Food Commodity Futures: Are They Useful for Inflation Forecasting? José A. Murillo 1 Tonatiuh Peña 2 Banco de México 3. Abstract

Transcription

1 Food Commodity Futures: Are They Useful for Inflation Forecasting? José A. Murillo Tonatiuh Peña Banco de México 3 Abstract Inflation forecasting has been challenged by the largely unexpected upward cycle of grain spot prices that started in. The phenomenon induced significant inflationary pressures around the globe, bringing to the attention of central bankers the need to understand the workings of food commodity markets in order to improve their inflation forecasts. A common response has been to use commodity futures as spot price predictors. However, the predictive power of these instruments has been questioned by several economists, which contend that forecasts based on spot prices are as reliable as future based forecasts. This paper revisits the work of French and Fama (97) by analyzing a longer span of time in food commodity markets. Predictive power capacity and stability are evaluated for the futures of the following commodities: corn, wheat, soybeans, cattle and hogs. The contributions of the study are summarised as four main findings: first, it is confirmed that forecasting ability of commodity futures varies over time; second, despite variations, this forecasting ability has progressively increased along the years towards market efficiency; third, animal futures tend to provide better forecasts than grain futures; fourth, evidence suggests grains and cattle futures may have lost some of this predictive power from onwards. Results suggest that futures usefulness to forecast commodity spot prices is state dependent, and therefore should be used with some reserves. JEL Classification: G, G3, G, E3, E37, E5, E5. Keywords: Commodity prices, market efficiency, futures predictive power, inflation forecasting, central banks policies, structural change detection. jmurillo@banxico.org.mx tpena@banxico.org.mx 3 The opinions expressed in this paper are the sole responsibility of the authors and do not necessarily reflect the views of Banco de México. We would like to thank Yenisey Farfán and Fabiola Cañas for having provided excellent research assistance and Arnulfo Rodriguez for valuable comments.

2 Introduction Inflation forecasting has been challenged by the largely unexpected upward cycle of grain spot prices that started a few years ago. As an example, corn, soybeans and wheat futures traded at record highs throughout in the Chicago Board of Trade (CBOT). This phenomenon induced significant inflationary pressures around the globe, bringing to the attention of central bankers the need to understand better the workings of food commodity markets in order to improve their inflation forecasts. Within the Latin American context, the impact of the price surge was particularly critical due the high proportion of spending that the population of the region allocates to buy food. One way to further the understanding of food commodity markets is to review once more if market based indicators (such as futures prices) are useful to forecast spot prices. Although the predictive power of these instruments has been both praised and criticised by different economists (e.g. Kenyon, Jones and McGwirk, 993; Leuthold and Tomek, 9), a re evaluation is required because of the concerns already mentioned. If futures prices forecast correctly any future trends of prices, then inflation forecasts could benefit from such market information. If on the contrary, futures prices are not reliable predictors of future price movements then policymakers should take into account such deficiencies or rely on alternative prediction methods (Chinn, LeBlanc and Coibion, 5). This paper revisits classical works like those of Tomek and Gray (97) and Fama and French (97) on the evaluation of market efficiency of agricultural and animal commodities. Special emphasis is given to corn, soybeans, wheat, feeder cattle and hogs futures, although some others are discussed throughout the paper. We follow (Serletis, 7) and do as him: conditional on the hypothesis that commodity markets are rational, this work evaluates market efficiency in terms of Fama s (9) variance decomposition approach to test the joint variation in the premium and the expected future spot price components, with respect to the so called basis. In contrast with previous work, a longer span of time is considered, including periods of low and high volatility: the food scare of the seventies and the recent episode of high commodity prices are some examples. The concepts of market unbiasedness and predictive power are defined in a (hopefully) more objective way than other sources in the literature. Furthermore, the time evolution of forecasting ability is monitored along time, just as Kenyon, Jones and McGwirk (993) did; however, structural changes in forecasting performance are detected in a more principled manner. Our results suggest the capacity of futures to predict spot prices has continuously evolved over time. Remarkably, in the long run this evolution has veered towards increased predictive power and therefore market efficiency. Nevertheless, episodes like the recently lived period of high

3 commodity prices seem to have weakened the forecasting performance of commodity futures. The main findings described in this paper are: Corn futures have been efficient predictors of spot prices for at least three decades. Specifically they had relatively good predictive power from 97 9 but had an increase in such power from 9 3. Soybeans are weak predictors and only had relatively good performance on the period 97 9, for some maturities. Regarding wheat futures, they turned out to be good predictors solely for the period 9 99, but for the rest of years had poor predictive performance. In a similar way to agricultural commodities, cattle futures had a sustained period of good predictive ability. From 9 99 they were moderately good predictors and from they increased their predictive power. Hog futures have been consistently good predictors, from 97, despite the market restructuring of 997. The comprised commodity futures have gone through phases of structural breaks in their forecasting performance. We found 973, 95, 99 and as potential years for structural breaks in most commodities. This paper is organised in the following way. Section summarises existing literature on the analysis of the predictive performance of futures prices. Section 3 introduces the mathematical model used to evaluate market efficiency. Section describes data used in experiments carried out to prove the theory. Sections 5 and are devoted to the presentation of results. Section 7 includes a discussion about the limitations and constraints of our work. Finally, Section presents conclusions and future work. Literature Review The theory of price of storage (Kaldor, 939 ; Hawtrey, and Working, 99) and the theory of normal backwardation (Keynes, 93 and Dusak, 973) are the leading theories of commodity price behaviour (Fama and French, 97). The first one explains the difference between current spot and futures prices in terms of the so called cost of carry, which is composed of the interest foregone in storing a commodity, the warehousing costs and the convenience yield incurred on inventory. While the second interprets the futures price as comprising two components, an expected risk premium and a forecast of the forthcoming spot price. The intuition that the futures price is the optimal forecast of the spot price is an implication of the efficient market hypothesis (EMH) popularised by Cootner (9) and Samuleson (95). EMH assumes that on average, market participants are risk neutral, have rational expectations and that prices fluctuate randomly about their intrinsic value at each moment in time (Taylor, 95 and 3

4 Fama, 97). Therefore no system based on past market behaviour can do other than break even; otherwise investors would generate unlimited profits. As mentioned by Carter (999), empirical testing for efficiency is difficult because this definition is very general. The link between efficiency and forecastability arises from realising the difference between the current futures price and the future spot price represents both the forecasting error and the opportunity gain or loss realised from taking certain positions. Stein (9) goes further and divides forecast error into avoidable and unavoidable social loss. If futures prices are unbiased forecasts of spot prices, then only unavoidable social loss exists. Tomek and Gray (97) and later Kofi (973), were the first to test the forecasting ability of the futures market within the context of market efficiency.. Forecasting performance of agricultural and animal commodities The forecasting performance of agricultural and animal commodity futures has been studied for at least thirty years, with the work by Tomek and Gray (97), Kofi (973) and Leuthold (97) on corn, wheat, soybeans and cattle as early examples. For the period 95 9, Tomek and Gray found that springtime futures contracts of corn and soybeans were good predictors of the subsequent harvest prices. They argued that storage across crop years links prices via storage costs and consequently harvest prices should never exceed current prices plus storage costs. Kofi made an extension by considering a wider range of commodities (potatoes, coffee, wheat, corn, soybeans and cocoa) and by applying a different period, Among other things, he found that the further away from the contract expiration date, the worse futures contracts perform as forecasts of spot prices. He also argued that forward pricing efficiency is a function of three variables: the nature of the commodity, the quality of information about supply and demand and the degree of government intervention. Finally, Leuthold analysed corn and cattle and similarly found the futures market to be an efficient predictor of spot prices up to certain horizons (four months approximately). A further update was done by Kenyon, Jones and McGwirk (993) up to the year 99 for soybeans and corn. They confirmed Tomek and Gray s finding of good predictive power for 95 9 (in fact up to 97) but also encountered that it declined for They removed 973 from their work because it was a year where the structure of futures prices changed. Whereas from corn and soybeans futures were unbiased forecasts of forthcoming spot prices, from their forecasting power declined to the point of becoming biased. Kenyon et al. reasoned this decline was due to the reduced role of the government in the marketplace and greater production uncertainty. Up to our knowledge their work is the first to consider the evolution of predictive power along time. On the realm of animal commodities, the research by Leuthold and Hartmann (979) on the forecast power of hog futures is one of the most cited ones. In their work, they conclude the live Interestingly French (9) argues that futures prices should perform better for longer time horizons under certain conditions.

5 hogs futures market does not reflect all publicly available information and is inefficient. Such conclusion was obtained after comparing the forecasting performance of a demand supply model against futures prices. Live cattle futures were found to have inadequate forecasting performance by Martin and Garcia (9). 3 A model for the joint variation of spot and futures price changes Assuming markets are rational, this section uses Fama s (9) variance decompostion approach to test a model for joint measurement of variation in the premium and the change of expected spot prices in terms of the basis. The model is an approximation to detect forecasting power and therefore is a measurment of EMH. It is worth noting that Fama s model is different from those applied in earlier works (e.g. Tomek and Gray, 97; Leuthold, 97) in that the non stationary nature of the data is addressed (see Appendix A for further discussion). 3. The model Fama and French (97) defined the relationship between the futures price and the current spot of a commodity as given by the sum of an expected premium and an expected change in the spot price F( t, T ) S( t) = E P( t, T ) + E S( T ) S( t) t { } { }. The following notation has been introduced. Let t and T be time stamps at which spot price S and futures price F of a given commodity are observed, then we will denote by S(t) and S(T) the spot price observed at times t and T, respectively; while F(t,T) is the futures price observed at time t for delivery at T. The premium is defined as the bias of the futures price as a forecast of the future spot price, i.e. P(t,T)=F(t,T) S(T), while the basis is defined as the difference F(t,T) S(t) and the change as S(T) S(t). We will assume there are t=[,n] observations for a given maturity period T. t If we assume that log premium and log spot rate follow separately a random walk with drift and that expectations are rational, then it is theoretically possible to model linear relationships for the time T t expected premium and the expected change in the spot rate, both in terms of the basis. In fact, the joint variation model F ( t, T ) S( T ) = α + β [ F( t, T ) S( t) ] + u( t, T ) () S ( T ) S( t) = α + β [ F( t, T ) S( t) ] + e( t, T has been used by several authors (e.g. Serletis, 7 and Fama, 9). Reliable evidence that β is positive indicates time varying expected premia, something that is not good for making predictions; while reliable evidence that β is, tells the basis is capturing changes in spot prices, something that is good for forecasting. Both () and () depend on the basis, so it is easy to deduce that constraints α + α = and β + β = apply (Serletis, 7). According to Kenyon, Jones and McGwirk (993), if the forecast is perfect (β = and β = ) there will be minimal social welfare loss. ), () 5

6 3. Tests for market efficiency and assessment of explanatory power Research to find evidence of market efficiency (i.e. unbiased forecasting performance) in futures markets has been carried by several researchers and as noted earlier, with remarkably mixed results. Barnhart and Szakmary (99) showed that conflicting results in the literature depend upon the particular econometric specification as well as differences in the time period of estimation. However, as relevant a factor has been the vague use of the term forecasting performance, as pointed by Martin and Garcia (9). The subsequent discussion aims to find a consistent specification of the terms forecasting performance and explanatory power in order to analyse the results in a more objective way. We will resort to Equations () and () to ellaborate our ideas. The term market efficiency will be used as synonym of unbiased forecasting performance and will refer to the basis ability to detect trends in spot price changes. Meanwhile explanatory power will be used to quantify such predictive ability. A revision of previous work shows great diversity to test for EMH. For example, Fama and French (97) along with Serletis (7) use the hypothesis H: β = for this purpose. Meanwhile Martin and Garcia (9); Kenyon, Jones and McGwirk (993) and Zulauf, Irwin and Sberna (999) prefer to make use of the joint test 5 H: α =, β =. Contrastingly, Chinn, LeBlanc and Coibion (5) test H: β = for market efficiency and use α > to identify any drifts in the price changes. As Barnhart and Szakmary mention, performing the joint test α =, β = implies testing simultaneously the complementary case α =, β =, and therefore only one needs to be done. Some authors dismiss the α intercepts on the assumption that non rejection of the hypothesis H:β = amounts to nonrejection of the efficient markets hypothesis. Some others, like Martin and Garcia (9) pay special attention on α because, according to them, futures prices should not systematically overor under estimate the level of spot prices Although application of the joint test H: α =, β = might be the most principled strategy, it certainly obscures any conclusions that may be drawn because rejection of the test might lie on either parameter α or β. Therefore, we prefer to test separately H:α = and H:β =, keeping in mind that the coupling of Equations () and () implies that the complementary tests H:α = and H:β = are carried out implicity. Our position regarding the α s is similar to that of Serletis (7) and consists of relying on β and β to test for market efficiency and biasedness. Establishing if futures prices are unbiased forecasts is relevant, but just as important is to determine how much explanatory power they have on spot prices. French (9); Kenyon, Jones and McGwirk (993); Zulauf, Irwin and Sberna (999) and Chinn, LeBlanc and Coibion (5) all use the coefficient of determination (R ) to evaluate the explanatory power of futures prices. However, not all of them use it in the same way. For example Zulauf et al. and Chinn et al. are the 5 Better known as the Wald test for coefficient restriction.

7 only ones to test the hypothesis H:R = to determine if its value is statistically different from zero. In this work we use the coefficient of determination associated with Equation (), subsequently denoted as R. Table below shows a summary of the approaches taken in selected literature to determine market efficiency and measure the explanatory power of futures prices. Model Market efficiency Authors H: β = Fama and French (97); Serletis (7) H: α =, β = Martin and Garcia (9); Kenyon, Jones and McGwirk (993); Zulauf, Irwin and Sberna (999) H: β = and α > Chinn, LeBlanc and Coibion (5) Equation Explanatory power Authors () R French (9); Kenyon, Jones and McGwirk (993); Zulauf, Irwin and Sberna (999); Chinn, LeBlanc and Coibion (5) H:R = Zulauf, Irwin and Sberna (999) Table. Summary of different approaches taken in the literature to determine forecasting performance (i.e. market efficiency) and to assess the explanatory power of futures prices. The parameters α, α and β, β are those of Equations () and (). R is the coefficient of determination associated with Equation (). Data We used time series generated from the daily quotations of futures contracts traded in the Chicago Board of Trade and Chicago Mercantile Exchange, CBOT and CME respectively. The time series were used to construct monthly observations on the basis, the change and the premium according to the widely used approximation of the spot price defined by Fama and French (97), for different forecasting horizons. The approximation consists of using the future price on the delivery month as a proxy of the spot price and was used because measuring the basis presents two problems. As expressed by Fama and French (97), in first place most futures contracts do not have specific maturity date but instead have a delivery period of three to four weeks at the beginning of the maturity month. In second place, it is hard to homologate spot and futures data to coincide with the same type of commodity and to be sampled at the same frequency. The Fama and French approximation allowed us to overcome these limitations. Therefore, as they also explain, this means for example that the spot price for wheat on March 99 was approximated with the quotation of the futures price of the contract that matures in March of 99. Regarding futures prices, we used for example as months futures price the quotation on March 99 for the May 99 contract; as 3 month quotation the February 99 price and so forth. Kenyon, Jones and McGwirk (993) report that estimation results of the joint variation model of Section 3. are mostly invariant to the date specified for making the spot price approximation. Most data (9 ) was obtained from Turtle Traders website: The rest was collected from Bloomberg, for the period 3 and occasionally from the Commodity Research Bureau s data yearbook of. 7

8 Regarding grains, Tomek and Gray (97) used the settlement price on the last day of the trading month as proxy of the spot price, while Kenyon et al. used the 5 th of each month. Moreover, Martin and Garcia (9) made the approximation through third week closing prices. Table below summarises the structure of the commodity price data used in this paper. Each row shows the sample period for a commodity and the standard months in which the contracts mature. Futures contracts for these standard months usually begin trading to months prior to the delivery period, which is of 3 to weeks on the maturity month (Fama and French, 97). Hogs data is composed of live and lean hogs futures. As explained in Section 7, in 997 the CME revamped this market by replacing futures of live animals by those of lean ones (just the carcass), The change had as purpose the creation of a more efficient market. Cmdty Exchange Start Date End Date Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Corn CBOT Mar May 9 H K N U Z Wheat CBOT Mar May 9 H K N U Z Soybeans CBOT Mar May 9 F H K N Q U X Hogs CME Feb May 97 G J K M N Q V Z Feeder Mar Nov CME cattle 9 F H J K Q U V X Table. Layout of commodity futures data used in this work. CBOT and CME are the Chicago Board of Trade and Chicago Mercantile Exchange, respectively. Letters F, H, K, etc. are the contract keys used by CBOT and CME to refer to the different contracts according to their delivery month. Hogs contract K was introduced in. Based on (Fama and Frech, 97). 5 Preliminary analysis: forecasting performance over time Tomek and Gray (97) and later Kofi (973) employed data from 97 or earlier in their analyses and concluded that spring futures prices were reasonable forecasts of realised harvest prices for corn and soybeans. Both of them argued that inventories of storable commodities provide a link between the springtime prices of the post harvest futures and the subsequent harvest time prices. However, in later research Kenyon, Jones and McGwirk (993) noted that grain markets had changed dramatically over the years and consequently Tomek s conclusions were subject to revision. By 993 Kenyon et al. noticed that for example in the US trading volumes had increased, exchange rates had become market determined and government programs had become more market oriented (e.g. the loan defficiency payment 7 ). Furthermore, at present time nominal prices have more than tripled w.r.t. those of 9 for the agricultural commodities comprised in this work, while almost doubled since 9 for the animal ones. Consequently there is a reasonable amount of evidence to presuppose the forecasting ability of futures has changed throughout time, perhaps even more than once. 7 Introduced by the Federal agricultural improvement and reform act of 99.

9 The approach taken by most authors for the assessment of forecasting evolution consists of estimating Equation () for their full available sample and then continue by comparing such results with those of previous research. For example Kenyon et al. use grain data from to update the results of Tomek and Gray, which comprised the period In a similar way, Olimov () used foreign exchange rate data from to revisit the work done by Fama (9) for the period 973 9; the split is therefore arbitrarily set according to the date the research was done. A sketch of the recursive variance of the in sample forecast error of December corn and November soybean futures that matured in April allowed Kenyon et al. to detect a considerable change of forecasting ability in 973. This observation made them divide their sample (95 99) into two subsamples, pre and post 973 in order to have a more realistic assessment. As a refinement, they later computed the R statistic in a windowised fashion to assess more carefully the change of predictive power 9. In this work we pursue a similar approach to detect changes in forecasting ability. As a preliminary step for assessing and locating changes, we start the analysis by obtaining rescursive estimates of the variance of the forecast error, the R statistic and the F statistic (Chow, 9); all from the regression model specified in Equation (). The analysed commodities were those of Table, with forecast horizons of T=[,] months for corn, soybeans and wheat and T=[,] months for hogs and feeder cattle. Some of the results are shown in Figure below; shades indicate possible periods of structural break. Several plots in the figure coincide on showing a change of performance around 973 and (local minima or maxima are observed), however it is evident that different dates of prospective change will be produced by applying either R or the F statistic. Therefore it is relevant to define which one is best suited for monitoring changes in forecasting ability, although there is no standard methodology in the literature to define one. Plots of the recursive variance are useful to determine if the forecast error has changed considerably over time, by showing if the homoscedasticity assumption of OLS holds for all the sample; whereas R is useful to determine changes by measuring the degree of variation of the dependent variable in terms of the independent one. However these statistics are not designed to determine whether there is a significant change in the regression relationship that is kept between two or more subsamples within the complete sample. Considering the F statistic of Chow (9) is based on performing an ANOVA of the residuals of two linear models in order to determine if they belong to the same group, we thought of it as the most adequate alternative to detect changes in predictive power. The subsequent analysis will proceed as follows for all forecast horizons. First, prospective dates of structural change in market efficiency will be detected through the regression of Equation () in a In most of the cases a single forecasting horizon is considered. 9 They used year windows. The coefficient of determination associated with Equation (). 9

10 recursive way. Later data will be splitted into subsamples (with the prospective years of change removed) and then market efficiency tests will be carried out on the subsamples, along with an assessment of the evolution of explanatory power. Out of sample performance will be measured in future work. Our approach is similar to that of Kenyon, Jones and McGwirk (993) and is supported by the work of Bai and Perron (99) on structural break detection methods. Structural break detection This section briefly reviews existing literature on structural break detection methods, with the aim of defining the best strategy to determine the existence (if any) of breaks in the relationship between basis, change and premium of the model of Section 3... The recursive Chow statistic There is a large amount of statistical and econometric literature studying issues related to structural change detection. Most classical tests look for changes in the parameters of a linear regression model by assuming there is only a single change under the alternative or that the timing and type of change are known (Zeileis et al., 3). However, more recent research such as that of Bai and Perron (99), Sullivan (), and Bai and Perron (3) aim to detect one or more shifts without knowing the dates a priori. This section concerns the application of F statistics (Hansen, 99; Andrews, 993; Andrews and Ploberger, 99) to test and date multiple unknown structural changes in the linear model specified by Equations () and (3). Consider the regression model of Equation (), here rewritten as C t, T ) = α + β B( t, T ) + e( t, T ) i [, ], (3) ( i i i N where the basis and change have been denoted as B(t,T)=F(t,T) S(t) and C(t,T)=S(T) S(t), respectively. In the standard Chow (9) test the idea is to try the hypothesis that the regression coefficients remain constant, i.e. H : β = β () i where i is some break point in the interval [,N]. If the location of the point is known, Chow suggested fitting two separate regressions, one for each of the subsamples, obtained by partitioning the data at location i and reject whenever T T uˆ uˆ eˆ eˆ Fi = T eˆ eˆ /( n k) (, ) T is too large. The vector uˆ is filled with the residuals from the complete model, while eˆ = uˆ A uˆ B are the residuals from the two models generated from the split. A major drawback of Chow s test is that in practice the breakpoints are rarely given exogenously and are usually unknown; therefore they have to be estimated from the data (Zeileis et al., 3).

11 A straightforward generalisation to locate a single unkown break is to compute F i in a recursive way for as many observations as possible within the sample, i.e. for i=[n h,n n h ] (where n h is a trimming parameter) and reject H when one of the F i s is larger than some type of functional, like the average or the supremum, ave(f i ) and sup(f i ) respectively. As an example, in Figure the Chow statistic was estimated for every i=[,n ] by regressing recursively Equation (), with n h set to data points; the maturities depicted are T=,, months for agricultural commodities and T=,, for animal ones. Bai and Perron (99) recommend to set the trimming parameter n h to 5 or percent of the total number of observations, however in this example we rely on the observation made by Toyoda (97) that F i is well behaved as long as one of the two subsamples is relatively large. Proceeding in this way was necessary because our interest lies on the most recent years, specially onwards and this period lies at the extreme of the sample.. Testing and dating multiple structural breaks Figure shows the null hypothesis is rejected more than once for some commodities. Indeed it is not unreasonable to hypothesise that more than one structural break has taken place in the futures contracts examined, since the datasets encompass exceptionally large time spans. Furthermore, a wide range of factors may have come into play during the last decades affecting market structures. Therefore an important issue is to decide how many structural breaks occurred and when they happened in terms of Equation (). Up to our knowledge, no previous work has considered this feature when analysing the predictive performance of futures prices. Appendix B details the approach taken to detect breaking years and the results are summarised in Table 3 below. From the table it is interesting to see that agricultural commodities have been subject to basically the same breaks; all of them share 973 as a breaking year, which is associated with the food scare episode. Additionally, corn and wheat produced 95 as a year of change, while corn and soybeans,. Remarkably, 997 is a breakpoint for wheat, perhaps associated to the introduction of the loan defficiency payment program (Section 5). Animal commodities have been more resilient and only produced a shift in 99 and on feeder cattle, the former related to the mad cow disease episode and the latter to the recently lived period of high commodity prices. Remarkably, hog futures did not produce statistically significant changes, despite the 997 restructuring previously mentioned yet this year appears as a local maximum in the plots of Figure. The average and the supremum are methods for aggregating the Chow statistic Fi so that it can be tested for significance (Andrews, 993; Andrews and Ploberger, 99).

12 Commodity Proposed Proposed Break years Commodity subsamples subsamples Break years Corn Wheat Feeder cattle Soybeans 5 5 Hogs 97 None Table 3. Summary of breaking years detected along with subsamples proposed for market efficiency testing. The breaking years were obtained from recursive application of the Chow test (Section.). Each subsample represents a time range whereby the joint model of Equations () and (3) operated under the same linear relationship, in terms of the residual variances specified by the statistic F i..3 Interpreting the results The subsequent discussion is about interpreting the regression results (later presented) in a more systematic way, considering that Equations () and () would require running two sets of regressions, one for the premium and one for the change variables (Section 3.). However, considering that both equations are tied to each other, only one regression is necessary provided the results are interpreted in the correct way. Considering the utilised model implies the constraint β +β = needs to be taken into account, we included the tests H:β = and H:β = in the summary of results; noting that by doing so the complementary tests H:β = and H:β = were carried out automatically. Therefore, as shown in Table there are four possible results from these slope hypotheses tests and should be interpreted in the following way (if β and β are relatively close to zero or one). Condition H:β = H:β = Regarding β and β Implications Reject Reject It is possible that <β < AND also it is possible that <β < Most probably there is a combination of time varying premium along with predictive ability of the basis. Reject Non reject β but it is possible that β is AND β but it is possible that β is 3 Non reject Reject β but it is possible that β is AND β but it is possible that β is Non reject Non reject It is possible that β AND it is possible that β There seems to be absence of premium but presence of predictive power. There seems to be presence of time varying premium but absence of predictive power. Most probably there is a combination of time varying premium along with predictive ability of the basis. Table. Interpreting the slope hypothesis tests H:β = and H:β = for the slope coefficients of the joint variation model specified by Equations () and ().

13 It is also clear that the higher the value β, the better the predictions while the lower the value β, the stronger the absence of a time varying risk premium. Moreover, using the approach of Kenyon, Jones, & McGwirk (993), the higher the coefficient of determination associated with Equation (), R, the stronger the evidence of predictive power explained by the basis. Therefore, when interpreting the results, the values of the slopes along with those of R should be considered. Testing for presence of drifts in futures predictions is achieved by means of the test H:α =, which as previously mentioned, implies testing H:α = simultaneously. Given the constraint α +α =, rejection of any of these tests implies that most probably both intercepts lie within the unit interval, in other words <α < and <α <. According to the discussion of Section 3., we consider that good predictions are made whenever the nulity of the α's is not rejected. Finally, serial correlation tests and unit root tests on all series involved in the model (basis, change and premium) are included. The former by means of the Durbin Watson (DW) statistic and the latter by means of the augmented Dickey Fuller test (ADF). 3

14 Corn Soybeans Wheat Feeder cattle Hogs /5/99 /3/97 /5/97 /3/977 /5/979 /3/9 /5/9 /3/97 /5/99 /3/99 /5/99 3/3/997 3/5/999 /3/ 3/5/ /3/7 /3/97 3//99 3/7/97 3/3/975 //977 /7/9 /3/93 //95 /7/9 /3/99 //993 /7/99 /3/999 // /7/ /3/7 Corn Soybeans Wheat Feeder cattle Hogs.9 R^.9 R^.9 R^.9 R^.9 R^ /5/99 /3/97 /5/97 /3/977 /5/979 /3/9 /5/9 /3/97 /5/99 /3/99 /5/99 3/3/997 3/5/999 /3/ 3/5/ /3/7 Corn Soybeans Wheat Feeder cattle Hogs Residual Variance Residual Variance Residual Variance Residual Variance Residual Variance /5/99 /3/97 /5/97 /3/977 /5/979 /3/9 /5/9 /3/97 /5/99 /3/99 /5/99 3/3/997 3/5/999 /3/ 3/5/ /3/7 /3/97 3//99 3/7/97 3/3/975 //977 /7/9 /3/93 //95 /7/9 /3/99 //993 /7/99 /3/999 // /7/ /3/7 /5/99 /3/97 /5/97 /3/977 /5/979 /3/9 /5/9 /3/97 /5/99 /3/99 /5/99 3/3/997 3/5/999 /3/ 3/5/ /3/7 /5/93 //95 /9/9 //9 //99 /5/99 //993 /9/99 //99 3//997 3/5/999 // /9/3 //5 // //97 //973 //975 3//97 //9 //9 //95 3//97 //99 //99 //99 //99 //999 // //5 //7 /3/97 3//99 3/7/97 3/3/975 //977 /7/9 /3/93 //95 /7/9 /3/99 //993 /7/99 /3/999 // /7/ /3/7 /5/99 /3/97 /5/97 /3/977 /5/979 /3/9 /5/9 /3/97 /5/99 /3/99 /5/99 3/3/997 3/5/999 /3/ 3/5/ /3/7 /5/93 //95 /9/9 //9 //99 /5/99 //993 /9/99 //99 3//997 3/5/999 // /9/3 //5 // //97 //973 //975 3//97 //9 //9 //95 3//97 //99 //99 //99 //99 //999 // //5 //7 /5/99 /3/97 /5/97 /3/977 /5/979 /3/9 /5/9 /3/97 /5/99 /3/99 /5/99 3/3/997 3/5/999 /3/ 3/5/ /3/7 /5/93 //95 /9/9 //9 //99 /5/99 //993 /9/99 //99 3//997 3/5/999 // /9/3 //5 // //97 //973 //975 3//97 //9 //9 //95 3//97 //99 //99 //99 //99 //999 // //5 //7 Figure. Recursive versions of the Fi statistic, the residual variance and the R coefficient for a forecast horizon of T= months. The statistics were generated from the model of joint variance specified in Equation (). Note how for all commodities (except feeder cattle) a change of forecasting performance is detected in 973 and, mostly by the Chow statistic and R. Shadings indicate possible periods for structural break. The residual variance captures the change of the seventies but fails to detect the others.

15 Corn (T=) Soybeans (T=) Wheat (T=) Feeder cattle (T=) Hogs (T=) α=% α=% α=% α=% α=% α=5% α=5% α=5% α=5% α=5% α= α= α= α= α= /5/9 /3/97 /7/973 3/5/97 /3/979 /7/9 /5/9 /3/97 3/7/99 /5/99 /3/995 /7/997 /5/ 3/3/3 /7/5 Corn (T=) Soybeans (T=) Wheat (T=) Feeder cattle (T=) Hogs (T=) /9/99 /3/97 3/9/97 /3/977 /9/979 /3/9 /9/9 /3/97 /9/99 /3/99 /9/99 3/3/997 /9/999 /3/ /9/ /3/7 Corn (T=) Soybeans (T=) Wheat (T=) Feeder cattle (T=) Hogs (T=) α=5% 7 α=5% α=5% α=5% α= α= α= α= 5 α=% /7/97 //97 /5/975 /9/977 3/3/9 /7/9 3//9 /5/97 /9/99 /3/99 /7/99 //99 3/5/999 /9/ /3/ 3/7/ //9 /9/9 /7/9 3/3/9 //97 //99 /5/99 //993 /9/99 /7/99 /3/99 //999 // /5/3 //5 /9/979 /5/9 //9 /7/9 3/3/9 /9/97 /5/99 3//99 /7/99 /3/99 /9/995 /5/997 //99 3/7/ /3/ /9/3 //93 //9 /9/9 //9 //99 3/9/99 //993 //99 3/9/99 //99 //999 /9/ // //5 /9/7 //97 //973 //975 3//97 //9 //9 //95 3//97 //99 //99 //99 //99 //999 // //5 //7 /3/97 3//99 3/7/97 3/3/975 //977 /7/9 /3/93 //95 /7/9 /3/99 //993 /7/99 /3/999 // /7/ /3/7 /9/99 /3/97 3/9/97 /3/977 /9/979 /3/9 /9/9 /3/97 /9/99 /3/99 /9/99 3/3/997 /9/999 /3/ /9/ /3/7 /5/93 //95 /9/9 //9 //99 /5/99 //993 /9/99 //99 3//997 3/5/999 // /9/3 //5 // /5/9 /3/97 /7/973 3/5/97 /3/979 /7/9 /5/9 /3/97 3/7/99 /5/99 /3/995 /7/997 /5/ 3/3/3 /7/5 //93 //95 /9/9 /3/9 //99 //99 //993 /9/99 /3/99 3//997 //999 // /9/3 /3/5 // //97 //973 //975 3//97 //9 //9 //95 3//97 //99 //99 //99 //99 //999 // //3 // α=% α=% α=% α=% α=% α=5% α=5% α=5% α=5% α=5% α= α= α= α= α= //97 //973 //975 3//97 //9 //9 //95 3//97 //99 //99 //99 //99 //999 // //5 //7 /3/97 3//99 3/7/97 3/3/975 //977 /7/9 /3/93 //95 /7/9 /3/99 //993 /7/99 /3/999 // /7/ /3/7 9 α=% α=% α=% α=% 3 α=5% α=% Figure. Recursive estimates of the Chow statistic (Fi) obtained from the joint variation model of basis change premium specified in Equations () and (3). The maturities depicted are T=, and months for agricultural commodities and T=, and months for animal ones. The null hypothesis of no presence of breaks is rejected whenever Fi is higher than the specified level of significance, α=, 5 and %. It is clear that dating structural changes is a complex problem because of the difficulties conveyed on discerning starting and ending dates of the breaking processes. Noticeably the null hypothesis is not rejected on hogs. 5

16 . Estimation results We regressed the segments of Table 3 for all available maturities, that is, from to months for agricultural commodities and from to, for animal ones. However, time and space constraints make us concentrate exclusively on the analysis of the horizons T=,, and T=,, for each of the referred groups, respectively. Estimation results are shown from Table 5 through Table 9 below. The year 95 was included as a partition for soybeans to see how this commodity behaved before and after this year, although it was not detected as a structural breakpoint. Using corn in Table 5 as an example, the period with the most suitable conditions for good predictive performance is 9 3, because in two out of the three reported maturities, the slope hypotheses tests fall in condition of Table ; i.e. absence of varying premium but presence of predictive ability. Furthermore, the value β is close to and the R is relatively high on this period. Intercept tests indicate the absence of drifts in the predictions. Lastly, serial correlation and unit root tests validate the regression results for all reported maturities, except for the last one, 5. A similar analysis can be extracted from the rest of the commodities. By doing so, the overall conclusion obtained from the figures presented in Table 5 Table 7 is that grains futures, particularly those of corn, progressively gained forecasting ability up to but later lost some ground on 5. On the contrary, soybeans are weak predictors for most of the maturities and analysed periods. While wheat futures have good predictive performance in the period 9 99 but also suffer a decline in the more recent years. Regarding animal products, in Table and Table 9, the results are the following. Feeder cattle has a similar behaviour to that of grains because its futures have increasingly good predictive performances along the years (specially on 993 3) but these later fall on the most recent years, specifically on 5. Hogs are strangely consistently good predictors and interestingly our statistical tests do not seem to have captured the structural break of 997 caused by the introduction of lean hog contracts. A more ammenable way for visualising the arguable loss of prediction of is by applying a rolling window approach to do the regressions. Figure 3 below shows the plots generated by applying such strategy with a window size of ten years. The lines show the most recent evolution of the parameters β and β. Remarkably, all agricultural commodities go through a change of predictive performance around ; while feeder cattle has a change in 99 and soybeans in 997. These years coincide with those of Table 3 and therefore support the methodology used to detect structural breaks. Interestingly, these changes of behaviour would have been lost if we had solely relied on recursive estimations, as shown Figure.

17 Corn Years α β α β SE(α) SE(β) t(α ) H:α = T= T= T= t(β ) Η:β = *** **.93*.3.79*.5**.77 t(β ) Η:β =.3.53** **.*** 5.555***.59 R Eq. ().3..9*** *.7* *.39**.337 DW Eq. () ADF Basis 3.57***.3*** 5.539***.3 3.7** 3.3**.53* **.97** 3.7**.55 ADF Chnge.9*** 5.***.537***.9.7*.73***.7*** *** 7.59*** 9.35***.3 ADF Premium.9*** 5.7***.35*** 3.* 3.75** 3.773** 5.3*** **.*** 5.9***.57 Table 5. Corn regression results. Periods were selected according to the structural change selection criteria specified in Section.. Standard errors for both β and β, α and α are identical due to the relationship kept between Equations () and (). Note that break years have been taken out of the samples. *,**,*** Indicate statistical significance at,5 and % levels. None of the DW statistics validated the presence of serial correlations in the residuals. Var Basis Var Chng Var Prem N Soybea ns T= T= T= Years α β α β SE(α) SE(β) t(α ) H:α = * ***.39** t(β ) Η:β = t(β ) Η:β =.9*** ** ***.7.7***. 3.7***.73.9*.93* 7.3***.73.** 3.939*** 3.99*** ***.73 DW Eq. () Eq. ().337*** **.9.957***.7 R.**.557.***.33.33*.597.7***.55.9**.***.3*** ADF Basis ADF Chnge ADF Premium Var Basis.737* 3.** 7.3***.3.93*** 7.9*** 7.9***. 7.35***.***.*** ** 3.937**.3.*** 3.9***.*.39.53*** 5.595*** 5.35***.9 5.***.3*** 3.7*** *** *** 3.93**.39.***.995***.39***. 3.7** 5.7** 3.779**.3 Table. Soybeans regression results. The periods were selected according to the structural change selection criteria specified in Section.. Standard errors for both β and β, α and α are identical due to the relationship kept between Equations () and (). Note that break years have been taken out of the samples. *,**,*** Indicate statistical significance at,5 and % levels. The period at T= months is not included because time series did not go back that far away in time. None of the DW statistics validated the presence of serial correlations in the residuals. Var Chng Var Prem N

18 Wheat Years α β α β SE(α) SE(β) t(α ) H:α = T= T= T= t(β ) Η:β = t(β ) Η:β = *.733* *** 3.395*** 5.3*** R Eq. () *** *** DW Eq. () ADF Basis **.9*** ***.***.337.3* 3.3** 3.53** ADF Chnge.7*** 9.97*** 5.999*** 3.3** 3.5** 3.9*** 5.59*** 3.95***.75***.73***.7*** ADF Premium ***.95*** 3.9** **.5*** 3.** 3.73***.3***.335*** Table 7. Wheat regression results. The periods were selected according to the structural change selection criteria specified in Section.. Standard errors for both β and β, α and α are identical due to the relationship kept between Equations () and (). Note that break years have been taken out of the samples. *,**,*** Indicate statistical significance at,5 and % levels. The period 9 97 for T= is not reported due to lack of data. None of the DW statistics validate the presence of serial correlations in the residuals. Feeder cattle T= T= T= Years α β α β SE(α) SE(β) t(α ) H:α =.5**..79.7* t(β ) Η:β = ** t(β ) Η:β = ***.59.97** 3.337***.9 R Eq. ()..337***..33**.***.* DW Eq. () ***.9.9**.95.9***.5.393*.73 ADF Basis ADF Chnge 5.9***.3955***.735***.33*** 3.**.93*.33*** 5.*** 3.5**.5***.579***.933*.9***.97***.3*** 3.93*** 3.***.5999*** ADF Premium.7***.59*** *** 5.7*** 3.55** 3.57*** 3.753*** 3.773** Var Basis Var Chng Var Prem N Var Basis Var Chng Var Prem N Table. Feeder cattle regression results. The periods were selected according to the structural change selection criteria of Section.. Standard errors for both β and β, α and α are identical due to the relationship kept between Equations () and (). Breaking years have been taken out of the samples. *,**,*** Indicate statistical significance at,5 and % levels. None of the DW statistics validate the presence of serial correlations in the residuals. Hogs Years α β α β SE(α) SE(β) t(α ) t(β ) t(β ) DW ADF ADF ADF Var Var Var N H:α = Η:β = Η:β = Eq. () Eq. () Basis Chnge Premium Basis Chng Prem T= ***.537***.3*** ***.73*** 3.795*** T= ***.5737***.3*** ***.57***.799***..75. T= ** 9.5***.995**.95*** *** 7.399***.*** Table 9. Hogs regression results. The periods were selected according to the structural change selection criteria of Section.. Standard errors for both β and β, α and α are identical due to the relationship kept between Equations () and (). Breaking years have been taken out of the samples. *,**,*** Indicate statistical significance at,5 and % levels. None of the DW statistics validate the presence of serial correlations in the residuals. R

19 Corn (T=) Soybeans (T=) Wheat (T=) Feeder cattle (T=) Hogs (T=) 3 β (Change) β (Change) β (Change) β (Change) β (Change) /3/997 //997 /7/99 /3/999 //999 /7/ /3/ // /7/ /3/3 //3 /7/ /3/5 //5 /7/ /3/7 //7 Betas - Corn (T=) Soybeans (T=) Wheat (T=) Feeder cattle (T=) Hogs (T=) /9/99 /5/997 //99 /9/99 /5/999 // /9/ /5/ // /9/ /5/3 // /9/ /5/5 // /9/ /5/7 Betas /5/99 //997 /9/997 /5/99 //999 /9/999 /5/ // /9/ /5/ //3 /9/3 3/5/ //5 /9/5 /5/ //7 /9/7 Betas - /3/99 //99 /7/997 /3/99 //99 /7/999 /3/ // /7/ /3/ // /7/3 /3/ // /7/5 /3/ // /7/7 /9/99 /5/997 //99 /9/99 /5/999 // /9/ /5/ // /9/ /5/3 // /9/ /5/5 // /9/ /5/7 Betas Betas Betas /5/99 //997 /9/997 /5/99 //999 /9/999 /5/ // /9/ /5/ //3 /9/3 /5/ //5 /9/5 /5/ //7 /9/7 //99 //99 //993 //99 /9/995 //99 /7/997 //99 /5/999 // /3/ // //3 //3 // //5 /9/ //7 Betas Betas Betas //99 //99 //993 //99 /9/995 //99 /7/997 //99 /5/999 // /3/ // //3 //3 // //5 /9/ //7 Corn (T=) Soybeans (T=) Wheat (T=) Feeder cattle (T=) Hogs (T=) /3/99 /3/993 /3/99 /3/995 /3/99 /3/997 /3/99 /3/999 /3/ /3/ /3/ /3/3 /3/ /3/5 /3/ /3/7 Betas //99 //993 //993 //99 //995 /9/99 //997 /7/99 //999 /5/ // /3/ //3 // // //5 // /9/7 Betas //99 //993 //993 //99 //995 /9/99 //997 /7/99 //999 /5/ // /3/ //3 // // //5 // /9/7 3 3 β (Change) β (Change) β (Change) β (Change) β (Change) 3 3 β (Change) β (Change) β (Change) β (Change) β (Change) //99 //99 //993 //99 //995 //99 //997 //997 //99 //999 // // // // //3 // //5 // //7 Betas - /3/99 //99 /7/997 /3/99 //99 /7/999 /3/ // /7/ /3/ // /7/3 /3/ // /7/5 /3/ // Betas Betas - - //99 //99 /3/997 //997 /5/99 //99 /7/999 // /9/ // // // //3 //3 /3/ // /5/5 //5 /3/99 /9/99 /3/997 /9/997 /3/99 /9/99 /3/999 /9/999 /3/ /9/ /3/ /9/ /3/ /9/ /3/3 /9/3 /3/ /9/ /3/5 Betas Figure 3. Forecasting evolution of the analysed commodities in terms of the parameters β and β of Equations () and (). Plots were generated through a rolling window approach with window size adjusted to years. Remarkably, the plots exhibit local maxima or minima around the years 99 for cattle, 997 for wheat, and for grains, much in coincidence with the breaking points specified in Table 3. 9