Full Length Research Paper
ABSTRACT
INTRODUCTION
FUNDAMENTALS OF CORN AND WHEAT MARKETS
VOLATILITY, COEFFICIENT OF VARIATION AND STANDARD DEVIATION OF PRICES OF CORN AND WHEAT
EXAMINATION OF ALTERNATIVE PREDICTORS OF SPOT PRICES
Where It is the filtration incorporating all information until date t, and u is an error term with conditional expected value of 0 and uncorrelated to the information at time t.
By adding the no- arbitrage assumption and changing the probability measure, the above relationship can be written as an exact equality.
In this paper, we adapt the tests of the REH in the style of Muth (1961) to find the optimal lag h, if any, for an estimate of the future spot price.
Individual forward contracts as predictors of future spot prices
In order to test the relationship between spot and forward prices, we use log prices of Futures daily data for corn and wheat. Under constant interest rates or absence of correlation of these to the underlying asset, arguably the case for agricultural commodities, forward and Future prices are equal. Both commodities have Future contracts with delivery months in March, May, July, September and December (examples of forward curves in Figure 6) and their last trade date is the last business day prior to the 15th calendar day of the contract month. The first test involves running the regression:
We pose two questions. First, do forward prices before the planting period of corn predict spot prices after the harvest in the US? Second, will these estimates be affected by the proximity of the observed forward prices to the contract expiry date? In order to answer these questions, we test the predictive power of each maturity with its corresponding spot price, that is, we compare how the July Future price observed at time t-h predict July spot prices, the September Future prices predict September spot prices, etc.
First, we place ourselves at two particular points in time: the beginning of February and the beginning of April. These are the dates when observations of the forward curve are taken; date t-h in Table 3, for a length of 10 business days. The corn heading (stage of development of grains where the head pushes its way through the flag leaf sheath) and harvesting happen during the summer months.
The farmer will be interested in inferring information about prices after the harvest, that is, after September, from the forward curve. Accordingly, the October corn option contract is the most traded.
From Table 3, we clearly see that forward prices observed at the beginning of February produce better estimates of corn spot prices than the ones observed in the beginning of April, when planting is already underway (most planting is done in the US from April to May). Although the March Futures contract maturing the following year offers unbiased predictions of future March spot prices in both cases, the earliest contract that provides some post-harvest information is the December Futures contract (Table 3).
We note an important effect on the predictive power of the forward prices as the contracts get closer to expiry. When we compare results from Table 3 with the results from Table 4, where we observe the forward curve during the last 10 trading days before maturity of the contract, in general, the predictive power of the forward prices is greatly reduced.
Similar questions can be asked for wheat, although the case of wheat is markedly different. First, as we did in the case of corn, we compare the results derived from forward curves observed at the beginning of February to those observed at the beginning of April (Table 5). At the beginning of February we only obtain unbiased estimates of spot prices from the September Futures contract (it is important to note that March is a weather/moisture critical period in the heading of wheat in the southern hemisphere), whereas at the beginning of April, we obtain unbiased estimates from all maturities. When we turn our attention to the issue of closeness-to-expiry effects in wheat, we note that the predictive power of many of the maturities is greatly reduced (Table 6). Furthermore, as with corn, short term maturities have little predictive power for future spot prices.
In conclusion, the predictive power of individual forward contracts seems to be most negatively impacted at times of planting, heading and harvesting, and in the days days when Future contracts are close to expiry.
Optimal lags of prediction of future contracts
A study of forward prices, not by maturity but by their position inside the current forward curve, may better represent traders’ daily activities. In order to build consistent monthly data series, we use the individual maturities to create continuous series of deliveries, based on how close they are to the spot price. We refer to them as second nearby Future contracts, that is, F2, third nearby F3, etc. (Table 7). We adapt Equations (1) and (2) to find the optimal lag among the first 24 lags for each nearby, F2 to F7:
With i = 1,2,3,…, 24 months. Additionally, we extend the methodology proposed by Muth (1961) with a non-para-metric test, the Wilcoxon signed-rank test, which allows for the absence of the strict assumptions needed to apply the F-test, such as the absence of serial correlation, which is present in both commodities. This test also takes into account the magnitude of the changes in the compa-rison of both distributions (Campbell and Dufour, 1991).
By studying each nearby we can infer how the position of the individual maturities on the forward curve affect their predictive power. For example, in Table 7, at the beginning of Year 1, March of year 2 occupies the penultimate point of our forward curve, F6, and as time passes the same March maturity will become the fifth, fourth, third, second and finally at the beginning of year 2, that March contract will be the first nearby and reach expiry.
We depict the distance h for each Future contract from the examples in previous subsections in the first two columns of Table 8, which we extend to all contracts up to the seventh nearby.
When we study each contract, since we have unequally spaced maturities, we can only obtain an interval of lags where the prediction is unbiased and an average lag when each nearby will have the highest predictive power. The ‘theoretical’ optimal lag will depend on the point in time when we observe the forward curve. For example, in the case of the fourth nearby, if we observe F4 in March, it corresponds to the September Future contract, and the theoretical optimal lag should be six months, that is, the September Future price predicts the September spot price. If we observe F4 in May, it corresponds to the December Future contract and the optimal lag is seven. If we are in July, F4 corresponds to the March Future con-tract and lag eight, and so on. Hence, a result between six and eight would mean all individual maturities on average give an unbiased prediction at F4. We derive all the theoretical optimal lag intervals with the help of Table 8 for each nearby in the first column of Table 9.
With our tests, we obtain a choice of lags in Equation (2) that includes the theoretical lag interval for each nearby, with the only partial exception of F3 in corn, mea-ning that, in general, individual maturities keep predictive power as time passes (Table 9). However, Durbin-Watson tests reveal autocorrelation in the residuals across all lags in both commodities. The presence of autocorrelation could be explained by the behaviour of the many market players who use technical analysis, which is based on signals such as moving averages for momentum trading.
When we study the optimal lags in Table 9 (lags with the highest p-values from Equation (2)), in some cases they fall outside their respective theoretical lag interval. In the case of CBOT corn, only the optimal lags for F2 and F3 are inside the theoretical lag interval, while for the rest of the nearby Future contracts the optimal lags are lower. Lower optimal lags indicate that when individual Future contracts are in nearby positions F4 to F7, the best predictions do not correspond to the months sug-gested by the theoretical interval but to future spot prices that happen earlier. In contrast, in the case of CBOT Wheat, only the optimal lags for F6 are inside the theoretical lag interval, while optimal lags obtained for F2 to F5 are higher, that individual Future contracts offer a better prediction of later future spot prices. Consequently, while for CBOT wheat, maturities expiring one year ahead a twelve month prediction (F6 is exactly at lag 12), they only offer a nine month prediction for CBOT Corn.
These features could be explained by a fundamental difference in the global trade of corn and wheat. In the case of corn, world prices are usually set by the US domestic supply-demand forces and farmers in the Southern hemisphere, namely Argentina (generally the second largest exporter of corn), adjust their crop output in reaction to US corn harvests and prices (with US news during the summer curtailing the predictive power of the forward curves). Wheat, on the other hand, is grown in more places and climatic conditions than any other cereal grain, from cold environments near the Arctic Circle to tropical regions close to the Equator; there are up to 20 species and more than 25,000 varieties in existence. Hence, CBOT wheat (it is worth noting that although the CBOT Wheat futures contract is linked to the price of No. 2 Soft Red winter wheat, it is generally used in hedging activities for all kinds of wheat), is less dependent on a single country of production and the arrival of news from all over the world has an influence in the predictive power of the forward curves in the short term, although long term predictions are more reliable than in the case of CBOT corn.
Testing the geometric average as a predictor of future spot prices
The seasonal cost-of-carry model for commodity forward curves developed by Borovkova and Geman (2006) introduces the geometric average of the forward prices as an alternative to the spot price for the first state variable when managing a portfolio of seasonal or non-seasonal commodity Futures:
CONCLUSION
CONFLICT OF INTEREST
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