estimates and that GMM is preferred on these grounds. However, ML methods are asymptotically more efficient. The ML algorithm is preferred because of its greater efficiency. In addition, ML estimation allows us to study the behavior of the serial correlation. In particular, in equation (2), it is modelled as an M A k process. Our interest in studying the behaviour of any serial correlation is motivated by Lewis (1989), who argues that economic agents trading in forward markets must be capable of learning about new market conditions within the forecast interval. Otherwise any assumption about serial correlation cannot be justified. The GMM estimation method is adjusted for serial correlation and does not allow this analysis to be made. Gathering our assumptions together, the model to be estimated is: 1 y t+k = 0 a+ 1 ah 2 t+k + b 1 y t + b 2 y t-1 + (1-y 1 L-y 2 L γ k L k )ε t+k (6) ε t+k N φ t ~ (0,h t+k ) (7) 2 h t+k = a aε t+k-1 + a 2 h t+k : k = 19 (8)

9 RISK PREMIUM ON AUSTRALIAN DOLLAR 55 We relate the results reported in Table 2 below to the objectives of the paper. First, consider the results for the full sample: is there a risk premium on the USD/AUD spot exchange rate in the 30 day market? The conclusion about the risk premium is summarised in estimates of the parameters a 0 and a 1 for the constant and time varying component respectively. There is evidence of a constant risk premium (a 0 = ). This estimate is significant at all acceptable levels (t = 6.045). So, earlier evidence about the presence of a constant risk premium up to the end of July 1985 is confirmed for a much longer time period to the end of December Table 2. Estimates of (6) to (8) Equation Coeffi- Full Sub Period Sub Period Sub Period cients Sample a (6.045) (2) ( 0.090) (3.212) (0.406) a (0.484) ( 3.009) ( 0.278) ( 1.751) b (2.017) ( 1.627) ( 1.702) ( 6.288) b (0.262) ( 1.671) (2.234) ( 2.333) (4.430) (1.852) (3.544) (2.448) (8.040) (2.906) (5.970) (3.648) (62.366) (3.729) (39.025) (75.579) log-likelihood Notes: Estimates of MA terms are reported in Table 3 enclosed at the end of the test. t-ratios are shown in brackets There is no evidence in the full sample supporting the presence of a time varying risk premium. This inference is drawn from the estimate of a 1, which is not significant at any acceptable confidence level (the t-ratio for a 1 = is 0.484). The results for estimates of (6) to (8) in each of the 3 sub periods is revealing. Like Felmingham and Buchanan (1993) and Tease (1988), we find no evidence of a constant risk premium in sub period 1 (a 0 = 0.229, t = 0.090). However there is

10 56 B. S. FELMINGHAM AND P. MANSFIELD evidence of some volatility. The continuous component is significant (a 1 = 0.860, t = 3.009). However in sub period 2, the constant component of the premium is significant, (a 0 = 9.590, t = 3.211). However, a continuous variation of the premium is not evident (a 1 = 0.065, t = 0.279). In sub period 3, this pattern is similar to sub period 1, an insignificant constant term but a significant time varying component of the premium. The 30 day Australian forward market does not appear to be efficient in a rational sense in estimates for the full sample and for each sub period. The coefficient on the additional information variable y t is significant. The second of these variables is not significant but b 2 is significant in the last two sub periods. The MA 19 process, which adjusts estimates for serial correlation becomes insignificant at lag 19 indicating that serial correlation is fully adjusted within the forecast period. This is indicated by the insignificance of γ 19 in Table 3. Table 3. Estimates of MA Error Terms Lag Full Sample SP1 SP2 SP3 Coeff t E s t i m a t e s t E s t i m a t e s t E s t i m a t e s t E s t i m a t e s t γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ Notes: In all replications of the model (6) to (8) the learning process implied by Lewis (1989) is complete. The serial correlation is fully adjusted by MA 19.

11 RISK PREMIUM ON AUSTRALIAN DOLLAR SUMMARY AND CONCLUSIONS Our objective was to examine the Australian 30 day foreign exchange to determine if the USD/AUD market was affected by a risk premium and market inefficiency. The study was based on a daily data set spanning the period 15th December 1983 to 31st December The results of the analysis are clear cut. A constant risk premium was evident across the period, but there is no evidence to support the notion of a time varying risk premium. Agents in this market complete any learning process about fundamental market changes within the sample period. The M A k process fades within the forecast interval. However, there is some evidence of market inefficiency because the lagged forward rate error does influence the current forward rate error. In sub period estimates, we find no constant risk premium prior to the February 1985 depreciation, but a time varying component. In sub period 2 following the 1985 depreciation; a constant component of the premium is present, but no time varying component. And following the February 1989 depreciation we return to the outcomes for the first sub period, no constant but a significant time varying p r e m i u m. A pattern is suggested here. Depreciation creates uncertainty and the premium varies continuously until the market settles. Then the premium is constant and the volatility has disappeared. REFERENCES Baillie, R. T. and Osterberg, W. P., The Risk Premium in Forward Foreign Exchange Markets and G-3 Central Bank Intervention: Evidence of Daily Effects , Federal Reserve Bank of Cleveland, Discussion Paper 109, Bera, A. K., Higgins L. and Lee, S., Interaction Between Autocorrelation and Conditional Heteroskedasticity: A Random Coefficients Approach, Journal of Business and Economic Statistics, April 1992, Berndt, E. K., Hall, B. H., Hall, R. E. and Hausman, J. A., Estimation and Inference in Non Linear Structural Models, Annals of Economic and Social Measurement, Vol. 3, 1974, Bilson, J. F., The Speculative Efficiency Hypothesis, Journal of Business, J u l y 1981, Bollerslev, T., Generalised Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, Vol. 31 (3), 1986, , T., A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return, Review of Economic and Statistics, November 1987, Boothe, P. and Glassman, D., The Statistical Distribution of Exchange Rates: Empirical Evidence and Implications, Journal of International Economics, May 1987,

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13 RISK PREMIUM ON AUSTRALIAN DOLLAR 59 GARCH Models Models, Unpublished Manuscript, Lewis, K. K., Changing Beliefs and Systematic Rational Forecast Errors With Evidence From Foreign Exchange, American Economic Review, September 1989, Lucas, R. E., Asset Pricing in an Exchange Economy, E c o n o m e t r i c a, N o v e m b e r 1978, , Interest Rates and Currency Prices in a Two Country World, Journal of Monetary Economics, November 1982, Lumsdaine, R., Asymptotic Properties of the Maximum Likelihood Estimator in GARCH and I GARCH Models, Unpublished Manuscript, Harvard, Mark, N., On Time Varying Risk Premia in the Foreign Exchange Market, Journal of Monetary Economics, August McDonald, A. D., Kendall, J. D. and Ridley, T. L. A., GARCH-M Estimates of Variable Risk Premia for 180 Day Australian Bank Bills, Economic Record, March 1993, McFarlane, I., The Exchange Rate, Monetary Policy and Intervention, E c o n o m i c Papers, Vol, 13, 1994, Rich, R. W., Raymond, J. and Butler, J.S., Generalised Instrumental Variables Estimation of Autoregressive Conditional Heteroskedastic Models, E c o n o m i c Letters, Vol. 35, 1991, Roper, D. E., The Role of Expected Value on Analysis for Speculative Decisions in the Forward Currency Market: A Comment, Quarterly Journal of Economics, February 1975, Svensson, L. E. O., Currency Prices, Terms of Trade and Interest Rates, Journal of International Economics, February 1985, Siegel, J. J., Risk Interest Rates and Forward Exchange, Quarterly Journal of Economics, November 1972, Tease, W. J., Speculative Efficiency and the Exchange Rate: Some Evidence Since the Float, Economic Record, March 1988, West, K. D., Edison, H. J. and Cho, D., (1993), A Utility Based Comparison of Some Models of Exchange Rate Volatility, Journal of International Economics, February 1993, Mailing Address: Professor Bruce S. Felmingham, Economics Department, University of Tasmania, GPO Box 252C, Hobart Tasmania, AUSTRALIA. Tel:(002)202312, Fax:(002)234520, Bruce.Felmingham@econ.utas.edu.au Mailing Address: Professor Peter Mansfield, Accounting and Finance, University of Tasmania, GPO Box 252C, Hobart Tasmania, AUSTRALIA. Tel:(002)207591, Fax:(002)207845, Peter.Mansfield@accfin.utas.edu.au