TESTING THE EFFICIENT MARKETS HYPOTHESIS WITH FUTURES MARKETS DATA: FORECAST ERRORS, MODEL PREDICTIONS AND LIVE CATTLE JASON KING Monash University At the forefront of empirical research into the examination of the ef ciency of futures commodity markets, two fundamentally different testing techniques have been popularised ± the `forecast error' and `model prediction' approaches. This paper assesses the relative strengths of these techniques by contrasting results obtained when both approaches are used to examine the ef ciency of the Sydney live cattle futures market. While neither model provides evidence to suggest that this market is inef cient, it is clearly shown that the model prediction approach enjoys a number of distinct advantages over its rival. Indeed, the model prediction approach provides additional information that is important not only for those interested in testing the ef ciency of futures markets, but is important for anyone interested in developing a greater understanding of the determination of prices and the behaviour of agents in futures markets. I. Introduction The importance of the ef ciency of futures markets in an informational sense has long been known. As demonstrated in studies like those undertaken by Helmuth (1977), Hurt and Garcia (1982) and Gardner (1976), signi cant numbers of agricultural producers follow futures prices and futures prices affect the planned future supply, production, processing levels, and marketing of many different commodities. Informational inef ciencies result in a misallocation of scarce resources and in greater adjustment costs associated with hedging or forward contracting activities, inter alia. Indeed, issues of informational ef ciency are important because only in semi-strong ef cient futures markets can agents base their decisions about the inter-temporal allocation of resources on ``the most useful signals that the market can provide'' (Goss, 1990, p. 973). Past research examining the ef ciency of futures markets has popularised two very different testing techniques ± the `forecast error' and `model prediction' approaches. 1 This paper assesses the relative strengths of these I am grateful to Barry Goss, Gulay Avsar, an anonymous referee and the participants at the conference for which this paper was originally prepared, the Growth, Performance and Concentration of International Financial Markets conference in Prato, Italy, November 2000, for helpful comments and suggestions. Thanks also go to Anita Lacey for her assistance in collecting data. The usual disclaimer applies. 1 For examples of the forecast error approach, see Hansen and Hoderick (1980), Goss(1983, 1986, 1987) and Sephton and Cochrane (1990), while Rausser and Carter (1983), Brasse (1986) and Leuthold and Garcia (1992) and Goss and Avsar, (1996) adopt the model prediction approach. # Blackwell Publishers Ltd, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden MA 02148, USA and the University of Adelaide and Flinders University of South Australia 2001.
582 AUSTRALIAN ECONOMIC PAPERS DECEMBER approaches. The forecast error approach is used to test the ef ciency of the Sydney live cattle futures market. The results and methodology are juxtaposed in the subsequent section with those of Goss and Avsar (1999), who examined the ef ciency of the same market using the alternative approach. II. The ForecastError Approach Adopting Fama's (1970) terminology, a semi-strong ef cient market re ects all publicly available information fully and instantly. The forward rate quoted at time t for delivery at time t k (F t,t k ) is therefore the market's forecast at time t of the expected spot rate of the commodity at time t k (A t k ) given the information set Ù t F t,t k ˆ E(A t k =Ù t ) (1) The difference between the futures price and subsequent spot price is a forecast error. Forecast errors arise because of the incorporation of new information between time t and t k. The arrival of new information in an ef cient market is unpredictable and random and therefore no systematic relationship exists between current and prior forecast errors of own or related commodities. The set of publicly available information in this study is assumed to be contained within prior forecast errors between 1980:1 and 1985:10 of the Sydney trade steers contract, as this represents information contained within own past prices; forecast errors from the Chicago live cattle contract, because information that affects the supply and demand for beef in the U.S. also affects the price of beef traded in Sydney; and forecast errors from the Australian dollar/ U.S. dollar forward contract, as the U.S. is a large export market for Australian cattle and the exchange rate clearly affects the level of competitiveness of, and therefore the demand for, Australian beef. The speci c relationship that was estimated was A t k F t,t k ˆ á Xn â j (A j t F j t k,t ) å t k (2) jˆ1 where j is 1 for Sydney trade steers; 2 for Chicago live cattle; 3 for U.S. dollar per Australian Dollar; t is time in months; k is one month and å t k is the error term. Futures price data are the futures price on the median trading day of the month, for a contract one month prior to delivery. The Sydney cattle futures price data are `last traded' futures prices of live steers from the Sydney Futures Exchange Statistical Yearbook 1980±85. The Chicago live cattle futures price data are provided by the Chicago Mercantile Exchange while the Australian dollar/u.s. dollar contract is the one month `Forward Telegraphic Transfer Buying Rate' as reported in The Australian Financial Review. Sydney trade steers spot price data are prices for `futures type steers', on the median trading day of the month, provided by the New South Wales Meat Industry Authority. Chicago live cattle spot price data are the `last settlement price' of the contract as quoted by the Chicago Mercantile Exchange. 2 The Australian dollar/u.s. dollar spot rate is the Reserve Bank middle rate or the buying rate for the Australian dollar as quoted in The Australian Financial Review on the nal day of trading of the Sydney trade steers contract. Only contracts delivered on even months were used, as this 2 As noted by Leuthold and Garcia (1992, p. 62), `For cattle, calculated differences between monthly average cash and future prices in the maturity month were not signi cantly different from zero'.
2001 TESTING THE EFFICIENT MARKETS HYPOTHESIS 583 is when the Chicago live cattle contract is delivered. Overlapping observations are not included. The number of observations used in this analysis is 33. Estimation was achieved using instrumental variables with past forecast errors of cattle and Australian/U.S. dollars chosen as instruments. Ordinary least squares (OLS) is not an appropriate method of estimation because of the presence of the lagged dependent variable in the estimating equation. 3 A number of versions of the equation are tested and reported in Table I. In order to test whether Sydney live cattle prices re ect all public information embodied in the chosen variables jointly, the hypothesis H(á, â 1, â 2, â 3 ) ˆ 0 is also tested using a 2 test with k degrees of freedom, where k is the number of explanatory variables used in the model (including the constant term). Results for this test are also reported, together with the critical 2 test values at the ve per cent level. Diagnostic tests were performed and no autocorrelation was found to be present. The Jarque-Bera test suggests that all residuals are normally distributed. The results suggest that past Sydney live cattle forecast errors and forecast errors from related commodities included in the study do not help explain current forecast errors neither at an individual nor a joint level. The semi-strong form of the ef cient market hypothesis (EMH) cannot be rejected for this market over this time-frame. Further, the ^á parameter is not signi cant, suggesting a possible absence of a constant risk premium. However, one must recognise the small sample size used limits the power of the procedure. III. The Model Prediction Approach Goss and Avsar (1999) examine the same market over approximately the same time-frame using the model prediction approach. The model prediction approach was rst proposed by Hamberger and Platt (1975) and better developed by Leuthold and Hartmann (1979). The advantage lies in its methodology, which involves the development of a model of the market that not only tests levels of ef ciency, but can also help provide an important insight into the determinants of prices in the market ± an insight not provided by the forecast error approach. This is best illustrated by Goss and Avsar (1999), who use a simultaneous rational expectations model to con rm, for example, that behaviour of short hedgers and short speculators, and of long hedgers (such as meat processors and exporters) and long speculators, interact to determine the outcome in this market. Table 1 ESTIMATED COEFFICIENTS: K ˆ 1 month ESTIMATED 2 TEST STATISTICS Version ^á ^â1 ^â2 ^â3 Calculated 2 Critical 2 I(j ˆ 1, 2, 3) 4.54 0.36 0.22 206.77 6.73 9.49 ( 0.84) (0.22) (0.03) ( 0.48) II ( j ˆ 1, 2) 3.03 0.31 2.91 2.39 7.81 ( 0.49) ( 0.13) ( 0.51) III ( j ˆ 1, 3) 5.86 0.13 256.94 5.13 7.81 ( 0.14) (0.02) ( 0.13) t-statistics in parentheses. 3 See Hoderick, (1987), Ch. 3.
584 AUSTRALIAN ECONOMIC PAPERS DECEMBER Another important advantage of the model prediction approach is its ability to include variables that are not commodities in the relevant information set Ù t. Goss and Avsar demonstrate that the number of cattle in current yardings and the rationally expected change in future consumption based on the expected level of future real income, affects the future price of beef. These few variables are highlighted because they clearly affect the price of beef and yet cannot be directly incorporated into the forecast error approach. The choice of variables included in the forecast error approach is limited by the fact that a futures market for the variable must be in existence. Compared to the model prediction approach, where variables are included based on economic theory, the ultimate choice of variables in the forecast error model can appear somewhat ad hoc and arbitrary. After specifying and estimating the model for a sample period (1980.5±1985.12), the model is used to forecast spot prices outside the sample period (1986.2±1988.12). The out of sample period contains 35 observations. A necessary (but not suf cient) condition for the existence of an inef cient market is established if the model's predictions of the future spot price are consistently and signi cantly more accurate than the market's. In this case, while all estimates of the structural parameters of the model are statistically signi cant at the 5 per cent level, and all have signs that are consistent with the underlying economic theory, the model's predicted future spot prices are not signi cantly more accurate than those of the market. While the model prediction approach yields the same conclusions as the forecast error approach, namely that the semi-strong form of the EMH cannot be rejected for the Sydney live cattle market, important additional information about the functioning of the market is provided by the model prediction approach. For example, there is support for the rational expectations hypothesis assumed in the model, and for the variables used, that are shown to collectively determine futures and spot live cattle prices. A risk premium was discovered, and a positive relationship between the risk premium at the margin, and the number of market commitments of short and long speculators was identi ed. Further, the supply of futures contracts by short hedgers and speculators is shown to be a speculative relationship. The provision of these additional insights into the operation of the market suggests that the model prediction approach is potentially signi cantly more powerful than the forecast error approach. IV. Conclusion This paper has compared two approaches commonly used to test the semi-strong form of ef cient markets hypothesis. Using the Sydney live cattle market as a common point of reference (albeit across slightly different time periods), the forecast error approach provided no evidence to reject the semi-strong form of ef ciency (for 1980±85). Goss and Avsar (1999) developed a rational expectations model of the same market. Even though they estimate between 1980±85 and forecast between 1986±88, their conclusions concerning ef ciency are the same. More importantly, additional information was discovered about the processes of price determination within the market using the model prediction approach. The forecast error approach also suffers from the additional limitation of imposing severe data requirements upon an analyst, as it is only information captured in forecast errors that may be included. A greater range of variables supported by economic theory can be used in the model prediction approach. Failure to detect inef ciencies using either approach does not prove a market is ef cient
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