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Efficiency in Commodity Futures Markets

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1990
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An important characteristic of the 1970s and 1980s has been the large volatility of primary commodity spot prices. For instance, from 1971 to 1974 prices of food commodities (in SDRs) rose by over 100 percent, and then fell by 25 percent from 1974 to 1977. More recently, during 1983–86 prices of metals and minerals fell by 23 percent, then rose by 54 percent from 1986—88. This instability in commodity prices has affected the export earnings of a large number of developing countries dependent on the export of a handful of commodities, or even a single commodity. To the extent that many developing countries are net importers of these commodities, their import bills have also fluctuated considerably. The fluctuations have had a serious impact on their income and consumption, leading them to seek ways of reducing the fluctuations, or at least reducing their impact. At the macroeconomic level the impact on economic management can be reduced, for instance, by the authorities’ use of additional official funding as provided by the International Monetary Fund’s (IMF) compensatory and contingency financing facility (CCFF).1 At the more disaggregated level the risks being faced by individual agents or groups of agents can be reduced by using available market instruments. It is in the latter context that hedging via the futures markets can play an important role, which in turn may also have important stabilizing effects in the aggregate.

Commodity futures are, of course, hardly new. The operations of several of the futures markets go back nearly a century. However, the recent sharp expansion in the size of these operations, together with advances in communications, means that futures markets could make a substantial contribution to improving developing countries’ welfare.

A critical issue for any developing country contemplating the use of futures markets is the cost of using these markets. The costs are essentially of two kinds. The first one arises from the returns that may be demanded by other investors for assuming the risk of future spot price volatility—that is, the risk premium. The second cost arises from any market failure. If the market is not using publicly available information efficiently, futures prices become biased predictors of future spot prices, entailing additional costs in using the markets.2

An evaluation of these two types of costs revolves around the issue of market efficiency. According to the efficient-market hypothesis, the expected excess rate of return to speculation in the futures market for commodities should be zero. Since excess returns to futures speculation can be decomposed into two components—the risk-premium component and the forecasting-error component—a test of the efficiency hypothesis can provide an indication of the costs due to one or both of these components.

Despite extensive empirical research on futures markets, there is little agreement on the extent to which these markets can be characterized as approximately efficient. The reasons for the lack of consensus include empirical evidence based on nonuniform commodity samples, time periods, and econometric techniques. In any case, very few studies have examined the data for the 1980s, which has been a highly volatile period. The exercises this paper undertakes focus on the futures prices for seven commodity markets over the period 1976–88. A number of different econometric tests are used to evaluate the degree of efficiency of these markets and the ability of futures prices to forecast accurately future spot prices.

The rest of the paper is arranged as follows. Section I contains a discussion of the efficient-market hypothesis and of the existing main empirical studies on the validity of this hypothesis in commodity markets. Section II presents some simple descriptive statistics of excess returns in futures markets. Here, the paper focuses primarily on the unconditional prediction errors of the futures prices. The regression tests for conditional unbiasedness are undertaken in Section III. Section IV notes the main implications of the empirical results and suggests directions for future research.

I. The Efficiency Hypothesis: Theory and Existing Empirical Studies

The concept of efficiency as applied to commodity futures markets is no different from the concept as applied to any other asset market: the market is said to be (informationally) efficient if it uses all of the available information in setting futures prices. The intuitive idea behind this concept of efficiency is that investors process the information that is available to them and take positions in response to that information as well as to their specific preferences. The market aggregates all this diverse information and reflects it in the price.3

Formally, the market is said to be efficient with respect to some information set, Ф, if futures prices would be unaffected by that information being revealed to all participants. Moreover, efficiency with respect to the information set Ф implies that it is impossible to make economic profits by trading on the basis of Ф. This notion of efficiency can be made empirically operational by noting that the expected excess returns to speculation in the futures markets should be zero. Excess returns vt+n are defined by

where (ft+n, T) denotes the log of the futures price at time t + n, for any given contract maturing at some time T (T > t + n). Similarly, (ft, T) denotes for the same contract (maturing at time T) the futures price at time t. Since we only compare contracts of the same maturity, in order to simplify the notation in the subsequent discussion we will denote (ft, T) by ft, (ft+n, T) by ft+n, and so on.

The null hypothesis of efficiency is that on average excess returns are equal to zero:4

Rejection of H0 would imply that there is a systematic bias in futures prices, with prices at time t + n being on average higher or lower than prices at time t.5

It is important to emphasize that a rejection of H0, although indicating bias, does not necessarily imply that investors behave irrationally or that investors can make economic profits by speculating in the futures markets. This can be seen by noting that the excess returns in equation (1) can be decomposed into two components—one reflecting forecast error and one reflecting the risk premium:

The first term on the right-hand-side [E(ft+n)–ft] is the risk premium, RPt. It is the difference between the expectation at time t of a contract’s price at t + n and the contract’s price at time t. If RPt > 0, it implies that a hedger is selling a commodity by locking into a price that is lower than what may be expected to prevail in future, in order to have no price uncertainty. One way to interpret this term is to regard it as the compensation demanded by risk-averse investors for taking over the risk of future price changes. The second term is the forecast error, μt+n. It is the difference between the actual price at time t + n and the price expected at time t to prevail at t + n. If investors’ expectations are rational, the forecast error would be zero. Clearly if RPt is nonzero, vt+n being nonzero does not imply that investors’ expectations are not rational.6

The above two components of efficiency in futures markets reflect directly the twin roles of futures markets. The first, related to the notion of risk premium, is that futures markets act as insurance markets allowing diversification of commodity price risk. The second function is akin to the forecasting role—that is, futures prices provide forecasts of future spot prices. There is an extensive theoretical literature on both these roles. An example of the insurance role can be found in the model devised by Danthine (1978), in which producers of commodities purchase inputs in a given period in order to deliver output in the following period. Future demand is uncertain, and this generates price uncertainty. In this environment, Danthine shows that the role played by the futures price in the producers’ decision problem turns out to be exactly analogous to the role of a certain output price. Firms act as if they were hedging the totality of their production on the futures market.

The role of futures prices as predictors of future spot prices was first rigorously analyzed by Samuelson (1965). He showed that under certain assumptions the sequence of futures prices for a given contract follows a martingale; in other words, today’s futures prices are the best unbiased predictor of tomorrow’s futures prices. Furthermore, since by arbitrage futures prices and spot prices are equalized at maturity, futures prices are also unbiased predictors of future spot prices.

The two roles of futures markets are closely related. In particular, forecasting accuracy of futures prices is, as Danthine showed, linked to the degree of risk aversion of the participants in the market. For example, on the one hand, if speculators (as opposed to hedgers) are risk neutral, and if agents use all the available information rationally, it can be shown that futures prices will follow a martingale, as Samuelson demonstrated. On the other hand, if speculators are risk averse, they will require a premium from hedgers as compensation for taking over risk. As noted above, in such a case of risk aversion, futures prices will not be unbiased predictors of spot prices, since they will also include the risk premium.

In Danthine’s model, with only one asset market, the risk premium is necessarily positive. This does not need to be true in the more general models, such as that of Sharpe and Lintner’s “capital asset pricing model” (CAPM) or Lucas’s “intertemporal asset pricing model” (IAPM) (see, for example, Lucas (1978)). Neither CAPM nor IAPM makes any presumption about the sign of the risk premium, although they both assume that investors are risk averse and prefer assets that help to reduce the risk of their well-diversified portfolio (CAPM), or that they prefer assets that help to smooth consumption over time (IAPM). For example, in the latter model, if the expected gain from investing in the futures market covaries positively with investors’ consumption, the risk premium will be positive, because when the return is high, its marginal value to investors will be small. But if over time the conditional covariance of returns of futures assets and other assets in investors’ portfolios is changing and may also change signs, the risk premium will also be changing, and can fluctuate from positive to negative.

Empirically, the hypothesis of the efficiency of futures markets has been examined by a number of economists. Most of them imposed the condition of rational expectations to see whether excess returns in the futures market reflected a risk premium. Since under rational expectations the average forecasting error would be expected to be zero, nonzero returns would indeed reflect a risk premium. For example, Dusak (1973) analyzed the determinants of futures prices in the context of CAPM. In this framework, returns on futures market assets are governed by these assets’ contribution to the risk of a large and well-diversified portfolio. Dusak tested this model using bimonthly data for three commodities (wheat, corn, and soybeans) for the 1952–67 period and found that the risk premium in these contracts was not significantly different from zero.7 More recently, Hazuka (1984) tested a consumption-oriented CAPM for several commodities that were classified according to storage characteristic. Only futures contracts with one month to expiration were used. Hazuka found that the risk premium involved in the futures contracts was significantly different from zero, although the estimates of the coefficients in the model were different from their theoretical values.8

Both Dusak (1973) and Hazuka (1984) imposed the condition that the covariance of the return from holding a long position in the futures contracts and the return on market portfolio, or the covariance of the return and the marginal utility of consumption, was constant. To the extent that this is not so, their estimates of risk premia are not consistent.

The third detailed study of market efficiency is by Jagannathan (1985). Again assuming rational expectations, he analyzed the determinants of risk premium to determine whether two-month returns to futures speculations for three commodities (corn, wheat, and soybeans) for the 1960–78 period were consistent with the consumption-beta model of risk premium. This model requires that the relative return to two different assets move proportionally to the relative conditional covariances of the return to each asset and the rate of change of consumption. Jagannathan modeled the time-varying conditional covariance between the rate of change of consumption and the real return to forward speculation by projecting the observed covariances on a set of variables that included U.S. industrial production growth and the U.S. terms of trade. He found that although the co-movements of the estimated ex ante returns to forward speculation and the estimated conditional covariances were broadly consistent with the predictions of the consumption-beta model, on the whole the evidence suggested that this model does not provide an adequate description of returns to futures speculation.

As these studies indicate, and as noted earlier, the empirical evidence on efficiency in the commodity markets is diverse at best. The following analysis applies uniform tests to a large set of commodities over different time periods to see if any generalizations can indeed be made about the efficiency of the futures markets. In order to examine this issue, in Sections II and III we analyze the in-sample forecasting ability of futures prices and some alternative models over different sample periods.

II. Tests of Unconditional Unbiasedness

Some preliminary evidence on the forecasting ability of futures prices can be obtained by testing whether the excess returns from holding a futures contract for n periods are, on average, equal to zero. Excess returns, vt+n = ft+n–ft, as in equation (1), where ft and ft+n denote, respectively, the log of the futures price at time t and t + n. We test whether futures prices are unbiased forecasts of future spot prices by testing the null hypothesis9

where n denotes number of months. The reason that testing the null hypothesis is equivalent to testing whether futures prices are unbiased predictors of spot prices at the maturity of the contract is that futures prices at maturity, fT, are equal to spot prices, sT, by arbitrage.10 Since futures contracts do not mature each month, by using futures prices from contracts maturing at different times we can increase the sample size substantially.11 Therefore, the unbiasedness test based on excess returns as described in equation (1) has more power than similar tests based on excess returns over maturity spot prices, ST–fT.

Table 1 presents the results of this test for seven different commodities for the 13-year period 1976–88. It shows the mean excess returns from holding a futures contract for one, three, six, and nine months (that is, a forecast horizon of one, three, six, and nine months), and the corresponding t-statistic for the test of the null hypothesis of unbiasedness. In the case of corn, for instance, for a forecast horizon of one month, the mean excess return was—0.003, which is not significantly different from zero. Although mean excess returns are positive for some commodities such as cocoa and coffee, they are not statistically different from zero for any of the seven commodities, over any of the four forecast horizons.

Table 1.Tests of Unconditional Unbiasedness: Complete Sample
Forecast Horizon

(months)
Excess Returns

(ft+i–ft)
CommodityMeant-statistic
Food
Corn1–0.003–1.289
3–0.008–1.372
6–0.014–1.304
9–0.020–1.340
Soybeans1–0.001–0.281
3–0.002–0.241
6–0.001–0.117
9–0.000–0.029
Wheat1–0,002–1.129
3–0.006–1.061
6–0.012–1.069
9–0.017–1.005
Beverages
Cocoa10.0010.479
30.0020.309
60.0030.150
0.0070.242
Coffee10.0041.222
30.0131.344
60.0191,000
90.0321.100
Raw Materials
Copper10.0010.317
30.0010.207
6–0.001–0.117
9–0.006–0.309
Cotton10.0010.608
30.0020.326
60.0040.296
90.0080.445
Note: The t-statistics use standard errors corrected for autocorrelation (using method of moments). The i subscript refers to the forecast horizon (i = 1, 3, 6, 9). The sample is from March 1976 to December 1988.

The results in Table 1 suggest, at least superficially, that the null hypothesis of a zero bias in futures prices cannot be rejected. However, the evidence is also consistent with the presence of a time-varying bias; that is, bias that may be positive during some years and negative in others, and has zero mean. Since there is evidence from other asset markets, such as the foreign exchange market, that a time-varying bias exists, it would be important to check whether there is such a bias in the commodity futures markets.

One simple procedure for isolating any such bias would be to divide the sample into subperiods over which it is expected to display differential behavior. The method of obtaining the subsamples is based on the evidence on investor expectations in the foreign exchange market. This evidence suggests that, in general, investors consistently underpredict the value of an asset when the asset is appreciating (for example, the dollar in the early 1980s) and systematically overpredict it when it is de-preciating (as was the case after 1985 when the dollar started to depreciate; see Frankel and Froot (1987), and also Kaminsky (1988)). Following this type of evidence, we divided the 1976–88 period into subperiods according to whether the commodity spot price was increasing or falling. As it turned out, the results for futures markets were quite similar to those for other asset markets.

For illustrative purposes, Table 2 presents the results for two commodities. Consider first the results for wheat, for which the period March 1976 to December 1988 was divided into four subperiods: March 1976 to December 1976, December 1976 to January 1981, January 1981 to July 1986, and July 1986 to December 1988. During the third subperiod, the excess returns in the futures market were consistently negative for all four forecast horizons, indicating that futures prices overpredicted future spot prices. Conversely, during the last subperiod, excess returns had the opposite sign. In the case of cocoa (again with four different subperiods), during 1976–77 the excess returns were consistently positive, whereas over 1986—88 they were negative. For both commodities, the forecasting bias is generally significantly different from zero and is substantial in magnitude, reaching as much as 8 percent a year.

Table 2.Tests of Unconditional Unbiasedness: Selected Subsamples for Wheat and Cocoa
Horizon

(months)
Sample

Period
Excess Returns

(ft+i–ft)
CommodityMeant-statistic
Wheat103/76–12/76–0.020–1.75
3–0.046–1.86
6–0.075–3.32
9–0.067–2.11
112/76–01/810.0020.44
30.0060.58
60.0040.21
90.0010.04
?01/81–07/86–0.007–2.63
3–0.020–3.41
6–0.039–3.86
9–0.054–3.95
107/86–12/880.0051.16
30.0182.44
60.0393.39
90.0482.37
Cocoa103/76–03/770.0444.27
30,1199.81
60.2219.31
90.2927.70
103/77–08/820.007–0.53
30.040–0.51
60.074–0.51
90.128–0.06
108/82–01/840.0101.08
30.0140.87
60.0130.36
90.0000.01
101/86–12/88–0.009–1.82
3–0.029–2.95
6–0.053–3.75
9–0.067–3.53
Note: The t-statistics use standard errors of means corrected for autocorrelation (using method of moments).

As in the foreign exchange market, the nature of the bias changes over time, and is, on average, positively correlated with the sign of the change in the commodity spot price. For example, during 1981–86 the price of wheat declined almost continuously (see Figure 1), and realized excess returns during this period were negative. During 1986–88, when the price of wheat followed an upward trend, the excess returns in the futures market were consistently positive. In the case of cocoa during 1986–88, spot prices were expected to rise, but instead showed a downward trend with consistently negative excess returns (Figure 2).

Figure 1.Wheal Spot Prices and Excess Returns

(March 1976-December 1986)

Note: Nine-month forecast horizon.

Figure 2.Cocoa Spot Prices and Excess Returns

(March 1975-December 1988)

Note: Nine-month forecast horizon.

Similar results, although not included here, were obtained for the other commodities for different subperiods. For example, during the early 1980s, when spot prices in the soybean and the corn markets showed a trend decline, excess returns in the futures market for both commodities were consistently negative. In some cases these excess returns were over 20 percent a year, such as for corn from January 1981 to October 1982, or 16 percent, in the case of soybeans from November 1980 to October 1982. A similar pattern was found in the other markets, although the results were less significant.

This evidence of excess returns significantly different from zero does not necessarily imply market failure. There are two main reasons for this. The first has to do with the possibility that although expectations are rational ex ante, they may appear biased ex post. An explanation can be provided by a simple example in which investors use all the available information efficiently but still make nonzero forecast errors because the information is incomplete. The example is based on agents’ expectations of changes in a monetary policy regime: suppose a country’s monetary authority follows a contractionary monetary policy during some years and reverts to an expansionary monetary policy in subsequent years. Other things given, investors will in general observe that nominal prices of commodities will be falling when monetary policy is contractionary and increasing otherwise. Suppose that in these circumstances the spot price of a given commodity can be written as follows:

where δi, is positive if the monetary policy is expansionary (δe) and negative (δc) otherwise, and єt, is a white-noise process.12 Suppose that investors know that the monetary authority can change its policy from contractionary to expansionary but do not know with certainty when the change will be implemented. Of course, being rational they will use all the information available to predict the time of the change. But the prediction can only be probabilistic: the best they can do is to estimate the probability that the policy will be changed in a given period.13 Suppose that the current policy is contractionary, and denote by pt the probability of switching to an expansionary policy in period t. In this case the expected decline in the future spot price, using all available information up to period t—1, will be

Suppose now that the change in policy turns out not to be implemented for several periods. If we estimate the forecast errors during this period, we will obtain

which are, on average, different from zero, even though expectations were completely rational ex ante. In such a situation, as Frankel and Froot (1987, p. 150) concluded (in the case of the foreign exchange market), “investors could even be rational, and yet make repeated mistakes of the kind detected here, if the true model of the spot process is evolving over time.” In other words, when a given variable follows a process that is changing over time, agents in the process of learning will make mistakes. However, it does not mean that agents are not rational or that it will be possible to make money speculating in a market with such an environment.

Of course, over a long-run period—such as the 13-year period for our sample—there are likely to be periods of both upswing and downswing in prices, or periods of both contractionary or expansionary policies. This would mean that over a large sample period, investors’ forecasting errors, positive in some periods, negative in others, would tend to balance each other out. In such a situation the forecasting error will not be significantly different, on average, from zero—exactly the result obtained earlier in Table 1 for our full sample.

A second reason why nonzero excess returns do not imply market failure is the existence of a nonzero time-varying risk premium. Earlier it was shown that the excess returns in futures markets can be decomposed into a forecast error, μt+n, and a risk premium, RPt (equation (3)). Conditional on the assumption of a zero forecast error, a nonzero excess return could simply be interpreted as evidence of a nonzero risk premium—indicating that investors are risk averse. As noted in Section I. modern theories of asset pricing suggest that the risk premium separating futures prices in a given period from futures prices in subsequent periods will vary through time in proportion to the movements in the covariance of the returns of futures contracts and consumption. Since this conditional covariance may change signs, no bias need be found over a large time interval, even though over any given time period the expected excess return may be different from zero.

Although the above tests for efficiency appear fairly clear, they are based on a sample that relies on an ex post choice of possible breakpoints. Although such a procedure has been followed in the literature, it may not be wholly legitimate, since by definition the information on breakpoints is not available to investors ex ante. The next section presents tests of efficiency that overcome this problem.

III. Weak and Semistrong Tests of the Efficiency Hypothesis

The aim of this section is twofold: first, to examine the efficiency of futures markets without the imposition of ex post sample separation; second, in the event that the null hypothesis of efficiency appears not to hold, to find those variables that can consistently predict excess returns and hence improve over the forecast of spot prices made by using futures prices only.

The tests undertaken below are the standard tests used in the finance literature to test the efficient market hypothesis. These tests, proposed by Fama (1970), distinguish two levels of market efficiency: (1) the “weak” form, which asserts that current prices fully reflect the information contained in a historical sequence of prices; thus, investors who rely on past price patterns cannot expect to receive any abnormal returns (this is the random-walk hypothesis); and (2) the “semistrong” form, which asserts that current asset prices reflect not only historical price information but also all publicly available information relevant to futures markets. If markets are efficient in this sense, then no publicly available information (such as that, say, concerning the macroeconomic environment) can yield abnormal returns.14

Efficiency tests as applied to the futures market exploit the proposition that if information is used efficiently and there is no risk premium, the excess return from holding a futures contract for n periods (ft+n—ft) should not be correlated with information up to time t. This is because in such a case the excess return is just the forecasting error, and efficiency requires the forecasting error to be orthogonal to variables in the information set, It.15 This null hypothesis of market efficiency can be examined by testing the hypothesis that β0 = βm = 0 in the following regression:

where xt is a vector of variables in the information set It, and βm is a vector of m coefficients. Since under the null hypothesis, xt, and єt+n are orthogonal, ordinary least squares (OLS) will generate consistent estimates of the coefficients. In our case, however, the OLS estimates of the standard errors will not necessarily be consistent for two reasons. First, the errors might not be homoscedastic. The results of the White test (Table 3) suggest that for the majority of commodities the null hypothesis of heteroscedasticity cannot be rejected. Second, the errors in equation (7) may not be uncorrelated, since the sampling interval does not necessarily equal the forecasting interval. In this case, as Hansen and Hodrick (1980) show, the errors will be moving averages of order (n—1), where n is the forecast horizon. To obtain consistent estimates of the standard errors, we computed the correct asymptotic covariance matrix using the method-of-moments estimator proposed by Hansen (1982). Since in small samples the covariance matrix so estimated may not be positive-definite, we apply the Newey-West (1987) correction to guarantee positive definiteness.

Table 3White Test for Heteroscedasticity
CommodityX2(4)aMarginal Significance Level
Food
Corn3.3670.4984
Soybeans33.7128.537 (E-7)
Wheat1.5540.8170
Beverages
Cocoa6.6160.1576
Coffee9.5210.0493
Raw Materials
Copper46.3362.0966 (E-6)
Cotton17.6270.0015
Note: The dependent variables are the excess returns to a long futures position in each of the seven commodity markets. The right-hand-side variables include the lagged dependent variable with one and two lags and the square of the lagged dependent variable, also with one and two lags.

Although any element of the information set It could be used in a test of the hypothesis that (ft+n—ft) is orthogonal to It, in order to have a test with sufficient power one would want to use elements that are a priori likely to be important determinants of the excess returns. The elements in It, that we have selected fall into three categories, with the first category corresponding to the weak form of efficiency, and the second and third categories corresponding to the semistrong form. Thus, the first category includes past excess returns from the same commodity market, the second category includes past excess returns from the same and other commodity markets, and the third category includes past excess returns from the same commodity market, as well as some macrovariables such as aggregate consumption, industrial production, and the terms of trade that are likely to affect savings or investment, and therefore, rates of return on futures assets.

Table 4 presents the estimates of the weak test based on the following equation, which indicates excess returns in a given market as a function of a constant and three lagged excess returns:

In this table we present the point estimates of the β’s and the corresponding t-statistics, as well as the test of the null hypothesis that expected returns are zero (X2 statistic) with the corresponding significance levels. As the results indicate, the strongest evidence against the joint hypothesis of no market failure and zero risk premium occurs in the cocoa and the copper markets at the three- and six-month forecast horizon, respectively. In both cases some of the lagged excess returns have marginal significance levels smaller than 10 percent. Although the constants are not significantly different from zero, the null hypothesis is rejected that all coefficients for these two commodities are zero at marginal significance levels smaller than 5 percent. For wheat and coffee also, we can reject the null hypothesis for the nine-month forecast horizon at better than 10 percent level of significance. But for other maturities for wheat and coffee, and for other commodities, there is no strong evidence against the null hypothesis. In other words, for three of the seven commodities, namely corn, soybeans, and cotton, the futures markets cannot be said to be inefficient in the weak form. For the other four commodities, however, the null hypothesis of efficiency appears rejected for some of the forecast horizons at the conventional levels of significance.

Of course, the tests in Table 4 only use data from the “own” market. Since, as is generally accepted, these tests may not have enough power, we next discuss the results of the semistrong efficiency test (Tables 5 and 6). Table 5 presents the results of the own forecast error and the six other commodities’ lagged forecast errors, as indicated by the following equation:

Table 4Weak Test of Efficiency: Complete Sample
CommodityForecast Horizon (months)β0β1β3β3χ2 (4) Marginal Significance Levela
Food
Corn1–.003–.010.051–.0503.35
(–1.24)(–.08)(.85)(–.82)(0.5011)
3–.008–.038–.041.0012.31
(–1.42)(–.31)(–.42)(.01)(0.6789)
6–.014–.102–.022.1622.93
(–1.26)(–.64)(–.17)(1.08)(0.5696)
9–.024–.082–.176.1732.99
(–1.44)(–.40)(–1.57)(.81)(0.5595)
Soybeans1–.011–.620–.311–.2222.23
(–1.09)(–.95)(–.92)(–1.43)(0.6935)
3–.012.061–.522.3272.53
(–1.15)(.40)(–1.16)(.92)(0.6393)
6–0.0030.029–0.0370.0490.32
(–0.29)(0.27)(–0.24)(0.30)(0.9885)
9–0.005–0.087–0.1410.1421.31
(–0.32)(–0.41)(–1.00)(0.64)(0.8597)
Wheat1–0.002–0.0400.001–0.0581.94
(–1.10)(–0.51)(0.01)(0.84)(0.7468)
3–.005.028.037.0522.45
(–.94)(.28)(.36)(.53)(0.6536)
6–.003.306.027.0176.11
(–.31)(1.83)(.22)(.12)(0.1911)
9–0.0020.0090.1210.3318.22
(–0.08)(0.04)(1.21)(1.87)(0.0838)
Beverages
Cocoa1.001.045–.081.0181.36
(.44)(.56)(–.84)(.25)(0.8511)
3.000–.007.157.32619.59
(.63)(–.08)(1.16)(2.74)(0.0006)
6–.011.217–.072.2889.14
(–.79)(1.49)(–.72)(2.02)(0.0577)
9–.019.140.043.2256.02
(–0.94)(0.68)(0.32)(1.14)(0.1977)
Coffee1.004–.027.101.0712.78
(1.09)(–.26)(1.04)(.79)(0.5953)
3.013.194.072–.2235.58
(1.50)(1.66)(.67)(–1.52)(0.2328)
6.007.042.051.0330.49
(.43)(.33)(.43)(.21)(0.9745)
90.019–0.3740.1050.1668.32
(0.83)(–2.19)(0.96)(0.77)(0.0805)
Raw Materials
Copper1.001.051–.130.0772.65
(.33)(.47)(–.94)(.90)(0.6180)
3.002–.028–.004.091.69
(.23)(–.19)(–.20)(.66)(0.9526)
6–.002.347.067–.09710.69
(–.18)(3.18)(.49)(–.60)(0.0303)
–0.0020.090.200.115.20
(–0.11)(0.43)(1.04)(0.59)(0.2674)
Cotton1.001–.216.151–.1312.50
(.41)(–.97)(1.23)(–.95)(0.6446)
3.001.094.003–.1230.58
(.13)(–56)(.02)(–.67)(0.9653)
6–0.001–0.0220.0450.1130.78
(–0.13)(–0.16)(0.28)(0.66)(0.9411)
90.002–0.277–0.0660.1423.86
(0.11)(–1.54)(–0.34)(0.57)(0.4253)
Note: These are the estimates for equation (8) in the text. The dependent variable is the excess return in each of the seven commodity markets; the right-hand-side variables include a constant and the lagged dependent variable with one, two, and three lags. The χ2 is a test of the null hypothesis that expected excess returns are zero. The figures in parentheses below the coefficients are the t-statistics.
Table 5Semistrong Test of Efficiency: Full Sample
CommodityForecast Horizon (months)β0β1β2β3β4β5β6β7χ2 (8) Marginal Significance Level
Food
Wheat1–0.0030.059–0.1370.0200.011–0.038–0.0260.0017.41
(–130)(0.53)(–1,45)(0.19)(0.10)(–0.76)(–0.63)(–0.02)(0.4931)
3–0.0030.179–0.018–0.102–0.1600.065–0.1190.08815.92
(–0.59)(1.54)(–0.15)(–1.04)(–1.51)(–1.00)(–2.49)(0.93)(0.0435)
6–0.0040.157–0.204–0.2130.122–0.036–0.1950.27631.25
(–0.44)(1.48)(–1.33)(–1.99)(0.94)(–0.48)(–3.01)(2.56)(0.0001)
9–0.0040.403–0.610–0.2710.3970.052–0.2150.34776.78
(–0.46)(3.26)(–4.44)(–2.19)(2.95)(0.66)(–3.04)(3.45)(0.0000)
Corn
1–0.0030.065–0.1630.0340.210–0.0270.036–0.11010.85
(–1.40)(0.55)(–1.18)(0.75)(1.53)(–0.29)(0.88)(–2.06)(0.2103)
3–0.007–0.1380.124–0.108–0.1550.052–0.0540.23419.68
(–1.19)(–1.09)(0.77)(–1.11)(–0.96)(0.70)(–1.06)(2.46)(0.0116)
6–0.007–0.0910.124–0.1170.0960.040–0.176–0.39724.78
(–0.71)(–0.54)(0.62)(–1.05)(0.62)(0.44)(–2.92)(3.33)(0.0017)
9–0.015–0.065–0.174–0.016–0.006–0.013–0.1460.54436.26
(–1.12)(–0.26)(–0.82)(–0.14)(–0.04)(–0.11)(–1.79)(4.33)(0.0000)
Soybeans
1–0.0010.0480.173–0.048–0.2280.068–0.005–0.0693.81
(0.47)(–0.35)(–1.06)(0.30)(1.34)(0.87)(–0.9)(–1.05)(0.8738)
3–0.002–0.0680.1370.018–0.264–0.146–0.062–0.1668.86
(–0.34)(–0.56)(0.72)(0.15)(–1.11)(1.97)(–0.94)(–1.38)(0.3542)
6–0.000–0.252–0.130–0.143–0.228–0.201–0.1550.46273.69
(–0.02)(–1.55)(–0.65)(–1.14)(–1.06)(–2.46)(–2.70)(3.18)(0.0000)
9–0.004–0.067–0.2010.219–0.2880.126–0.1260.632107.72
(–0.27)(–0.35)(–1.47)(1.58)(–1.80)(1.30)(–1.65)(5.54)(0.0000)
Beverages
Cocoa
10.001–0.2820.0100.140–0.1030.038–0.0530.02310.67
(0.32)(–1.79)(0.08)(1.02)(–0.67)(0.46)(–0.76)(0.31)(0.2211)
3–0.003–0.359–0.0570.0350.3050.1720.055–0.05918.67
(–0.46)(–2.07)(–0.37)(–0.38)(2.08)(1.62)(–0.67)(–0.51)(0.0050)
6–0.011–0.4770.3770.2540.0580.2840.137–0.81641.34
(–0.89)(–2.52)(1.64)(1.59)(0.28)(2.42)(1.56)(–0.51)(0.0000)
9–0.023–0.4490.5930.392–0.3770.3470.153–0.22620.08
(–1.19)(–1.79)(1.94)(1.35)(–0.94)(2.11)(1.07)(–1.21)(0.0100)
Coffee
10.0040.035–0.178–0.1790.0700.147–0.018–0.1158.50
(1.52)(–1.08)(1.79)(–1.85)(–1.18)(2.49)(0.79)(1.32)(0.3862)
30.011–0.2150.377–0.310–0.2680.2850.0640.22729.79
(1.52)(–1.08)(1.79)(–1.85)(–1.18)(2.49)(0.79)(1.32)(0.0002)
60.014–0.6540.517–0.0590.1540.239–0.0440.35512.67
(0.96)(–2.75)(1.39)(–0.24)(–0.37)(1.65)(–0.33)(1.95)(0.1237)
90.031–0.3270.8130.062–0.7100.411–0.2020.25411.14
(1.54)(0.93)(2.07)(0.21)(–1.61)(1.92)(–1.14)(1.28)(0.1939)
Raw Materials
Copper
10.0010.118–0.0260.086–0.117–0.1030.0150.0945.99
(0.41)(0.94)(–0.28)(–0.92)(–0.89)(–1.48)(–0.31)(0.78)(0.6484)
30.0030.4280.089–0.062–0.2200.0480.027–0.03812.20
(0.45)(3.03)(–0.41)(–0.41)(–1.62)(–0.66)(0.40)(–0.28)(0.1425)
–0.0030.461–0.4910.0300.286–0.109–0.0810.26234.00
(–0.24)(2.94)(–2.49)(0.22)(1.33)(–1.25)(–0.95)(0.18)(0.0000)
9–0.0090.661–0.9730.0050.497–0.034–0.1490.134171.89
(–0.79)(5.10)(–6.75)(0.02)(2.93)(–0.42)(–2.39)(0.96)(0.0000)
Cotton
10.0010.0720.0250.1030.0360.079–0.0380.2226.25
(0.51)(–0.71)(0.19)(0.78)(0.27)(1.36)(–0.71)(0.38)(0.6193)
30.0030.192–0.0110.113–0.1960.016–0.0350.6135.95
(0.54)(1.39)(–0.05)(1.14)(–1.35)(0.25)(–0.46)(0.57)(0.6528)
0.0010.313–0.1940.1920.238–0.034–0.0520.04015.32
(0.14)(1.40)(–0.66)(1.73)(–1.11)(–0.36)(–0.67)(0.34)(0.0532)
9–0.0020.430–0.444–0.069–0.144–0.0820.0800.15234.90
(–0.12)(2.08)(–1.36)(–0.67)(–0.61)(–0.73)(0.95)(0.76)(0.0000)
Note: These are estimates of equation (9). The dependent variable is the excess return for a given commodity. The right-hand-side variables are the excess returns for all commodities lagged once. The figures in parentheses be Low the coefficients are the t-statistics.
Table 6Test of Efficiency Using Macrovariables
χ2 (8) Forecast Horizon (months)
Commodity1369
Corn9.193.858.2215.69
(0.3265)(0.8704)(0.4123)(0.0470)
Soybeans4.3710.1616.7829.80
(0.8223)(0.2540)(0.0325)(0.0002)
Wheat5.353.2612.1517.48
(0.7196)(0.9170)(0.1446)(0.0255)
Cocoa16.2927.8935.0041.86
(0.0384)(0.0005)(0.0000)(0.0000)
Coffee6.9718.3717.7551.23
(0.5399)(0.0186)(0.0232)(0.0000)
Copper7.744.5422.8717.42
(0.4593)(0.8054)(0.0035)(0.0260)
Cotton15.0414.5441.557.80
(0.0584)(0.0687)(0.0000)(0.4532)
Note: The table shows the χ2 and the marginal significance level for each of the seven commodities and four forecast horizons. The dependent variable in the equations for which the χ2 was computed is the excess return, and the right-hand-side variables include the following: lagged dependent variable, U.S. consumption, industrial production, terms of trade, money supply, interest rate, and the consumer price index. Figures in parentheses are the marginal significance levels.

where the superscript j refers to commodity j.

Intuitively, the use of past price information concerning other commodity markets, in addition to the own price information, should make it easier to earn excess returns, compared to using the commodity’s own price history only. This is so since presumably futures prices in other markets yield information that will complement or supplement the information from a commodity’s past history.

The results of this test are presented in Table 5. Contrary to the results in Table 4, the null hypothesis that all the coefficients are zero is rejected for six out of seven commodities for the six- and nine-month horizons, at 5 percent level of significance or lower. However, for the one-month horizon, the null hypothesis cannot be rejected for any of the commodities, and for the three-month horizon, it is rejected for four out of the seven commodities. Given that this multicommodity test is more powerful, the results in Table 5 do suggest that for short horizons the joint hypothesis of zero risk premium and no market failure cannot be rejected. However, for longer horizons these results can be regarded as fairly strong evidence against the efficiency of these futures markets, especially since the results are based on a 13-year period.

These conclusions are further corroborated by the final test of efficiency, whose results are presented in Table 6. As discussed earlier, in testing for nonzero expected real profits using the semistrong test, we should run a regression with the excess returns on the left-hand side, and variables in the publicly available information set on the right-hand side. As in the literature on efficient markets, we assume that if the information was in the public domain then it was available to the public and should have been reflected in prices. Of course, this assumption ignores the cost of acquiring the information, but the justification for this position is that the costs of acquiring such public information are small compared to the potential rewards. In principle, any variable in such an information set is a candidate in the regression equation. However, to improve the power of the test, we should include those variables more closely related with, for example, the risk premia in these markets. In the following test we have introduced different macroeconomic variables for the United States, such as the growth rate of consumption, the terms of trade, the inflation rate, the growth rate of industrial production, the growth rate of money supply and the riskless interest rate as measured by the treasury bill yield, as well as the own lagged forecast error. These were chosen as explanatory variables, because a number of existing studies suggest that they should affect investment and consumption decisions and possibly, therefore, rates of returns in the asset markets (see Jagannathan (1985)). It is worth emphasizing that the use of the data for the United States is likely to be as good a proxy as any for the macrovariables in the information set. In particular, the use of U.S. data would not lead to any weakening of the test or introduce any spurious bias.

For the above test, the following equation was estimated:

where xl denotes the six macrovariables noted above. Table 6 contains results of estimating equation (10) for each of the commodity markets over the 1976–88 period for the four forecast horizons examined earlier. In the table, rather than present estimates for each of the coefficients in each of the equations, only the value of the χ2 statistic is shown for the null hypothesis that excess returns are zero in each of the commodity markets for the four forecast horizons; that is, the composite hypothesis that β and γ are zero. The results here reject the efficiency hypothesis for only two commodities (cocoa and cotton) for the one-month forecast horizon, and three commodities (cocoa, coffee, and cotton) for the three-month horizon. However, for the six- and nine-month horizons, the null hypothesis is rejected for most commodities. For instance, for the nine-month horizon the null hypotheses is rejected at a very low level of significance for all commodities except cotton.16

V. Conclusions

The aim of this study has been to examine the extent to which futures markets for a number of widely traded commodities can be regarded as efficient. Whether or not the markets are efficient is of considerable importance to agents in developing countries, or indeed to any investor who may want to use these markets to hedge against price risk. If markets are not efficient, then apart from the transaction costs of using these markets, investors have to incur additional costs due to inefficiency. The methodology adopted in this study examined excess returns in seven different commodity markets over the 1976–88 period to investigate the issue of efficiency. Four main results emerged from the analysis:

  • For the entire sample period, unconditional excess returns were not significantly different from zero. If one assumes rational expectations, this would be consistent with zero risk premium and the observation that the costs of using the markets were not significant.

  • A detailed analysis of subperiods revealed, however, a more complex picture; for several of the commodities, excess returns continued to be statistically insignificant, but for the rest, especially cocoa and wheat, returns were significantly positive. It was argued that this result could be interpreted in two ways: first, there is no market failure (that is, futures prices are not biased predictors of future spot prices), and excess returns simply reflect a nonzero risk premium; or second, the risk premium is zero, but that does not necessarily imply market failure if the underlying processes generating spot prices are changing.

  • The weak form tests of conditional efficiency showed that the null hypothesis of efficient markets is not rejected for three commodities but is rejected for the other four for most forecast horizons.

  • The semistrong test confirmed that for short forecast horizons of one and three months, one cannot reject efficiency for most commodities. However, for horizons of six and nine months, for most commodities efficiency is rejected at high levels of significance.

These four results indicate that it is not possible to make any strong generalizations about the efficiency of the commodity futures market for short-term forecast horizons. For longer periods, however, it does appear that several of the markets may not be fully efficient. Of course, even in these latter cases, the empirical rejection of the efficiency hypothesis does not imply market failure. In particular, if investors are risk averse, a nonzero excess return may only reflect a time-varying risk premium. The results of this study do not allow one to distinguish whether in fact this is the case. A natural extension of this study would be to isolate the risk premium and to examine how it varies over time.

APPENDIX

Data Sources and Definitions

This Appendix describes the data used for the empirical tests as well as the methodology employed for computing excess returns.

Data

The bulk of the data on futures prices for the period March 1976 to December 1988 for food and raw material commodities were obtained from the Commodity Futures Trading Commission (CFTC). The rest of the data for these commodities and almost all of the data on coffee and cocoa contracts were culled from the daily Wail Street Journal. For each of the seven commodities, data were obtained on price per unit of commodity for all of the outstanding contracts. (Table 7 gives the delivery months and other descriptive information for each of the commodities.)

Table 7Commodity Futures: Descriptive Data
CommodityExchangePrice/Unit of CommodityUnits of Commodity/Trading UnitDelivery Months
Food Products
CornChicago Board of Tradecents/bushel5,000 bushelsMarch, May, July, September, December
SoybeansChicago Board of Tradecents/bushel5,000 bushelsJanuary, March, May, July, August, September, November
WheatChicago Board of Tradecents/bushel5,000 bushelsMarch, May, July, September, December
Beverages
CocoaCoffee, Sugar, and Cocoa Exchangecents/pound22,046 pounds (10 metric tons)March, May, July, September, December
CoffeeCoffee, Sugar, and Cocoa Exchangecents/pound37,500 pounds (approximately 250 bags)March, May, July, September, December
Raw Materials
CopperCommodity Exchange Inc.cents/pound25,000 poundsJanuary, March, May, July, September, October, December
Cotton (No. 2)New York Cotton Exchangecents/pound50,000 poundsMarch, May, July, September, December
Note: For all seven commodities the sample period is March 1976 to December 1988.

For soybeans and copper, the analysis was limited to the five major contracts per year. The price quotation was the settlement price on the first operating day of each month. In general, contracts trade for 12 months or more, but the markets for 9 months or before the contract expiry date are fairly thin.

Methodology for Computing Excess Returns

Excess returns for seven commodities were computed for one-, three-, six-, and nine-month horizons. The key step in the computation was to form a continuous series of returns using the nearest contracts. This procedure is illustrated in Table 8 for wheat for one and six months. Consider, for example, the one-month return. To obtain a value for March 1988, the difference in the February 1988 and March 1988 price for the March 1988 contract is taken. For April and May values, the May contract is used, and so on. Consider next the six-month return: for the March 1988 value, the difference in the September 1987 and March 1988 price for the March 1988 contract is taken. For the next two values for April and May, the May 1988 contract is used. For April 1988, the difference in the October and April prices is taken for this contract. For May 1988, the difference in the November and May prices is taken for the same contract. The returns for three months and nine months were constructed similarly for the same contract.

Table 8Computation of Excess Returns: An Illustration
ReturnContract Montha
One-month forecast horizon
03/88–02/88March
04/88–03/88May
05/88–04/88May
06/88–05/88July
07/88–06788July
08/88–07/88September
09/88–08/88September
10/88–09/88December
11/88–10/88December
12/88–11/88December
Six-month forecast horizon
03/88–09/87March
04/88–10/87May
05/88–11/87May
06/88–12/87July
07/88–01/88July
08/88–02/88September
09/88–03/88September
10/88–04/88December
11/88–05/88December
12/88–06/88December

The next step was to take the time series for different returns and use them for the tests undertaken in the text. For example, in the case of the weak efficiency test with three lags, the following regression was run for the six-month horizon:

In this case, if the excess return is given by the price difference over December 1988-June 1988. then prices over June 1988-December 1987, May 1988-November 1987, and April 1988-October 1987 are the three explanatory variables. The key point to note in this methodology is that the excess return for any given time period is computed using only one contract’s prices; in each case, the contract is the one with the maturity date at, or nearest to, the time period for which observation is required.

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Graciela Kaminsky, an Assistant Professor of Economics at the University of California at San Diego, was a Visiting Scholar in the Research Department when this paper was written.

Manmohan S. Kumar, an Economist in the Research Department, is a graduate of the London School of Economics and Political Science. He received his Ph.D. from Cambridge University, where he also taught before joining the Fund.

The authors are grateful to Bijan Aghevli, Guillermo Calvo, and Peter Wick-ham for valuable advice and comments. Comments from Michael Dooley. Roger Pownall, Assaf Razin, Blair Rourke. and participants in a Research Department seminar are also gratefully acknowledged.

The CCFF was established in August 1988 replacing the former compensatory financing facility (CFF). The new facility preserves the basic features of compensatory financing and in addition provides contingency financing from the IMF to help members maintain the momentum of IMF-supported adjustment programs. For an account of the operations of the facility, see Pownall and Stuart (1988).

Another cost of operating in the futures market is the transaction cost (which includes brokers’ and other commission fees, the cost of maintaining margins, and others). This cost is, however, likely to be much smaller than the two discussed above and. in any case, does not raise any important conceptual issues.

See Ross (1987). The use of efficiency in the informational sense is different from the notion of Pareto efficiency, whereby an economy is efficient if it is not possible to produce more of any one good or service without lowering the output of some others.

As we discuss below, this is a necessary but not a sufficient condition for efficiency.

Although the information set at t + n is different from that at t, if markets are efficient there is no presumption, on average, that ft+n would exceed, or be less than ft.

Even more strongly, as will be discussed presently, when RPt = 0 (because investors are risk neutral, or because the sign of risk premium changes over time with its average being zero), μr+n ≠ 0 docs not necessarily imply that investors are irrational.

In a more recent study, Bodie and Rosansky (1980) found that if the Dusak sample is extended to a longer period (1950–76), the unconditional excess returns are significantly positive.

Hazuka (1984) examined one-month-to-maturity returns of futures contracts for agricultural commodities including corn, oats, sugar, and wheat, and metals such as copper and silver.

The reason for calling this a test of “unconditional” unbiasedness is that it is not dependent on any specific information set based on which expectations are to be taken. For instance, in subsequent analysis, the information set consists only of past prices of the same commodity or information on macro variables. In this case all publicly available information is included.

To see the equivalence of the null hypothesis and the proposition that futures prices are unbiased predictors of future spot prices, apply iteratively the unbiasedness hypothesis to k periods and note that the time t information set is a subset of the t + 1 information set. This gives

See Appendix for the methodology for combining different futures contracts.

It can be shown using the Lucas (1980) model that this will be the stochastic process followed by spot prices if money supply follows a random-walk process with a changing drift δi, and output is constant.

This issue can also be analyzed in the standard Bayesian approach. Agents acquire new information in each period and revise prior beliefs continuously. The distribution of the information set, therefore, becomes tighter over time. This approach is consistent with the fact that markets appear to be more efficient over the short-term horizon than over the longer term.

There is a third “strong” form of efficiency, which asserts that all information that is known to any investor, including privately held information, is reflected in market prices. Thus, no abnormal excess returns are possible.

Note that in these tests the notion of efficient use of the available information imposes stronger restrictions than the one discussed in the previous section in which investors had incomplete information about the stochastic process followed by the variable in question.

It should be noted that the rejection of the efficiency hypothesis for forecasts greater than three months was corroborated by an analysis of the out-of-sample predictive power of futures excess returns vis-à-vis the model in Table 5. For instance, the efficiency gain by using the model in Table 5 for soybeans for a nine-month forecast horizon for the period 1986–88 was 32 percent; for copper, for the same forecast horizon and time period, it was nearly 30 percent. The detailed results of these tests are provided in Kaminsky and Kumar (1989).

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