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Evaluating the Forecasting Performance of Commodity Futures Prices

Trevor A. Reeve and Robert J. Vigfusson1 2

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at http://www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at http://www.ssrn.com/.


Abstract:

Commodity futures prices are frequently criticized as being uninformative for forecasting purposes because (1) they seem to do no better than a random walk or an extrapolation of recent trends and (2) futures prices for commodities often trace out a relatively flat trajectory even though global demand is steadily increasing. In this paper, we attempt to shed light on these concerns by discussing the theoretical relationship between spot and futures prices for commodities and by evaluating the empirical forecasting performance of futures prices relative to some alternative benchmarks. The key results of our analysis are that futures prices have generally outperformed a random walk forecast, but not by a large margin, while both futures and a random walk noticeably outperform a simple extrapolation of recent trends (a random walk with drift). Importantly, however, futures prices, on average, outperform a random walk by a considerable margin when there is a sizeable difference between spot and futures prices.

Keywords: Financial markets, forecasting, commodities

JEL classification: G13, E37, Q47



1  Introduction

Commodity futures prices are frequently criticized as being uninformative for forecasting purposes because (1) they seem to do no better than a random walk (Alquist et al., 2011) or an extrapolation of recent trends and (2) futures prices for commodities often trace out a relatively flat trajectory even though global demand is steadily increasing. In this paper, we attempt to shed light on these concerns by discussing the theoretical relationship between spot and futures prices for commodities and by evaluating the empirical forecasting performance of futures prices relative to some alternative benchmarks.

The key results of our analysis are:

These results suggest that futures prices remain a reasonable guide for forecasting commodity prices. However, as we will discuss, futures prices may also, in principle, contain a risk premium that creates a wedge between the observed futures price and the spot price expected to prevail in the future. In the final section of this note, we attempt to identify such a risk premium. Our results suggest that controlling for a risk premium in real time does not materially improve the forecasting performance of futures prices.

There is a large literature on evaluating the forecasting performance of futures markets. In addition to classic articles such as Fama and French (1987), more recent contributions include Moosa and Al-Loughani (1994), Chin et. al. (2005), and Alquist and Kilian (2010). As we will discuss below, given variations in both the commodities and time periods that have been evaluated, the literature has not reached a consensus. Compared with these other papers, our discussion of the forecasting performance conditional on the difference between spot and futures prices is novel.


2  The Relationship Between Spot and Futures Prices for Commodities

Expectations of future commodity prices are a critical determinant of spot prices, and this linkage depends on the capacity to store commodities in inventory. Transactions in the spot market require the seller to accept that the price received is adequate compensation for forgoing the opportunity to hold the commodity in inventory to sell later. (For producers of commodities, a similar calculation applies to the decision to produce an extra unit of the commodity today versus in the future.) Likewise, the buyer must accept that the benefit of purchasing now outweighs the benefits of waiting to buy later. Accordingly, the spot price embodies an expectation of what prices will be in the future. As a corollary, changes in expectations of future supply and demand conditions will show up as movements in both current spot and futures prices.

The relationship between spot and futures prices can be derived from conditions that rule out profitable arbitrage opportunities, so that holders of commodities are indifferent between selling them in the spot market or holding them in inventory to deliver later at the contracted futures price. 3 To illustrate, denote the current spot price as $S$ and the current value of the one-year ahead futures price as $F$, and consider the following cases:


Combining these two conditions gives $F=(1+R+C-Y)S$ or, equivalently, $ F/S=(1+R+C-Y)$. As the storage costs ($C$) and the convenience yield ($Y$) tend towards zero, the difference between the spot and futures prices converge to the rate of interest. This convergence is equivalent to the familiar Hotelling's rule that spot commodity prices will rise at the discount rate, that is, $F$ $=(1+R)S$. In this case, the futures-based forecast is similar to a random walk forecast when interest rates are low. In contrast, the higher the storage costs and convenience yield, the more the futures price can differ from the spot price for any given interest rate.

The costs for storing a commodity should be a function of the level of inventories and the physical properties of the commodity. When inventories are very high and approaching storage capacity limits, the cost of additional storage ($C$) should also be high. For example, in the fall of 2008, conventional oil storage facilities were near capacity and, so, oil was stored in tanker ships, even though ship-based storage is much more expensive than land-based storage. These high storage costs allowed the difference between the spot price and the futures price to widen. In December of 2008, the spot price for oil was around $40 barrel and the twelve-month ahead futures price was above $55 per barrel.

In addition, storage costs also vary across commodities. For example, the storage costs for fresh cut flowers can be thought of as approaching infinity, which would be sufficient to break the link between the futures and spot prices. In such a market, inventories cannot be used to smooth prices. In contrast, other commodities such as metals have relatively low storage costs. For these commodities, inventory smoothing limits the extent that future prices can differ from spot prices.

Whereas inventory accumulation becomes more costly as inventories near capacity, the convenience yield ($Y$) of having an additional unit of stock is particularly high when inventories are low. For example, one might require the good to keep a production process running or avoid disappointing customers. As such, increases in the convenience yield may at times drive the spot price well above the futures price.

How well do these theoretical results conform with the observed structure of futures prices? Table 1 reports statistics on the distribution of the ratio of the one-year ahead futures price to the spot price ($F/S$) for a selection of commodities from 1990 through 2010.5 The values in column iii show the percent of the time that the futures price was within +/- 5 percent of the spot price (0.95 < $F/S$ < 1.05). By this score, copper ranks fairly high, with the futures price within 5 percent of the spot price 45 percent of the time. Towards the other extreme is natural gas, for which the futures price was within 5 percent of the spot price only 24 percent of the time. Crude oil, at 29 percent, is in between these extremes. The fraction of the time futures exceeded spot prices by more than 15 percent ($F/S$ > 1.15, shown in column v) was essentially zero for many metals, 6 percent for oil, and 28 percent for natural gas.

These distributions accord well with reported storage costs. For example, storage capacity for metals is virtually unlimited, as all that is required is a warehouse to protect stocks from the elements, vandals, and thieves. 6 Within the metals category, given that storage costs per pound are similar for the various metals, the high average price of nickel per pound and correspondingly low storage costs per unit value likely helps explain why its futures price was within 5 percent of the spot 73 percent of the time, the greatest percentage amongst the metals. Conversely, natural gas is notoriously difficult and dangerous to store, requiring specialized equipment or suitable underground caverns. And crude oil, which is typically stored in tanks, is between these extremes. Additionally, agricultural commodities, which can spoil, tend to have a wider distribution of $F/S$ than more durable commodities such as metals.

Figure 1 plots the observed values of $F/S$ for copper (on the vertical axis) against the level of inventories (on the horizontal axis). Consistent with the previously described results, when inventories of copper have reached unusually high levels, the futures price has remained close to the spot price; storage costs for copper do not rise sharply with inventory levels and the convenience yield of holding copper is depressed by ample stocks. As inventories get very low (and the convenience yield of having copper on hand rises), futures prices can lie well below spot prices. Historically, however, futures prices for copper have not tended to fall below 75 percent of the spot price.

Figure 2 shows a similar plot for crude oil. In contrast to copper, when oil inventories get large, storage capacity constraints begin to bind and the marginal cost of storage rises, resulting in futures prices lying well above spot prices. At low levels of inventories, however, the pattern, as expected, is more similar to copper, with futures prices lying well below spot prices.

To sum up, flat futures profiles for commodities are common when inventories are within typical ranges. The reason for this is that arbitrage across the futures curve ensures that spot prices incorporate information about future supply and demand conditions. When inventories are particularly low or high, however, the costs associated with arbitraging commodities over time are large, and futures prices can differ markedly from spot prices.


3  Forecasting Performance of Futures Prices

In this section, we compare the forecasting performance of futures-based forecasts with two alternatives: a random walk (where the forecasted value is the current spot price) and a random walk with drift (where the forecasted value rises in line with recent experience). We also present results showing that futures-based forecasts tend to outperform random walk forecasts by the largest margin when the forecasts are most divergent, that is, when futures prices differ the most from spot prices.

Our accuracy measure is the mean squared error (MSE) of the forecast. Futures-based forecasts are compared to the alternatives by examining the relative MSE, that is, the ratio of the MSE for the futures forecast to the MSE of the alternative. When the relative MSE equals 1, the forecast performance of the two methods is equivalent. When the relative MSE is less than one, futures dominate the alternative, and when it is greater than one, the alternative dominates futures.

Table 2 reports the relative MSEs for futures versus the random walk for two forecast horizons (3 months, and a year-ahead7) over two sample periods (1990 to 2010 and 2003 to 2010). As shown in the table, the relative MSEs are generally below 1 for the full sample, indicating that futures-based forecasts have outperformed a random walk over this period. For the 2003 to 2010 sample, however, the results are more mixed, with neither futures nor the random walk clearly dominating.

To shed light on the changing forecasting performance of these methods over time, Figure 3 shows the evolution of relative MSEs over 8-year moving windows for copper, corn, and crude oil. As the figure makes clear, futures consistently outperformed the random walk for all three commodities prior to the early 2000s and have continued to do so for corn. During the latter half of the 2000s, in contrast, a random walk outperformed futures for copper and oil. Most recently, however, futures and a random walk look about the same for oil.

The second alternative to a futures-based forecast is a random walk with drift, in which prices are projected to rise or fall at a rate comparable to that observed in the recent past. Such an approach would be consistent with arguments that commodity prices will continue to rise in line with global demand, thus extending recent trends. Table 3 reports relative MSEs for futures-based forecasts versus such a model where the drift term is assumed to be the average growth rate over the past year. As can be seen in the table, this model does very poorly when evaluated over the whole sample or just the observations since 2003.

Although futures do have a better record than a random walk over the entire sample, the improvement does not appear to be substantial. This result should not be terribly surprising in light of the discussion in the previous section. The storability of commodities and the elimination of arbitrage opportunities implies that spot and futures prices are linked. With modest storage costs and sufficient inventories to keep convenience yields low, we should expect the futures-based forecasts and random walk forecasts to be broadly similar.

That being said, there are times, as noted above, when futures prices can differ markedly from spot prices. When the futures price and the spot price differ, the futures price should in principle be more informative for forecasting prices relative to a random walk. Prices will differ when there are temporary factors that result in sharp inventory builds or declines. In these periods, the futures price should, in theory, look through these developments and, thus, produce a better forecast.

Figure 4 examines this proposition for oil prices. The figure plots the ratio of the one-year ahead futures price to the spot price. The blue dots denote the times when the futures-based forecast outperformed the random walk, and the red dots show the times when the random walk outperformed futures. It is evident that when the crude oil futures price is materially above the spot price (the upper range of the graph), futures have done a better job of forecasting prices in the vast majority of the cases.

When the futures price is below the spot price, the evidence is somewhat more mixed. In the 1990s, the futures price generally did better. However, between 2003 and 2005, the futures price generally did worse as the market mistook the permanent shift in oil prices for a temporary increase that would soon be reversed. Market participants did not fully appreciate the persistence of the shocks hitting commodity prices and expected commodity prices to moderate. Thus, in this period, the spot price proved to be a better predictor than the futures prices.

More systematically, Table 4 reports the relative MSEs for futures versus a random walk for a range of commodities as a function of the futures-spot relationship. For crude oil, the relative MSE is close to 1 when futures are within 5 percent of the spot price (column iii). But when futures are more than 5 percent above spot prices (columns iv and v), the relative forecasting performance of futures prices rises markedly. Although the results of this exercise vary considerably across commodities, the overall evidence suggests that futures are more informative the greater their divergence from spot prices.


4  Risk Premiums

The previous results suggest that futures prices remain a reasonable guide for forecasting commodity prices, at least relative to some basic alternatives. However, futures prices, in principle, could also contain a risk premium that creates a wedge between the observed futures price and the underlying expected future spot price. If such a risk premium can be identified in commodity futures prices, then controlling for it when making forecasts should improve accuracy.

To think about the risk premium, it is useful to consider three classes of futures market participants. The first class is producers of commodities whose incomes depend positively on commodity prices and who, therefore, would want to insure against price declines by selling (i.e. go short) in the futures markets. The second class is users of commodities whose incomes depend negatively on prices and who, therefore, would want to insure against price increases by buying (i.e. go long) in the futures markets. The third class is made up of market participants whose incomes neither increase nor decrease appreciably with commodity prices. This group (who could be defined as speculators) serves to balance the market by providing the net supply of insurance services to the other participants; that is, they fill the gap between buyers and sellers in the futures markets. The risk premium is the compensation given to the speculators to entice them to participate in these markets.

To illustrate the roles of the first two kinds of market participants, Figure 5 reports data from the U.S. Commodity Futures Trading Commission (CFTC) on the net long positions of producers/users as a fraction of open interest for eight commodities traded on U.S. futures markets. (The available public data only reports this aggregate category which includes producers, merchants, processors and users.) The following patterns are clear. For almost all categories, the producers/users are net short. Thus, it seems that the demand from producers to be insured against falling prices outweighs the demand from users to be insured against higher prices. For energy commodities, the net long positions of producers/users are relatively close to zero. Producers/users are almost always net short for agricultural commodities, but there can be some fairly large swings in the magnitude of these positions. Given these net short positions, speculators will have to go net long to balance the market. As such, holding everything else equal, we should expect the average risk premium to be positive and larger for agricultural commodities than for oil. By a positive risk premium, we mean that we should expect the futures price to be less than expected spot price, so that going net long - that is, contracting to buy commodities at the futures prices - is a profitable activity for the speculators. However, we should note that competition amongst speculators should serve to decrease the profitability of providing insurance to producers.8

To test for risk premiums, we follow the literature in estimating forecast efficiency regressions,9 which are defined as

\begin{displaymath} S_{t+k}-S_{t}=\alpha +\beta (F_{t,t+k}-S_{t})+v_{t+k} \end{displaymath}

In these regressions, the dependent variable is the error from a random-walk forecast, and the independent variable is the difference between the forecasted price from futures markets and that from a random walk. There are four tests of interest: the three individual tests of whether $\alpha $= 0, $ \beta $ = 0, and $\beta $ = 1 and the joint test of $\alpha $= 0 and $\beta =1$. If $\alpha $= 0 and $\beta =1$ then futures are an unbiased predictor of the spot price and there is no identifiable risk premium. If the difference between the estimated constant $\alpha $ and zero is statistically significant, then there is evidence of a constant risk premium. If the difference between the estimated slope coefficient $\beta $ and 1 is statistically significant, then the risk premium varies over time according to the tilt in the futures curve. Additionally, if the slope coefficient $\beta $ is significantly different from zero, then futures prices have explanatory power for the forecast error from a random walk. Thus, this regression provides an alternative method for comparing random walk and futures-based forecasts.

Table 5 reports the results of these hypothesis tests for the one-year ahead forecasts over the 1990 to 2010 sample period. Column (i) reports the point estimates of the intercept term $\alpha $. As indicated by column (ii), for most commodities, we fail to reject the null hypothesis that $\alpha =0$ at the 95 percent critical value, meaning that there does not appear to be a constant risk premium that is statistically significant. The point estimates for the slope coefficient $\beta $ are reported in column (iii). For nearly half of the commodities, we can reject the hypothesis that the slope coefficient equals 0, suggesting that there is useful information in the futures. Although we fail to reject for most commodities the hypothesis that the slope coefficient equals one (column v), the point estimates can be quite different from one, suggesting that the risk premium varies with the shape of the futures curve. As reported in the final column of the table, we get four rejections (zinc, cotton, live cattle and wheat) for the joint hypothesis that $\alpha =0$ and $\beta =1$ suggesting some bias and the presence of a risk premium.

Because the estimated $\beta ~$coefficients for many commodities are less than one, it is possible that forecasting performance could be improved by attenuating the slope of the futures curve somewhat, which is equivalent to controlling for a variable risk premium. However, making such corrections in real time is not so simple. We can only estimate the values of $\alpha $ and $\beta $ using the data that was available when the forecast would have been made. In order to allow for structural breaks, the values of $\alpha $ and $ \beta $ were estimated over a rolling sample of 30 monthly observations. As reported in Table 6, forecasts based on these real-time estimates do not perform better than the simple, unadjusted futures-based forecast over the 2003-2010 sample. The reason for this outcome is that the values of $\alpha $ and $\beta $ are not stable over time and hence using estimated values results in poor predictors for subsequent periods. The only exception is a slight improvement for natural gas at the three-month horizon.


5  Conclusions

Our main conclusions are the following:

These results suggest that futures prices remain a reasonable guide for forecasting commodity prices. Although, in principle, futures prices may also contain a risk premium, we find that controlling for a risk premium in real time does not materially improve the forecasting performance of futures prices.


Bibliography

Alquist, Ron and Lutz Kilian, 2010, "What Do We Learn from the Price of Crude Oil Futures?" Journal of Applied Econometrics 25(4).

Alquist Ron, Lutz Kilian and Robert J. Vigfusson, 2011, "Forecasting the Price of Oil," International Finance Discussion Paper No. 1022, Board of Governors of the Federal Reserve System.

Chernenko Sergey V., Krista B. Schwarz and Jonathan H. Wright 2004, "The Information Content of Forward and Futures Prices: Market Expectations and the Price of Risk," International Finance Discussion Paper No. 808, Board of Governors of the Federal Reserve System.

Chinn, Menzie D., Olivier Coibion, and Michael LeBlanc, 2005, "The Predictive Content of Energy Futures: An Update on Petroleum, Natural Gas, Heating Oil and Gasoline Markets," NBER Working Paper No. 11033 (January).

Fama, Eugene F. and Kenneth R. French, 1987, "Commodity Futures Prices: Some Evidence on Forecast Power, Premiums, and the Theory of Storage," The Journal of Business, 60(1) 55-73.

Hull, John C. 2002 Options, Futures, and Other Derivatives Prentice Hall; 5 edition.

Moosa, Imad and Nabeel Al-Loughani, 1994, "Unbiasedness and time varying risk premia in the crude oil futures market," Energy Economics 16(2), pp. 99-105.

Pindyck, Robert S., 2001, "The Dynamics of Commodity Spot and Futures Markets: A Primer," Energy Journal 22(3): 1-29.

Table 1. Destribution of the Slope of Futures Relative to Spot Prices (Percent)

 F/S: <0.85 (i)F/S: (0.85 to 0.95) (ii)F/S: (0.95 to 1.05) (iii)F/S: (1.05 to 1.15) (iv)F/S: >1.15 (v)
Energy: Crude Oil163129196
Energy: Heating Oil102539187
Energy: Natural Gas1216242028
Metals: Aluminum0238581
Metals: Copper51745276
Metals: Lead91850220
Metals: Nickel01173130
Metals: Tin61043410
Metals: Zinc122246200
Agricultural: Corn37232641
Agricultural: Cotton49282732
Agricultural: Coffee107303025
Agricultural: Live Cattle0250452
Agricultural: Soybeans51246370
Agricultural: Wheat519192036

 

Notes: For commodities in the energy category, statistics are calculated for 12-month ahead futures. For metals, the statistics are for 15-month ahead forwards. For agricultural commodities, the statistics are for 8-month ahead futures. Samples begin in 1985 or as available.

Table 2: Relative Mean Squared Error of Futures Based Forecasts to Random Walk

SampleThree Months Ahead: 1990-2010 (i)Three Months Ahead: 2003-2010 (ii)A Year Ahead*: 1990-2010 e (iii)A Year Ahead*: 2003-2010 (iv)
Energy: Crude Oil0.940.930.920.98
Energy: Heating Oil0.961.010.921.03
Energy: Natural Gas0.88*0.920.86*0.94
Metals: Aluminum1.000.990.930.95
Metals: Copper1.001.021.081.20
Metals: Lead0.981.011.001.05
Metals: Nickel1.001.011.001.05
Metals: Tin1.001.001.051.04
Metals: Zinc0.930.960.860.90
Agricultural: Corn0.910.920.770.71
Agricultural: Cotton0.961.040.970.93
Agricultural: Coffee1.000.910.930.92
Agricultural: Live Cattle0.75*0.76*1.591.63
Agricultural: Soybeans0.880.840.840.81
Agricultural: Wheat0.980.911.050.93

Notes: *The year ahead forecast is based on the appropriate and available futures contract. For commodities in the energy category, statistics are calculated for 12-month ahead futures. For metals, the statistics are for 15-month ahead forwards. For agricultural commodities, the statistics are for 8-month ahead futures. Samples begin in 1990 or as available.
**Indicates a statistically significant difference based on a Diebold-Mariano test.

Table 3: Relative Mean Squared Error of Futures Based Forecasts to Random Walk With Drift

SampleThree Months Ahead: 1990-2010 (i)Three Months Ahead: 2003-2010 (ii)A Year Ahead*: 1990-2010 e (iii)A Year Ahead*: 2003-2010 (iv)
Energy: Crude Oil0.74*0.640.36*0.34*
Energy: Heating Oil0.78*0.720.38*0.39*
Energy: Natural Gas0.69*0.68*0.30*0.35*
Metals: Aluminum0.740.740.570.63
Metals: Copper0.830.860.710.86
Metals: Lead0.770.760.580.62
Metals: Nickel0.800.830.430.46
Metals: Tin0.850.880.560.55
Metals: Zinc0.770.820.400.39
Agricultural: Corn0.69*0.71*0.41*0.43*
Agricultural: Cotton0.78*0.890.49*0.55
Agricultural: Coffee0.77*0.70*0.56*0.57
Agricultural: Live Cattle0.61*0.63*0.730.74
Agricultural: Soybeans0.67*0.63*0.47*0.45*
Agricultural: Wheat0.76*0.73*0.630.57

Notes: *For commodities in the energy category, statistics are calculated for 12-month ahead futures. For metals, the statistics are for 15-month ahead forwards. For agricultural commodities, the statistics are for 8-month ahead futures. Samples begin in 1990 or as available.
**Indicates a statistically significant difference based on a Diebold-Mariano test.

Table 4: Relative Mean Squared Error of Futures Based Forecasts, Conditional On Spread

 Value of F/S: <0.85 (i)Value of F/S: (0.85 to 0.95) (ii)Value of F/S: (0.95 to 1.05) (iii)Value of F/S: (1.05 to 1.15) (iv)Value of F/S: >1.15 (v)Value of F/S: Full Sample (vi)
Energy: Crude Oil0.931.341.010.700.310.92
Energy: Heating Oil0.441.371.000.750.510.92
Energy: Natural Gas0.570.941.010.990.760.86
Metals: AluminumNA2.7310.910.020.93
Metals: Copper1.431.050.960.87NA1.08
Metals: Lead1.501.040.980.920.731
Metals: Nickel0.721.211.030.91NA1
Metals: Tin0.031.1911NA1.05
Metals: Zinc0.420.810.980.76NA0.86
Agricultural: Corn0.100.850.981.160.670.77
Agricultural: Cotton0.400.711.061.080.970.97
Agricultural: Coffee0.470.801.021.500.600.93
Agricultural: Live CattleNA0.231.101.555.241.59
Agricultural: Soybeans0.321.420.940.81NA0.84
Agricultural: Wheat0.450.871.061.161.291.05

Notes: For commodities in the energy category, statistics are calculated for 12-month ahead futures. For metals, the statistics are for 15-month ahead forwards. For agricultural commodities, the statistics are for 8-month ahead futures. Samples begin in 1990 or as available.

Table 5: Forecast Efficiency Regressions, One Year Ahead

 Intercept, α: Point Estimate (i)Intercept, α: T-Test α=0 (ii)Point Estimate (iii)Slope, β: T-Test β=0 (iv)T-Test β=1 (v)Joint Test: α=0 and β=1 (vi)
Energy: Crude Oil0.091.710.943.67-0.233.16
Energy: Heating Oil0.071.330.932.66-0.191.83
Energy: Natural Gas0.010.140.853.21-0.590.36
Metals: Aluminum-0.02-0.261.191.190.190.07
Metals: Copper0.081.290.290.35-0.832.51
Metals: Lead0.060.810.390.63-0.971.06
Metals: Nickel0.080.880.791.22-0.331.02
Metals: Tin0.091.44-0.71-0.66-1.583.20
Metals: Zinc0-0.022.073.912.026.10
Agricultural: Corn-0.08-2.031.144.490.554.16
Agricultural: Cotton-0.07-1.80.83.82-0.957.23
Agricultural: Coffee0.020.240.692.74-1.231.61
Agricultural: Live Cattle0.011.01-0.06-0.22-3.6923.77
Agricultural: Soybeans0.020.570.933.06-0.220.36
Agricultural: Wheat0.010.210.392.51-3.9116.2

 

Notes: Bold indicates significance at 10 percent level.

Table 6: Relative Mean Squared Error of Futures Based Forecasts to Risk-Premium-Corrected Forecasts

 Three Months Ahead: Full Sample (i)Three Months Ahead: 2003-2010 Sample (ii)A Year Ahead*: Full Sample (iii)A Year Ahead*: 2003-2010 Sample (iv)
Energy: Crude Oil0.800.800.620.76
Energy: Heating Oil0.820.910.610.79
Energy: Natural Gas0.781.020.820.90
Metals: Aluminum0.820.800.600.59
Metals: Copper0.830.800.490.52
Metals: Lead0.840.870.620.70
Metals: Nickel0.640.710.080.64
Metals: Tin0.570.480.410.37
Metals: Zinc0.590.650.300.27
Agricultural: Corn0.800.840.810.74
Agricultural: Cotton0.870.970.950.83
Agricultural: Coffee0.750.570.540.54
Agricultural: Live Cattle0.830.850.240.24
Agricultural: Soybeans0.570.510.580.60
Agricultural: Wheat0.830.700.840.80

Notes: *The year ahead forecast is based on the appropriate and available futures contract. For commodities in the energy category, statistics are calculated for 12-month ahead futures. For metals, the statistics are for 15-month ahead forwards. For agricultural commodities, the statistics are for 8-month ahead futures. Samples begin in 1990 or as available.

Figure 1. Relationship Between Future/Spot Prices and Inventories for Copper

Data for Figure 1 immediately follows.

All data are from the London Metal Exchange. Sample period is 1990-2011.

Data for Figure 1

DATESCOPINVM - Inventory, tonsRelationship Between Future/Spot Prices and Inventories for Copper
Jan-89735000.8
Feb-89831250.8
Mar-8990912.50.78
Apr-89108232.50.81
May-89127847.50.91
Jun-89897000.95
Jul-8971712.50.88
Aug-8978812.50.84
Sep-89965460.84
Oct-8990157.50.87
Nov-89108062.50.93
Dec-891113120.99
Jan-90105927.50.98
Feb-9092568.750.97
Mar-90723200.9
Apr-9059987.50.87
May-9071121.430.85
Jun-9066181.250.89
Jul-9062480.560.85
Aug-90122052.50.85
Sep-90155471.250.83
Oct-90189562.220.9
Nov-90177452.230.95
Dec-90167805.720.95
Jan-91184166.670.99
Feb-91195192.50.97
Mar-91209172.50.97
Apr-91221177.50.95
May-91273217.160.97
Jun-91266646.250.99
Jul-91260055.560.98
Aug-912849200.99
Sep-91310176.660.98
Oct-91298451.090.97
Nov-91295631.250.97
Dec-91317267.51.02
Jan-92323466.691.08
Feb-92307051.251.06
Mar-92301843.341.05
Apr-92287923.751.07
May-92269438.341.06
Jun-92263004.471.04
Jul-92257957.781.01
Aug-92256061.231.02
Sep-92283127.51.05
Oct-92303994.471.07
Nov-92322734.441.07
Dec-92333461.691.06
Jan-93312342.51.03
Feb-93319916.251.04
Mar-93344654.441.06
Apr-93375042.51.08
May-93410134.281.08
Jun-93442806.281.06
Jul-93456822.221.01
Aug-93486513.720.99
Sep-93551922.251.01
Oct-93603581.251.06
Nov-93593977.751.07
Dec-93590423.751.05
Jan-946070501.05
Feb-945738351.05
Mar-94525864.441.03
Apr-94488697.531.03
May-94416695.720.98
Jun-94365401.120.97
Jul-94344266.660.95
Aug-94348301.250.97
Sep-94367073.340.97
Oct-94340802.50.96
Nov-94323231.120.88
Dec-94304852.50.82
Jan-95312003.750.85
Feb-95294283.750.88
Mar-952570400.89
Apr-952169500.89
May-95203701.440.91
Jun-95194666.660.85
Jul-95149483.750.8
Aug-95157551.250.82
Sep-95174905.560.86
Oct-95181368.890.89
Nov-95210461.250.84
Dec-95250152.50.84
Jan-96337541.250.89
Feb-96351536.250.9
Mar-963387500.89
Apr-963065200.9
May-96311001.440.86
Jun-962840750.92
Jul-962332800.96
Aug-96255673.750.93
Sep-962660250.98
Oct-96188226.670.96
Nov-96104576.660.88
Dec-96111338.750.87
Jan-97146202.220.83
Feb-97217037.50.86
Mar-97199838.580.87
Apr-971559200.88
May-97144143.50.85
Jun-97126591.910.84
Jul-97168619.130.88
Aug-972586490.93
Sep-972985350.99
Oct-973374001
Nov-97343688.51.01
Dec-97336694.281.05
Jan-983437381.06
Feb-98372015.51.06
Mar-98358217.721.04
Apr-98306002.51
May-98270961.061
Jun-98255289.091.02
Jul-98251475.221.02
Aug-98276342.51.02
Sep-98368885.471.03
Oct-98431514.781.05
Nov-98479390.941.06
Dec-98551042.871.07
Jan-99611801.51.08
Feb-996766381.08
Mar-99700825.621.08
Apr-997341861.07
May-99763905.811.07
Jun-99768742.751.09
Jul-997613301.06
Aug-99784716.621.05
Sep-99778160.941.04
Oct-99783263.811.05
Nov-99786339.561.06
Dec-99775778.941.06
Jan-007944591.05
Feb-00802059.061.06
Mar-00807677.811.06
Apr-00724956.131.06
May-00648353.811.03
Jun-005806051.02
Jul-00522837.161.01
Aug-00460726.811.01
Sep-00425987.621
Oct-00389121.810.99
Nov-00364296.371.01
Dec-00343283.691
1-Jan360906.811.01
1-Feb340456.51.01
1-Mar371120.471.03
1-Apr4266701.04
1-May438590.471.04
1-Jun429833.341.05
1-Jul578486.811.06
1-Aug664395.941.07
1-Sep683507.51.06
1-Oct739956.941.06
1-Nov741231.381.05
1-Dec783471.751.06
2-Jan817602.691.06
2-Feb8792621.05
2-Mar923427.51.05
2-Apr961569.561.04
2-May965429.121.04
2-Jun914525.621.04
2-Jul880946.941.05
2-Aug890927.621.05
2-Sep887217.631.06
2-Oct862268.691.05
2-Nov864436.691.04
2-Dec861572.621.04
3-Jan851001.811.04
3-Feb8319181.03
3-Mar829613.811.03
3-Apr792752.561.03
3-May774497.441.03
3-Jun697504.311.02
3-Jul641514.811.01
3-Aug621447.51
3-Sep601206.811.01
3-Oct548929.121.01
3-Nov493926.50.98
3-Dec452395.690.96
4-Jan400996.190.95
4-Feb321879.50.91
4-Mar237236.090.88
4-Apr165169.50.84
4-May144024.730.86
4-Jun117576.820.88
4-Jul94986.820.87
4-Aug94334.050.86
4-Sep103349.770.85
4-Oct87765.480.82
4-Nov67571.590.81
4-Dec54533.330.84
5-Jan45728.750.84
5-Feb53307.50.85
5-Mar48994.050.85
5-Apr52242.860.84
5-May54476.250.85
5-Jun36917.050.77
5-Jul27982.140.76
5-Aug51580.680.78
5-Sep775000.8
5-Oct67623.810.8
5-Nov67144.320.8
5-Dec772300.82
6-Jan100518.330.85
6-Feb1034730.89
6-Mar126299.130.9
6-Apr115537.230.91
6-May111201.420.86
6-Jun102737.050.87
6-Jul94563.090.87
6-Aug113700.910.9
6-Sep123239.050.9
6-Oct117107.270.91
6-Nov151016.360.96
6-Dec170628.950.98
7-Jan198450.450.95
7-Feb2129910.96
7-Mar193967.270.93
7-Apr171301.050.9
7-May141975.720.91
7-Jun119469.520.9
7-Jul102307.50.9
7-Aug119094.090.92
7-Sep134974.50.93
7-Oct143170.880.94
7-Nov178821.810.99
7-Dec192843.891.01
8-Jan187513.620.98
8-Feb155114.280.95
8-Mar126928.950.94
8-Apr113768.180.94
8-May1199600.94
8-Jun122625.230.94
8-Jul128017.830.93
8-Aug156009.50.96
8-Sep198488.190.98
8-Oct210227.831.01
8-Nov2707611.05
8-Dec313747.591.04
9-Jan399370.471.04
9-Feb522245.51.04
9-Mar508201.811.03
9-Apr4669201.01
9-May359667.341
9-Jun287456.811.01
9-Jul267813.911
9-Aug291837.50.99
9-Sep323894.090.99
9-Oct356637.721
9-Nov406524.281.01
9-Dec468659.031.01
10-Jan523469.531
10-Feb547179.51.01
10-Mar530614.381.01
10-Apr5082451
10-May484703.161.01
10-Jun462507.721.01
10-Jul427792.721
10-Aug406584.281
10-Sep387139.090.99
10-Oct370997.160.98
10-Nov361832.720.97
10-Dec359367.590.96
11-Jan383037.50.97
11-Feb4031280.98
11-Mar424651.441

Figure 2. Relationship Between Future/Spot Prices and Inventories for Oil

Data for Figure 2 immediately follows.

Prices are for WTI crude oil. Inventories are U.S. Stocks of crude oil and Petroleum products. Sample period is 1990-2011.

Data for Figure 2

DATES Relationship Between Future/Spot Prices and Inventories for OilFUTSPOTW
5-Jan-90 0.83
12-Jan-90 0.82
19-Jan-90 0.8
26-Jan-90 0.87
2-Feb-90 0.88
9-Feb-90 0.94
16-Feb-90 0.93
23-Feb-90 0.97
2-Mar-90 0.97
9-Mar-90 1
16-Mar-90 1.02
23-Mar-90 0.99
30-Mar-90 1.02
6-Apr-90 1.06
13-Apr-90 NA
20-Apr-90 1.11
27-Apr-90 1.07
4-May-90 1.11
11-May-90 1.04
18-May-90 1.07
25-May-90 1.12
1-Jun-90 1.15
8-Jun-90 1.17
15-Jun-90 1.18
22-Jun-90 1.13
29-Jun-90 1.13
6-Jul-90 1.15
13-Jul-90 1.13
20-Jul-90 1.06
27-Jul-90 1.07
3-Aug-90 0.96
10-Aug-90 0.88
17-Aug-90 0.85
24-Aug-90 0.83
31-Aug-90 0.87
7-Sep-90 0.82
14-Sep-90 0.8
21-Sep-90 0.74
28-Sep-90 0.74
5-Oct-90 0.71
12-Oct-90 0.69
19-Oct-90 0.72
26-Oct-90 0.76
2-Nov-90 0.73
9-Nov-90 0.73
16-Nov-90 0.81
23-Nov-90 0.78
30-Nov-90 0.81
7-Dec-90 0.84
14-Dec-90 0.81
21-Dec-90 0.83
28-Dec-90 0.82
4-Jan-91 0.84
11-Jan-91 0.78
18-Jan-91 0.95
25-Jan-91 0.86
1-Feb-91 0.87
8-Feb-91 0.84
15-Feb-91 0.83
22-Feb-91 1.01
1-Mar-91 0.97
8-Mar-91 0.97
15-Mar-91 0.92
22-Mar-91 0.94
29-Mar-91 NA
5-Apr-91 0.95
12-Apr-91 0.91
19-Apr-91 0.95
26-Apr-91 0.94
3-May-91 0.95
10-May-91 0.98
17-May-91 1.01
24-May-91 1
31-May-91 1
7-Jun-91 1.01
14-Jun-91 1.02
21-Jun-91 0.98
28-Jun-91 0.97
5-Jul-91 0.95
12-Jul-91 0.94
19-Jul-91 0.94
26-Jul-91 0.95
2-Aug-91 0.96
9-Aug-91 0.95
16-Aug-91 0.96
23-Aug-91 0.95
30-Aug-91 0.94
6-Sep-91 0.96
13-Sep-91 0.95
20-Sep-91 0.94
27-Sep-91 0.94
4-Oct-91 0.93
11-Oct-91 0.92
18-Oct-91 0.89
25-Oct-91 0.91
1-Nov-91 0.9
8-Nov-91 0.92
15-Nov-91 0.92
22-Nov-91 0.95
29-Nov-91 0.96
6-Dec-91 0.98
13-Dec-91 0.98
20-Dec-91 1.03
27-Dec-91 1.02
3-Jan-92 1.01
10-Jan-92 1.05
17-Jan-92 1.01
24-Jan-92 1.01
31-Jan-92 1.01
7-Feb-92 0.98
14-Feb-92 1.01
21-Feb-92 1.01
28-Feb-92 1.03
6-Mar-92 1.02
13-Mar-92 1
20-Mar-92 1
27-Mar-92 1
3-Apr-92 0.97
10-Apr-92 0.98
17-Apr-92 NA
24-Apr-92 0.98
1-May-92 0.97
8-May-92 0.98
15-May-92 0.99
22-May-92 0.99
29-May-92 0.96
5-Jun-92 0.94
12-Jun-92 0.95
19-Jun-92 0.96
26-Jun-92 0.94
3-Jul-92 NA
10-Jul-92 0.96
17-Jul-92 0.96
24-Jul-92 0.94
31-Jul-92 0.95
7-Aug-92 0.95
14-Aug-92 0.96
21-Aug-92 0.96
28-Aug-92 0.96
4-Sep-92 0.94
11-Sep-92 0.94
18-Sep-92 0.94
25-Sep-92 0.96
2-Oct-92 0.95
9-Oct-92 0.95
16-Oct-92 0.95
23-Oct-92 0.97
30-Oct-92 0.99
6-Nov-92 1
13-Nov-92 1
20-Nov-92 1
27-Nov-92 NA
4-Dec-92 1.02
11-Dec-92 1.02
18-Dec-92 1.01
25-Dec-92 NA
1-Jan-93 NA
8-Jan-93 1.03
15-Jan-93 1.04
22-Jan-93 1.03
29-Jan-93 1.01
5-Feb-93 1
12-Feb-93 1
19-Feb-93 1.03
26-Feb-93 1
5-Mar-93 0.99
12-Mar-93 1.01
19-Mar-93 1.01
26-Mar-93 1
2-Apr-93 1
9-Apr-93 NA
16-Apr-93 1.02
23-Apr-93 1.02
30-Apr-93 1.01
7-May-93 1.01
14-May-93 1.03
21-May-93 1.02
28-May-93 1.02
4-Jun-93 1.02
11-Jun-93 1.05
18-Jun-93 1.07
25-Jun-93 1.05
2-Jul-93 1.09
9-Jul-93 1.09
16-Jul-93 1.09
23-Jul-93 1.07
30-Jul-93 1.06
6-Aug-93 1.09
13-Aug-93 1.08
20-Aug-93 1.08
27-Aug-93 1.05
3-Sep-93 1.08
10-Sep-93 1.12
17-Sep-93 1.12
24-Sep-93 1.08
1-Oct-93 1.03
8-Oct-93 1.05
15-Oct-93 1.05
22-Oct-93 1.06
29-Oct-93 1.08
5-Nov-93 1.08
12-Nov-93 1.11
19-Nov-93 1.12
26-Nov-93 NA
3-Dec-93 1.14
10-Dec-93 1.16
17-Dec-93 1.22
24-Dec-93 NA
31-Dec-93 NA
7-Jan-94 1.12
14-Jan-94 1.12
21-Jan-94 1.09
28-Jan-94 1.07
4-Feb-94 1.07
11-Feb-94 1.14
18-Feb-94 1.14
25-Feb-94 1.12
4-Mar-94 1.12
11-Mar-94 1.1
18-Mar-94 1.07
25-Mar-94 1.07
1-Apr-94 NA
8-Apr-94 1.06
15-Apr-94 1.01
22-Apr-94 0.98
29-Apr-94 0.99
6-May-94 0.96
13-May-94 0.94
20-May-94 0.93
27-May-94 0.96
3-Jun-94 0.96
10-Jun-94 0.94
17-Jun-94 0.89
24-Jun-94 0.94
1-Jul-94 0.93
8-Jul-94 0.93
15-Jul-94 0.93
22-Jul-94 0.95
29-Jul-94 0.93
5-Aug-94 0.94
12-Aug-94 0.99
19-Aug-94 0.99
26-Aug-94 1.03
2-Sep-94 1.02
9-Sep-94 1.03
16-Sep-94 1.05
23-Sep-94 1.02
30-Sep-94 1.01
7-Oct-94 1.01
14-Oct-94 1.03
21-Oct-94 1.01
28-Oct-94 0.97
4-Nov-94 0.96
11-Nov-94 0.99
18-Nov-94 1
25-Nov-94 NA
2-Dec-94 1.02
9-Dec-94 1.03
16-Dec-94 1.05
23-Dec-94 1.01
30-Dec-94 1.01
6-Jan-95 1.01
13-Jan-95 1
20-Jan-95 0.95
27-Jan-95 0.98
3-Feb-95 0.94
10-Feb-95 0.96
17-Feb-95 0.94
24-Feb-95 0.95
3-Mar-95 0.95
10-Mar-95 0.99
17-Mar-95 0.98
24-Mar-95 0.95
31-Mar-95 0.93
7-Apr-95 0.93
14-Apr-95 NA
21-Apr-95 0.9
28-Apr-95 0.91
5-May-95 0.91
12-May-95 0.92
19-May-95 0.92
26-May-95 0.96
2-Jun-95 0.95
9-Jun-95 0.96
16-Jun-95 0.95
23-Jun-95 1.02
30-Jun-95 0.99
7-Jul-95 1
14-Jul-95 0.99
21-Jul-95 1.02
28-Jul-95 0.99
4-Aug-95 0.98
11-Aug-95 0.97
18-Aug-95 0.96
25-Aug-95 0.95
1-Sep-95 0.96
8-Sep-95 0.94
15-Sep-95 0.92
22-Sep-95 0.98
29-Sep-95 0.96
6-Oct-95 0.98
13-Oct-95 0.97
20-Oct-95 0.97
27-Oct-95 0.96
3-Nov-95 0.95
10-Nov-95 0.94
17-Nov-95 0.92
24-Nov-95 NA
1-Dec-95 0.93
8-Dec-95 0.92
15-Dec-95 0.9
22-Dec-95 0.91
29-Dec-95 0.9
5-Jan-96 0.88
12-Jan-96 0.93
19-Jan-96 0.9
26-Jan-96 0.95
2-Feb-96 0.95
9-Feb-96 0.95
16-Feb-96 0.89
23-Feb-96 0.9
1-Mar-96 0.88
8-Mar-96 0.87
15-Mar-96 0.79
22-Mar-96 0.81
29-Mar-96 0.84
5-Apr-96 NA
12-Apr-96 0.74
19-Apr-96 0.74
26-Apr-96 0.82
3-May-96 0.85
10-May-96 0.86
17-May-96 0.84
24-May-96 0.84
31-May-96 0.88
7-Jun-96 0.88
14-Jun-96 0.88
21-Jun-96 0.9
28-Jun-96 0.86
5-Jul-96 NA
12-Jul-96 0.84
19-Jul-96 0.86
26-Jul-96 0.89
2-Aug-96 0.86
9-Aug-96 0.86
16-Aug-96 0.82
23-Aug-96 0.85
30-Aug-96 0.85
6-Sep-96 0.81
13-Sep-96 0.79
20-Sep-96 0.83
27-Sep-96 0.82
4-Oct-96 0.82
11-Oct-96 0.83
18-Oct-96 0.81
25-Oct-96 0.84
1-Nov-96 0.86
8-Nov-96 0.88
15-Nov-96 0.87
22-Nov-96 0.85
29-Nov-96 NA
6-Dec-96 0.81
13-Dec-96 0.83
20-Dec-96 0.81
27-Dec-96 0.8
3-Jan-97 0.8
10-Jan-97 0.79
17-Jan-97 0.8
24-Jan-97 0.85
31-Jan-97 0.85
7-Feb-97 0.9
14-Feb-97 0.9
21-Feb-97 0.92
28-Feb-97 0.96
7-Mar-97 0.96
14-Mar-97 0.96
21-Mar-97 0.96
28-Mar-97 NA
4-Apr-97 1.02
11-Apr-97 1.01
18-Apr-97 0.98
25-Apr-97 0.99
2-May-97 1
9-May-97 0.98
16-May-97 0.95
23-May-97 0.96
30-May-97 0.99
6-Jun-97 1.04
13-Jun-97 1.04
20-Jun-97 1.05
27-Jun-97 1.02
4-Jul-97 NA
11-Jul-97 1.02
18-Jul-97 1.02
25-Jul-97 1
1-Aug-97 0.99
8-Aug-97 1.02
15-Aug-97 1.01
22-Aug-97 1
29-Aug-97 1.01
5-Sep-97 1.01
12-Sep-97 1.01
19-Sep-97 1.01
26-Sep-97 0.98
3-Oct-97 0.91
10-Oct-97 0.94
17-Oct-97 0.97
24-Oct-97 0.97
31-Oct-97 0.97
7-Nov-97 0.97
14-Nov-97 0.95
21-Nov-97 1
28-Nov-97 NA
5-Dec-97 1.03
12-Dec-97 1.05
19-Dec-97 1.04
26-Dec-97 1.03
2-Jan-98 1.07
9-Jan-98 1.09
16-Jan-98 1.1
23-Jan-98 1.12
30-Jan-98 1.06
6-Feb-98 1.08
13-Feb-98 1.11
20-Feb-98 1.11
27-Feb-98 1.14
6-Mar-98 1.18
13-Mar-98 1.2
20-Mar-98 1.17
27-Mar-98 1.07
3-Apr-98 1.1
10-Apr-98 NA
17-Apr-98 1.12
24-Apr-98 1.13
1-May-98 1.11
8-May-98 1.16
15-May-98 1.19
22-May-98 1.15
29-May-98 1.14
5-Jun-98 1.18
12-Jun-98 1.37
19-Jun-98 1.42
26-Jun-98 1.19
3-Jul-98 NA
10-Jul-9801.18
17-Jul-9801.17
24-Jul-9801.17
31-Jul-9801.14
7-Aug-9801.17
14-Aug-9801.18
21-Aug-9801.16
28-Aug-9801.15
4-Sep-9801.12
11-Sep-9801.13
18-Sep-9801.09
25-Sep-9801.07
2-Oct-9801.08
9-Oct-9801.12
16-Oct-9801.13
23-Oct-9801.12
30-Oct-9801.11
6-Nov-9801.13
13-Nov-9801.14
20-Nov-9801.28
27-Nov-980NA
4-Dec-9801.27
11-Dec-9801.29
18-Dec-9801.24
25-Dec-980NA
1-Jan-990NA
8-Jan-9901.09
15-Jan-9901.13
22-Jan-9901.08
29-Jan-9901.08
5-Feb-9901.13
12-Feb-9901.11
19-Feb-9901.12
26-Feb-9901.09
5-Mar-9901.06
12-Mar-9900.99
19-Mar-9900.99
26-Mar-9900.97
2-Apr-990NA
9-Apr-9900.96
16-Apr-9900.94
23-Apr-9900.9
30-Apr-9900.9
7-May-9900.93
14-May-9900.95
21-May-9900.96
28-May-9900.97
4-Jun-9900.96
11-Jun-9900.95
18-Jun-9900.98
25-Jun-9900.97
2-Jul-9900.93
9-Jul-9900.94
16-Jul-9900.93
23-Jul-9900.93
30-Jul-9900.92
6-Aug-9900.91
13-Aug-9900.88
20-Aug-9900.88
27-Aug-9900.89
3-Sep-9900.86
10-Sep-9900.83
17-Sep-9900.79
24-Sep-9900.81
1-Oct-9900.81
8-Oct-9900.9
15-Oct-9900.88
22-Oct-9900.88
29-Oct-9900.9
5-Nov-9900.84
12-Nov-9900.82
19-Nov-9900.78
26-Nov-990NA
3-Dec-9900.76
10-Dec-9900.8
17-Dec-9900.78
24-Dec-990NA
31-Dec-99943.5NA
7-Jan-00937.20.82
14-Jan-00934.80.77
21-Jan-00926.60.77
28-Jan-00912.80.8
4-Feb-00907.70.79
11-Feb-00900.60.77
18-Feb-00895.50.77
25-Feb-00894.80.75
3-Mar-00902.40.74
10-Mar-00895.90.73
17-Mar-00896.80.76
24-Mar-00895.80.84
31-Mar-00899.40.88
7-Apr-00905.10.9
14-Apr-00907.90.87
21-Apr-00916.1NA
28-Apr-00922.10.9
5-May-00928.20.84
12-May-00932.80.83
19-May-00938.20.84
26-May-009390.83
2-Jun-00946.80.82
9-Jun-00950.70.82
16-Jun-00946.20.77
23-Jun-00952.40.81
30-Jun-009530.81
7-Jul-00959.50.83
14-Jul-00958.90.84
21-Jul-00965.10.9
28-Jul-00956.50.92
4-Aug-00958.10.87
11-Aug-00958.50.84
18-Aug-00959.40.84
25-Aug-00958.50.85
1-Sep-00963.50.83
8-Sep-00961.80.83
15-Sep-00954.70.82
22-Sep-00954.80.88
29-Sep-00959.90.92
6-Oct-00965.20.93
13-Oct-00953.80.83
20-Oct-009530.84
27-Oct-00947.60.83
3-Nov-00944.90.81
10-Nov-00948.10.8
17-Nov-00948.30.78
24-Nov-00948.2NA
1-Dec-009540.81
8-Dec-009440.89
15-Dec-00947.50.86
22-Dec-00940.30.91
29-Dec-009300.9
5-Jan-01927.30.86
12-Jan-01923.10.83
19-Jan-01925.10.79
26-Jan-01922.60.84
2-Feb-019240.83
9-Feb-01923.70.85
16-Feb-01916.10.88
23-Feb-019190.88
2-Mar-01914.70.91
9-Mar-01919.20.93
16-Mar-01917.40.95
23-Mar-01925.50.93
30-Mar-01923.5NA
6-Apr-01927.40.93
13-Apr-01934.9NA
20-Apr-01940.20.95
27-Apr-01958.80.94
4-May-019620.92
11-May-019700.92
18-May-019760.9
25-May-01984.90.92
1-Jun-0110000.93
8-Jun-011000.70.93
15-Jun-011012.60.91
22-Jun-011015.40.94
29-Jun-011012.60.96
6-Jul-011013.70.9
13-Jul-011020.90.93
20-Jul-011021.60.96
27-Jul-011018.60.91
3-Aug-011017.80.9
10-Aug-011011.30.89
17-Aug-011004.50.9
24-Aug-011003.20.92
31-Aug-011001.10.92
7-Sep-011006.80.9
14-Sep-011007.3NA
21-Sep-011020.80.93
28-Sep-011026.61
5-Oct-011027.41.01
12-Oct-011024.71
19-Oct-011026.31.02
26-Oct-011025.11
2-Nov-011023.51.04
9-Nov-011022.40.99
16-Nov-011019.81.1
23-Nov-011021.1NA
30-Nov-011029.21.06
7-Dec-011024.81.09
14-Dec-011019.41.07
21-Dec-011012.41.05
28-Dec-011009.21.04
4-Jan-021015.41.01
11-Jan-021015.21.06
18-Jan-021017.21.11
25-Jan-021018.51.03
1-Feb-021017.31.03
8-Feb-021017.2NA
15-Feb-021010.5NA
22-Feb-021004.91
1-Mar-021001.40.99
8-Mar-021000.10.98
15-Mar-02999.30.96
22-Mar-02990.20.95
29-Mar-02996.6NA
5-Apr-02998.70.91
12-Apr-02992.30.95
19-Apr-02997.30.91
26-Apr-021004.30.91
3-May-021006.70.91
10-May-021007.30.89
17-May-021015.40.89
24-May-021018.90.95
31-May-021024.80.95
7-Jun-021026.60.97
14-Jun-021031.30.95
21-Jun-021029.60.95
28-Jun-021031.40.92
5-Jul-021028.2NA
12-Jul-021032.60.91
19-Jul-021030.40.91
26-Jul-021028.90.92
2-Aug-021025.30.91
9-Aug-021012.70.91
16-Aug-021014.10.87
23-Aug-021013.30.89
30-Aug-021007.20.89
6-Sep-0210100.87
13-Sep-021004.40.86
20-Sep-021002.90.84
27-Sep-02994.40.82
4-Oct-02982.10.84
11-Oct-02979.80.85
18-Oct-02982.10.85
25-Oct-02978.90.89
1-Nov-02983.40.88
8-Nov-02978.40.9
15-Nov-02980.20.92
22-Nov-02975.90.91
29-Nov-02976.9NA
6-Dec-02981.50.9
13-Dec-02976.50.86
20-Dec-02970.90.82
27-Dec-029550.77
3-Jan-039530.75
10-Jan-03951.30.78
17-Jan-03945.10.76
24-Jan-03935.40.79
31-Jan-03918.60.8
7-Feb-03912.40.78
14-Feb-03905.70.74
21-Feb-038980.77
28-Feb-038950.75
7-Mar-03884.80.74
14-Mar-03882.20.77
21-Mar-03886.80.91
28-Mar-03892.30.83
4-Apr-03884.70.86
11-Apr-03887.60.9
18-Apr-03899.2NA
25-Apr-03905.90.94
2-May-03905.20.95
9-May-03904.70.91
16-May-03912.10.87
23-May-03912.70.87
30-May-03921.70.86
6-Jun-03924.10.82
13-Jun-039300.82
20-Jun-03928.90.83
27-Jun-03924.60.88
4-Jul-03925.5NA
11-Jul-03930.90.85
18-Jul-03928.70.83
25-Jul-03931.30.88
1-Aug-03936.70.84
8-Aug-03932.10.85
15-Aug-03932.8NA
22-Aug-03929.70.86
29-Aug-039350.86
5-Sep-03939.60.9
12-Sep-03950.40.92
19-Sep-03958.7NA
26-Sep-03963.80.92
3-Oct-039670.87
10-Oct-03966.10.86
17-Oct-039660.88
24-Oct-03969.50.89
31-Oct-03966.50.91
7-Nov-03961.70.88
14-Nov-03960.10.85
21-Nov-039530.86
28-Nov-03953.8NA
5-Dec-03948.90.89
12-Dec-03937.20.87
19-Dec-03934.20.86
26-Dec-03929.1NA
2-Jan-04931.9NA
9-Jan-04928.30.86
16-Jan-04927.30.85
23-Jan-04915.30.86
30-Jan-04912.50.87
6-Feb-04902.20.88
13-Feb-04900.60.87
20-Feb-04895.90.84
27-Feb-04898.60.86
5-Mar-04905.50.85
12-Mar-04907.30.87
19-Mar-04913.10.86
26-Mar-04918.90.88
2-Apr-04912.90.9
9-Apr-04910.7NA
16-Apr-04912.30.87
23-Apr-04919.10.9
30-Apr-04927.10.89
7-May-04930.20.87
14-May-04933.70.86
21-May-04934.90.88
28-May-04943.60.89
4-Jun-049470.91
11-Jun-04951.6NA
18-Jun-04956.20.92
25-Jun-04960.30.93
2-Jul-04966.40.93
9-Jul-04966.80.9
16-Jul-04968.50.9
23-Jul-04975.80.9
30-Jul-04978.40.9
6-Aug-04976.30.89
13-Aug-04977.80.89
20-Aug-049790.87
27-Aug-04978.10.92
3-Sep-04978.50.91
10-Sep-04974.90.91
17-Sep-04961.80.89
24-Sep-04962.40.87
1-Oct-04962.40.87
8-Oct-04961.6NA
15-Oct-04958.50.86
22-Oct-04959.80.88
29-Oct-04963.70.92
5-Nov-04966.70.92
12-Nov-04964.80.93
19-Nov-04966.60.93
26-Nov-04973NA
3-Dec-04978.70.97
10-Dec-04975.70.99
17-Dec-04975.10.95
24-Dec-04968.3NA
31-Dec-04965.8NA
7-Jan-05960.20.94
14-Jan-05963.10.93
21-Jan-05960.90.94
28-Jan-05957.70.96
4-Feb-05952.70.97
11-Feb-05951.20.96
18-Feb-05950.60.96
25-Feb-059510.95
4-Mar-05952.60.95
11-Mar-05947.50.97
18-Mar-05947.71
25-Mar-05953.2NA
1-Apr-05955.91
8-Apr-05961.71.02
15-Apr-05960.51.04
22-Apr-05967.21.01
29-Apr-05972.21.06
6-May-05979.11.04
13-May-05987.31.06
20-May-05991.31.09
27-May-05998.71.02
3-Jun-05998.61.03
10-Jun-051001.41.05
17-Jun-051004.31.02
24-Jun-051013.71.01
1-Jul-051015.51.03
8-Jul-051016.41.03
15-Jul-051018.91.03
22-Jul-051016.61.03
29-Jul-051021.51.04
5-Aug-051024.91.04
12-Aug-051021.60.99
19-Aug-051022.11.01
26-Aug-051024.51.02
2-Sep-051009.61.01
9-Sep-051005.51.03
16-Sep-051012.31.03
23-Sep-051014.81.02
30-Sep-051004.91.01
7-Oct-059981.02
14-Oct-051004.31
21-Oct-0510041.01
28-Oct-051005.61.01
4-Nov-051017.21.03
11-Nov-051016.11.04
18-Nov-051017.71.06
25-Nov-051019.91.03
2-Dec-051025.71.05
9-Dec-051026.91.06
16-Dec-051019.11.06
23-Dec-051011.71.05
30-Dec-051009.61.05
6-Jan-061011.21.04
13-Jan-061016.41.05
20-Jan-061020.31.03
27-Jan-061022.21.04
3-Feb-0610251.06
10-Feb-061029.21.08
17-Feb-061027.21.1
24-Feb-061023.21.08
3-Mar-061024.51.09
10-Mar-061021.41.09
17-Mar-061015.91.07
24-Mar-061012.61.05
31-Mar-0610081.05
7-Apr-061005.31.05
14-Apr-06999.5NA
21-Apr-061002.31.02
28-Apr-061004.51.05
5-May-061009.91.06
12-May-061011.71.05
19-May-061015.31.07
26-May-061023.41.04
2-Jun-061029.71.04
9-Jun-061036.41.05
16-Jun-061044.21.04
23-Jun-061044.81.04
30-Jun-061045.11.03
7-Jul-061043.21.04
14-Jul-061049.81.04
21-Jul-061052.31.03
28-Jul-061057.51.05
4-Aug-061055.51.06
11-Aug-061056.71.06
18-Aug-061060.91.07
25-Aug-061064.91.05
1-Sep-061066.71.07
8-Sep-061071.11.09
15-Sep-061075.41.1
22-Sep-061084.61.09
29-Sep-061088.61.09
6-Oct-061089.11.11
13-Oct-061083.31.13
20-Oct-0610721.17
27-Oct-061068.61.12
3-Nov-061061.81.13
10-Nov-061052.81.13
17-Nov-061056.61.19
24-Nov-061049.11.13
1-Dec-061044.91.1
8-Dec-061037.41.09
15-Dec-061029.51.08
22-Dec-061022.11.09
29-Dec-061023.91.09
5-Jan-071031.31.12
12-Jan-071040.31.1
19-Jan-071041.81.13
26-Jan-071042.11.09
2-Feb-071031.71.09
9-Feb-071020.41.08
16-Feb-071009.31.07
23-Feb-071000.41.09
2-Mar-07984.61.09
9-Mar-079821.1
16-Mar-07979.11.14
23-Mar-07979.51.08
30-Mar-07982.21.06
6-Apr-07981.9NA
13-Apr-07982.21.12
20-Apr-079821.09
27-Apr-07982.21.08
4-May-07988.51.12
11-May-07995.41.11
18-May-071001.81.09
25-May-071003.51.09
1-Jun-071007.21.08
8-Jun-071007.91.07
15-Jun-071017.81.06
22-Jun-071018.31.05
29-Jun-071026.61.02
6-Jul-071029.11.01
13-Jul-071030.41
20-Jul-071035.10.97
27-Jul-071034.40.95
3-Aug-071034.10.97
10-Aug-071029.60.97
17-Aug-071030.10.96
24-Aug-071027.90.97
31-Aug-071022.50.95
7-Sep-071019.10.93
14-Sep-071016.30.93
21-Sep-071020.50.94
28-Sep-071021.40.93
5-Oct-0710210.94
12-Oct-071023.60.93
19-Oct-071015.70.91
26-Oct-071014.60.91
2-Nov-071013.70.9
9-Nov-071014.40.92
16-Nov-071007.50.91
23-Nov-071005.70.92
30-Nov-071001.90.96
7-Dec-071000.70.97
14-Dec-07992.40.97
21-Dec-07981.90.96
28-Dec-07974.60.95
4-Jan-08966.50.96
11-Jan-08970.10.96
18-Jan-08972.30.96
25-Jan-08971.30.97
1-Feb-08980.90.99
8-Feb-08981.60.98
15-Feb-08977.90.97
22-Feb-08980.60.97
29-Feb-08976.10.97
7-Mar-08982.70.94
14-Mar-08979.80.93
21-Mar-08973.3NA
28-Mar-08974.80.95
4-Apr-08966.20.95
11-Apr-08958.20.95
18-Apr-08958.90.95
25-Apr-08967.80.95
2-May-08973.30.95
9-May-08978.30.97
16-May-08977.90.99
23-May-08968.20.99
30-May-08968.40.99
6-Jun-08968.70.98
13-Jun-08969.31
20-Jun-08974.71
27-Jun-089771
4-Jul-08973.7NA
11-Jul-08981.21
18-Jul-08983.11.02
25-Jul-08985.71.01
1-Aug-08988.31.01
8-Aug-08982.91.01
15-Aug-08991.11.01
22-Aug-08993.41.02
29-Aug-08989.81.02
5-Sep-08974.61.03
12-Sep-08962.71.03
19-Sep-08944.80.99
26-Sep-08945.31.01
3-Oct-08964.91.01
10-Oct-08976.71.06
17-Oct-08986.21.07
24-Oct-08992.91.08
31-Oct-089981.09
7-Nov-08999.21.16
14-Nov-081001.91.16
21-Nov-081011.61.19
28-Nov-081011.21.19
5-Dec-081017.91.34
12-Dec-081015.21.27
19-Dec-081013.61.63
26-Dec-081009.41.36
2-Jan-091017.11.32
9-Jan-091025.31.46
16-Jan-091037.11.6
23-Jan-091040.71.23
30-Jan-091042.11.33
6-Feb-091044.71.41
13-Feb-091038.51.44
20-Feb-091035.61.29
27-Feb-091036.61.2
6-Mar-091039.21.17
13-Mar-091042.31.16
20-Mar-091045.11.21
27-Mar-091051.51.19
3-Apr-091054.41.22
10-Apr-091062.6NA
17-Apr-091073.91.24
24-Apr-091079.41.17
1-May-091087.31.19
8-May-091086.11.13
15-May-091085.31.13
22-May-091087.51.09
29-May-091102.61.07
5-Jun-091100.91.11
12-Jun-091099.41.08
19-Jun-091104.71.08
26-Jun-091109.11.07
3-Jul-091114.2NA
10-Jul-091115.71.13
17-Jul-091117.61.13
24-Jul-091123.11.13
31-Jul-091120.41.12
7-Aug-091121.51.12
14-Aug-091108.71.13
21-Aug-091105.61.07
28-Aug-091101.11.07
4-Sep-0910961.07
11-Sep-091092.81.07
18-Sep-091100.81.07
25-Sep-091105.41.08
2-Oct-091109.21.07
9-Oct-091103.41.07
16-Oct-091099.21.05
23-Oct-091097.61.06
30-Oct-091089.21.06
6-Nov-091090.21.07
13-Nov-0910861.08
20-Nov-091085.11.09
27-Nov-091090.61.1
4-Dec-091086.31.12
11-Dec-091073.61.13
18-Dec-091059.41.1
25-Dec-091051.3NA
1-Jan-101049NA
8-Jan-101052.61.06
15-Jan-1010511.07
22-Jan-101045.31.07
29-Jan-1010461.07
5-Feb-101047.91.07
12-Feb-101045.51.07
19-Feb-101046.91.04
26-Feb-101046.61.04
5-Mar-101041.31.04
12-Mar-101038.81.04
19-Mar-101039.21.03
26-Mar-101042.41.03
2-Apr-101049.61.12
9-Apr-101049.31.05
16-Apr-1010601.08
23-Apr-101072.91.08
30-Apr-101082.71.07
7-May-101086.11.13
14-May-101087.31.16
21-May-101093.21.09
28-May-101090.91.08
4-Jun-101090.451.1
11-Jun-101094.881.1
18-Jun-101097.561.08
25-Jun-101101.141.05
2-Jul-101101.51.06
9-Jul-101104.691.06
16-Jul-101109.811.06
23-Jul-101118.811.05
30-Jul-101124.911.06
6-Aug-101125.051.06
13-Aug-101130.391.06
20-Aug-101139.311.07
27-Aug-101143.351.08
3-Sep-101143.541.1
10-Sep-101140.621.08
17-Sep-101143.921.12
24-Sep-101138.811.08
1-Oct-101138.891.06
8-Oct-101134.221.06
15-Oct-101132.21.06
22-Oct-101132.781.05
29-Oct-101127.321.05
5-Nov-101115.511.04
12-Nov-101106.41.04
19-Nov-101106.151.04
26-Nov-101106.11.04
3-Dec-101100.791.01
10-Dec-101085.151.02
17-Dec-101079.151.04
24-Dec-101069.99NA
31-Dec-101063.671.03
7-Jan-111064.611.06
14-Jan-111066.971.06
21-Jan-111069.371.07
28-Jan-111074.911.1
4-Feb-111078.081.11
11-Feb-111069.71.15
18-Feb-111057.611.14
25-Feb-111051.081.04
4-Mar-111044.811.01
11-Mar-111039.691.03
18-Mar-111038.791.02
25-Mar-111042.121.01
1-Apr-111042.361
8-Apr-111037.411
15-Apr-111030.671.01
22-Apr-111033.58NA
29-Apr-111041.11
6-May-111047.521.01
13-May-111047.461.01
20-May-111054.221.02
27-May-111061.461.03
3-Jun-111062.931.03
10-Jun-111062.311.03

Figure 3. Relative MSE of Futures Versus Random Walk Forecasts Evaluated Over a Rolling Eight Year Window

Data for Figure 3 immediately follows.

For copper and Oil, the evaluated forecasts are at the 12-month horizon. For corn, the evaluated forecasts are at teh 8-month horizon.

Data for Figure 3

dateoilcopcrn
1990m01ndnd 
1990m02ndnd 
1990m03ndnd 
1990m04ndnd 
1990m05ndnd 
1990m06ndnd 
1990m07ndnd 
1990m08ndnd 
1990m09ndnd 
1990m10ndnd 
1990m11ndnd 
1990m12ndnd 
1991m012.53055.3631 
1991m022.319310.9970.30188
1991m032.3170.835750.2983
1991m041.68350.81319 
1991m051.64590.43244 
1991m061.37510.3503 
1991m071.21150.22329 
1991m081.03440.18632 
1991m090.71480.1594 
1991m100.478320.14497 
1991m110.423780.14041 
1991m120.386140.13917 
1992m010.320740.14672 
1992m020.33140.143950.27438
1992m030.332180.142950.35629
1992m040.329070.14328 
1992m050.329260.14816 
1992m060.334530.16962 
1992m070.339130.25132 
1992m080.339850.29131 
1992m090.344440.30278 
1992m100.344650.3006 
1992m110.341390.29853 
1992m120.341750.29963 
1993m010.342560.2993 
1993m020.342680.298490.60834
1993m030.34390.299760.84097
1993m040.344390.32944 
1993m050.345260.40146 
1993m060.350450.44364 
1993m070.359680.48355 
1993m080.363070.5171 
1993m090.377780.5559 
1993m100.382210.621140.66917
1993m110.39830.666230.47235
1993m120.440090.69945 
1994m010.476630.71031 
1994m020.518720.722290.43359
1994m030.549140.726340.43831
1994m040.564860.72813 
1994m050.569360.7292 
1994m060.567880.73982 
1994m070.563870.74915 
1994m080.566840.75476 
1994m090.577090.769590.46412
1994m100.584610.776840.50582
1994m110.58540.793730.55298
1994m120.578130.8103 
1995m010.57070.82576 
1995m020.5557nd0.54183
1995m030.551930.840820.54159
1995m040.55506nd 
1995m050.564730.85432 
1995m060.564960.86429 
1995m070.56139nd 
1995m080.561310.87415 
1995m090.55913nd0.51662
1995m100.55896nd0.49035
1995m110.558940.88770.47364
1995m120.55740.89932 
1996m010.55797nd 
1996m020.56017nd0.58102
1996m030.571550.891030.68362
1996m040.60536nd 
1996m050.615770.89417 
1996m060.62168nd 
1996m070.635590.85388 
1996m080.64820.83221 
1996m090.681390.821470.71394
1996m100.709050.813390.67384
1996m110.735810.80030.62476
1996m120.764250.78849 
1997m010.797910.7885 
1997m020.817060.787890.51698
1997m030.831570.788340.43366
1997m040.818420.78662 
1997m050.829760.78619 
1997m060.828810.79944 
1997m070.824360.80304 
1997m080.824460.80598 
1997m090.807870.807410.43511
1997m100.795470.809130.43499
1997m110.790130.80610.43737
1997m120.770880.79902 
1998m010.739870.78854 
1998m020.731110.780660.43898
1998m030.736160.770070.43897
1998m040.739880.76562 
1998m050.742760.75319 
1998m060.767590.74296 
1998m070.774510.73866 
1998m080.784460.74087 
1998m090.790020.744360.49478
1998m100.79280.747660.52553
1998m110.792480.750880.56079
1998m120.810810.75714 
1999m010.827740.76179 
1999m020.815120.766460.57515
1999m030.820990.773230.58938
1999m040.819780.77397 
1999m050.816930.77462 
1999m060.783860.77772 
1999m070.780920.77752 
1999m080.76910.77717 
1999m090.7670.777020.6162
1999m100.772060.776450.64506
1999m110.788950.774440.67755
1999m120.776860.76921 
2000m010.780450.77106 
2000m020.801710.769430.68339
2000m030.814280.772540.66615
2000m040.823740.77391 
2000m050.836190.78137 
2000m060.848420.78904 
2000m070.857250.79574 
2000m080.871190.7998 
2000m090.897790.800920.70966
2000m100.911680.802060.73793
2000m110.931990.803090.77357
2000m120.944260.803710.79099
2001m010.954790.804760.80655
2001m020.960070.805830.82109
2001m030.959850.805760.81399
2001m040.964650.8046 
2001m050.966790.80239 
2001m060.966170.80168 
2001m070.965060.80177 
2001m080.964980.804730.83319
2001m090.959830.809850.86013
2001m100.950190.812280.88928
2001m110.925370.814430.91676
2001m120.91680.815560.93994
2002m010.903610.816020.95187
2002m020.896870.81590.96441
2002m030.895140.814940.98093
2002m040.892390.81544 
2002m050.891530.81791 
2002m060.890190.81738 
2002m070.891250.8151 
2002m080.894580.80809 
2002m090.896490.801570.96005
2002m100.895370.796160.94143
2002m110.88940.793930.92936
2002m120.886370.791160.91637
2003m010.885070.789660.91548
2003m020.890110.789180.90833
2003m030.898510.789840.911
2003m040.902590.788270.90838
2003m050.904830.786690.90777
2003m060.905270.785910.9083
2003m070.908750.781730.91231
2003m080.91290.778590.91635
2003m090.913530.769890.91945
2003m100.918780.758490.92583
2003m110.92330.74620.92546
2003m120.929290.734340.92521
2004m010.93650.727240.92702
2004m020.940810.728960.92697
2004m030.9490.735180.89606
2004m040.957270.738870.87635
2004m050.962840.738130.86802
2004m060.970850.748510.85377
2004m070.979810.755560.85456
2004m080.990830.782850.85742
2004m090.99610.799470.86147
2004m101.0060.809710.86843
2004m111.01620.821490.85479
2004m121.02130.837990.84557
2005m011.02660.85120.84802
2005m021.03020.857650.84565
2005m031.03770.861440.85036
2005m041.04170.867140.86493
2005m051.0510.877160.88319
2005m061.05230.886480.8859
2005m071.05870.888750.87216
2005m081.06690.900270.88086
2005m091.07320.908740.8881
2005m101.08250.928330.89765
2005m111.08820.952040.90972
2005m121.0910.977280.91827
2006m011.10061.00340.91952
2006m021.11511.02940.92496
2006m031.12121.05140.93239
2006m041.12241.08150.93418
2006m051.11911.11360.9226
2006m061.1211.16640.92121
2006m071.11831.21810.90289
2006m081.1181.25130.9017
2006m091.11941.26910.9056
2006m101.11951.28750.89694
2006m111.12241.30560.8858
2006m121.12751.31870.86421
2007m011.1271.32290.85154
2007m021.12311.32390.81983
2007m031.11921.32420.79358
2007m041.11821.32770.76282
2007m051.121.32970.7454
2007m061.12481.3330.74928
2007m071.14671.33260.75854
2007m081.15331.33250.76763
2007m091.16511.33340.75496
2007m101.1681.33470.73715
2007m111.16881.33530.73033
2007m121.18161.33630.73824
2008m011.20721.34020.75207
2008m021.22941.34330.79983
2008m031.24351.34750.83482
2008m041.23651.35410.80281
2008m051.21071.35650.77867
2008m061.19161.35950.76385
2008m071.18451.36570.75241
2008m081.18341.36610.74897
2008m091.17691.36670.73444
2008m101.15281.35670.73544
2008m111.13021.34750.74061
2008m121.10241.33080.74161
2009m011.07731.31390.74578
2009m021.05851.2930.74542
2009m031.04081.27170.74995
2009m041.03171.26160.75805
2009m051.02471.25170.76663
2009m061.02281.24670.77474
2009m071.02381.24130.77653
2009m081.02621.24090.78086
2009m091.02861.24190.7772
2009m101.0331.24260.77479
2009m111.03771.23730.77195
2009m121.04721.22260.76789
2010m011.0161.20970.77194
2010m021.00121.20120.76963
2010m030.995551.19350.76197
2010m040.983111.1899 
2010m050.98141.1874 
2010m060.980681.186 
2010m070.978871.1855 
2010m080.977681.18540.75459
2010m090.975911.18480.74045
2010m100.974231.18380.7255
2010m110.973641.18260.71342
2010m120.975371.1815 

Figure 4. Relationship Between Future/Spot Prices and Forecasting Accuracy for Oil

Data for Figure 4 immediately follows.

Data for Figure 4

DATESFUTSPOTWZ1WZ2W
5-Jan-900.83 0.83
12-Jan-900.82 0.82
19-Jan-900.80.8 
26-Jan-900.87 0.87
2-Feb-900.880.88 
9-Feb-900.94 0.94
16-Feb-900.930.93 
23-Feb-900.970.97 
2-Mar-900.970.97 
9-Mar-9011 
16-Mar-901.02 1.02
23-Mar-900.990.99 
30-Mar-901.02  
6-Apr-901.061.06 
13-Apr-90   
20-Apr-901.111.11 
27-Apr-901.071.07 
4-May-901.111.11 
11-May-901.041.04 
18-May-901.071.07 
25-May-901.121.12 
1-Jun-901.151.15 
8-Jun-901.171.17 
15-Jun-901.181.18 
22-Jun-901.131.13 
29-Jun-901.131.13 
6-Jul-901.151.15 
13-Jul-901.131.13 
20-Jul-901.061.06 
27-Jul-901.071.07 
3-Aug-900.960.96 
10-Aug-900.880.88 
17-Aug-900.850.85 
24-Aug-900.830.83 
31-Aug-900.870.87 
7-Sep-900.820.82 
14-Sep-900.80.8 
21-Sep-900.740.74 
28-Sep-900.740.74 
5-Oct-900.710.71 
12-Oct-900.690.69 
19-Oct-900.720.72 
26-Oct-900.760.76 
2-Nov-900.730.73 
9-Nov-900.730.73 
16-Nov-900.810.81 
23-Nov-900.780.78 
30-Nov-900.810.81 
7-Dec-900.840.84 
14-Dec-900.810.81 
21-Dec-900.830.83 
28-Dec-900.820.82 
4-Jan-910.840.84 
11-Jan-910.780.78 
18-Jan-910.95 0.95
25-Jan-910.860.86 
1-Feb-910.870.87 
8-Feb-910.840.84 
15-Feb-910.83 0.83
22-Feb-911.011.01 
1-Mar-910.970.97 
8-Mar-910.970.97 
15-Mar-910.920.92 
22-Mar-910.940.94 
29-Mar-91   
5-Apr-910.95 0.95
12-Apr-910.910.91 
19-Apr-910.95  
26-Apr-910.940.94 
3-May-910.95 0.95
10-May-910.980.98 
17-May-911.01 1.01
24-May-9111 
31-May-9111 
7-Jun-911.011.01 
14-Jun-911.021.02 
21-Jun-910.98 0.98
28-Jun-910.97 0.97
5-Jul-910.95  
12-Jul-910.94 0.94
19-Jul-910.94 0.94
26-Jul-910.95 0.95
2-Aug-910.96 0.96
9-Aug-910.95 0.95
16-Aug-910.96 0.96
23-Aug-910.950.95 
30-Aug-910.940.94 
6-Sep-910.96 0.96
13-Sep-910.95 0.95
20-Sep-910.94 0.94
27-Sep-910.94 0.94
4-Oct-910.93 0.93
11-Oct-910.92 0.92
18-Oct-910.890.89 
25-Oct-910.910.91 
1-Nov-910.90.9 
8-Nov-910.920.92 
15-Nov-910.920.92 
22-Nov-910.950.95 
29-Nov-910.96  
6-Dec-910.980.98 
13-Dec-910.980.98 
20-Dec-911.031.03 
27-Dec-911.02  
3-Jan-921.01  
10-Jan-921.051.05 
17-Jan-921.01 1.01
24-Jan-921.01 1.01
31-Jan-921.011.01 
7-Feb-920.98 0.98
14-Feb-921.011.01 
21-Feb-921.011.01 
28-Feb-921.031.03 
6-Mar-921.021.02 
13-Mar-9211 
20-Mar-9211 
27-Mar-9211 
3-Apr-920.97 0.97
10-Apr-920.98  
17-Apr-92   
24-Apr-920.98 0.98
1-May-920.97 0.97
8-May-920.980.98 
15-May-920.990.99 
22-May-920.990.99 
29-May-920.960.96 
5-Jun-920.940.94 
12-Jun-920.950.95 
19-Jun-920.960.96 
26-Jun-920.940.94 
3-Jul-92   
10-Jul-920.960.96 
17-Jul-920.960.96 
24-Jul-920.940.94 
31-Jul-920.950.95 
7-Aug-920.950.95 
14-Aug-920.960.96 
21-Aug-920.960.96 
28-Aug-920.960.96 
4-Sep-920.940.94 
11-Sep-920.940.94 
18-Sep-920.940.94 
25-Sep-920.960.96 
2-Oct-920.950.95 
9-Oct-920.950.95 
16-Oct-920.950.95 
23-Oct-920.970.97 
30-Oct-920.990.99 
6-Nov-9211 
13-Nov-921 1
20-Nov-921 1
27-Nov-92   
4-Dec-921.02 1.02
11-Dec-921.02 1.02
18-Dec-921.01 1.01
25-Dec-92   
1-Jan-93   
8-Jan-931.03 1.03
15-Jan-931.04 1.04
22-Jan-931.03 1.03
29-Jan-931.01 1.01
5-Feb-931 1
12-Feb-931 1
19-Feb-931.03 1.03
26-Feb-931 1
5-Mar-930.990.99 
12-Mar-931.01 1.01
19-Mar-931.01 1.01
26-Mar-9311 
2-Apr-931  
9-Apr-93   
16-Apr-931.02 1.02
23-Apr-931.02 1.02
30-Apr-931.01 1.01
7-May-931.01 1.01
14-May-931.03 1.03
21-May-931.02 1.02
28-May-931.02 1.02
4-Jun-931.02 1.02
11-Jun-931.05 1.05
18-Jun-931.071.07 
25-Jun-931.05 1.05
2-Jul-931.091.09 
9-Jul-931.091.09 
16-Jul-931.091.09 
23-Jul-931.071.07 
30-Jul-931.061.06 
6-Aug-931.091.09 
13-Aug-931.08 1.08
20-Aug-931.08 1.08
27-Aug-931.05 1.05
3-Sep-931.08 1.08
10-Sep-931.12 1.12
17-Sep-931.12 1.12
24-Sep-931.08 1.08
1-Oct-931.03 1.03
8-Oct-931.05 1.05
15-Oct-931.05 1.05
22-Oct-931.06 1.06
29-Oct-931.081.08 
5-Nov-931.081.08 
12-Nov-931.111.11 
19-Nov-931.12 1.12
26-Nov-93   
3-Dec-931.141.14 
10-Dec-931.161.16 
17-Dec-931.221.22 
24-Dec-93   
31-Dec-93   
7-Jan-941.121.12 
14-Jan-941.121.12 
21-Jan-941.091.09 
28-Jan-941.071.07 
4-Feb-941.071.07 
11-Feb-941.141.14 
18-Feb-941.141.14 
25-Feb-941.121.12 
4-Mar-941.121.12 
11-Mar-941.11.1 
18-Mar-941.071.07 
25-Mar-941.071.07 
1-Apr-94   
8-Apr-941.061.06 
15-Apr-941.01  
22-Apr-940.98 0.98
29-Apr-940.99 0.99
6-May-940.96 0.96
13-May-940.94 0.94
20-May-940.93 0.93
27-May-940.96 0.96
3-Jun-940.96 0.96
10-Jun-940.94 0.94
17-Jun-940.890.89 
24-Jun-940.940.94 
1-Jul-940.930.93 
8-Jul-940.930.93 
15-Jul-940.930.93 
22-Jul-940.950.95 
29-Jul-940.930.93 
5-Aug-940.940.94 
12-Aug-940.990.99 
19-Aug-940.99 0.99
26-Aug-941.031.03 
2-Sep-941.021.02 
9-Sep-941.031.03 
16-Sep-941.051.05 
23-Sep-941.02 1.02
30-Sep-941.01 1.01
7-Oct-941.01 1.01
14-Oct-941.031.03 
21-Oct-941.01 1.01
28-Oct-940.970.97 
4-Nov-940.960.96 
11-Nov-940.990.99 
18-Nov-9411 
25-Nov-94   
2-Dec-941.021.02 
9-Dec-941.031.03 
16-Dec-941.051.05 
23-Dec-941.011.01 
30-Dec-941.011.01 
6-Jan-951.011.01 
13-Jan-951 1
20-Jan-950.95 0.95
27-Jan-950.980.98 
3-Feb-950.940.94 
10-Feb-950.960.96 
17-Feb-950.94 0.94
24-Feb-950.95 0.95
3-Mar-950.95 0.95
10-Mar-950.99 0.99
17-Mar-950.98 0.98
24-Mar-950.95 0.95
31-Mar-950.93 0.93
7-Apr-950.93  
14-Apr-95   
21-Apr-950.9 0.9
28-Apr-950.91 0.91
5-May-950.91 0.91
12-May-950.92 0.92
19-May-950.92 0.92
26-May-950.96 0.96
2-Jun-950.95 0.95
9-Jun-950.96 0.96
16-Jun-950.95 0.95
23-Jun-951.021.02 
30-Jun-950.99 0.99
7-Jul-951  
14-Jul-950.99 0.99
21-Jul-951.021.02 
28-Jul-950.99 0.99
4-Aug-950.98 0.98
11-Aug-950.97 0.97
18-Aug-950.96 0.96
25-Aug-950.95 0.95
1-Sep-950.96 0.96
8-Sep-950.94 0.94
15-Sep-950.92 0.92
22-Sep-950.98 0.98
29-Sep-950.96 0.96
6-Oct-950.98 0.98
13-Oct-950.97 0.97
20-Oct-950.97 0.97
27-Oct-950.96 0.96
3-Nov-950.95 0.95
10-Nov-950.94 0.94
17-Nov-950.92 0.92
24-Nov-95   
1-Dec-950.93  
8-Dec-950.92 0.92
15-Dec-950.9 0.9
22-Dec-950.91 0.91
29-Dec-950.9 0.9
5-Jan-960.88 0.88
12-Jan-960.93 0.93
19-Jan-960.9 0.9
26-Jan-960.95 0.95
2-Feb-960.95 0.95
9-Feb-960.95 0.95
16-Feb-960.89 0.89
23-Feb-960.9 0.9
1-Mar-960.88 0.88
8-Mar-960.87 0.87
15-Mar-960.79 0.79
22-Mar-960.81 0.81
29-Mar-960.84  
5-Apr-96   
12-Apr-960.740.74 
19-Apr-960.740.74 
26-Apr-960.820.82 
3-May-960.850.85 
10-May-960.86 0.86
17-May-960.84 0.84
24-May-960.84 0.84
31-May-960.88 0.88
7-Jun-960.880.88 
14-Jun-960.880.88 
21-Jun-960.90.9 
28-Jun-960.86 0.86
5-Jul-96   
12-Jul-960.840.84 
19-Jul-960.860.86 
26-Jul-960.89 0.89
2-Aug-960.86 0.86
9-Aug-960.860.86 
16-Aug-960.820.82 
23-Aug-960.850.85 
30-Aug-960.850.85 
6-Sep-960.810.81 
13-Sep-960.790.79 
20-Sep-960.830.83 
27-Sep-960.820.82 
4-Oct-960.82 0.82
11-Oct-960.830.83 
18-Oct-960.810.81 
25-Oct-960.840.84 
1-Nov-960.860.86 
8-Nov-960.880.88 
15-Nov-960.870.87 
22-Nov-960.850.85 
29-Nov-96   
6-Dec-960.810.81 
13-Dec-960.830.83 
20-Dec-960.810.81 
27-Dec-960.80.8 
3-Jan-970.80.8 
10-Jan-970.790.79 
17-Jan-970.80.8 
24-Jan-970.850.85 
31-Jan-970.850.85 
7-Feb-970.90.9 
14-Feb-970.90.9 
21-Feb-970.920.92 
28-Feb-970.960.96 
7-Mar-970.960.96 
14-Mar-970.960.96 
21-Mar-970.960.96 
28-Mar-97   
4-Apr-971.02 1.02
11-Apr-971.01  
18-Apr-970.980.98 
25-Apr-970.990.99 
2-May-971 1
9-May-970.980.98 
16-May-970.950.95 
23-May-970.960.96 
30-May-970.990.99 
6-Jun-971.04 1.04
13-Jun-971.04 1.04
20-Jun-971.05 1.05
27-Jun-971.02 1.02
4-Jul-97   
11-Jul-971.02 1.02
18-Jul-971.02 1.02
25-Jul-971 1
1-Aug-970.990.99 
8-Aug-971.02 1.02
15-Aug-971.01 1.01
22-Aug-971 1
29-Aug-971.01 1.01
5-Sep-971.01 1.01
12-Sep-971.01 1.01
19-Sep-971.01 1.01
26-Sep-970.980.98 
3-Oct-970.910.91 
10-Oct-970.940.94 
17-Oct-970.970.97 
24-Oct-970.970.97 
31-Oct-970.970.97 
7-Nov-970.970.97 
14-Nov-970.950.95 
21-Nov-9711 
28-Nov-97   
5-Dec-971.03 1.03
12-Dec-971.05 1.05
19-Dec-971.04 1.04
26-Dec-971.03  
2-Jan-981.07  
9-Jan-981.09 1.09
16-Jan-981.1 1.1
23-Jan-981.12 1.12
30-Jan-981.06 1.06
6-Feb-981.08 1.08
13-Feb-981.11 1.11
20-Feb-981.11 1.11
27-Feb-981.14 1.14
6-Mar-981.18 1.18
13-Mar-981.2 1.2
20-Mar-981.17 1.17
27-Mar-981.07 1.07
3-Apr-981.1  
10-Apr-98   
17-Apr-981.121.12 
24-Apr-981.131.13 
1-May-981.111.11 
8-May-981.161.16 
15-May-981.191.19 
22-May-981.151.15 
29-May-981.141.14 
5-Jun-981.181.18 
12-Jun-981.371.37 
19-Jun-981.421.42 
26-Jun-981.191.19 
3-Jul-98   
10-Jul-981.181.18 
17-Jul-981.171.17 
24-Jul-981.171.17 
31-Jul-981.141.14 
7-Aug-981.171.17 
14-Aug-981.181.18 
21-Aug-981.161.16 
28-Aug-981.151.15 
4-Sep-981.121.12 
11-Sep-981.131.13 
18-Sep-981.091.09 
25-Sep-981.071.07 
2-Oct-981.081.08 
9-Oct-981.121.12 
16-Oct-981.131.13 
23-Oct-981.121.12 
30-Oct-981.111.11 
6-Nov-981.131.13 
13-Nov-981.141.14 
20-Nov-981.281.28 
27-Nov-98   
4-Dec-981.271.27 
11-Dec-981.291.29 
18-Dec-981.241.24 
25-Dec-98   
1-Jan-99   
8-Jan-991.091.09 
15-Jan-991.131.13 
22-Jan-991.081.08 
29-Jan-991.081.08 
5-Feb-991.131.13 
12-Feb-991.111.11 
19-Feb-991.121.12 
26-Feb-991.091.09 
5-Mar-991.061.06 
12-Mar-990.99 0.99
19-Mar-990.99 0.99
26-Mar-990.97 0.97
2-Apr-99   
9-Apr-990.96 0.96
16-Apr-990.94 0.94
23-Apr-990.9  
30-Apr-990.9 0.9
7-May-990.93 0.93
14-May-990.95 0.95
21-May-990.96 0.96
28-May-990.97 0.97
4-Jun-990.96 0.96
11-Jun-990.95 0.95
18-Jun-990.98 0.98
25-Jun-990.97 0.97
2-Jul-990.93 0.93
9-Jul-990.94 0.94
16-Jul-990.93 0.93
23-Jul-990.93 0.93
30-Jul-990.92 0.92
6-Aug-990.91 0.91
13-Aug-990.88 0.88
20-Aug-990.88 0.88
27-Aug-990.89 0.89
3-Sep-990.86 0.86
10-Sep-990.83 0.83
17-Sep-990.79 0.79
24-Sep-990.81 0.81
1-Oct-990.81 0.81
8-Oct-990.9 0.9
15-Oct-990.88 0.88
22-Oct-990.88 0.88
29-Oct-990.9 0.9
5-Nov-990.84 0.84
12-Nov-990.82 0.82
19-Nov-990.78 0.78
26-Nov-99   
3-Dec-990.76 0.76
10-Dec-990.8 0.8
17-Dec-990.78 0.78
24-Dec-99   
31-Dec-99   
7-Jan-000.82 0.82
14-Jan-000.77 0.77
21-Jan-000.77 0.77
28-Jan-000.8 0.8
4-Feb-000.79 0.79
11-Feb-000.77 0.77
18-Feb-000.77 0.77
25-Feb-000.75 0.75
3-Mar-000.74 0.74
10-Mar-000.73 0.73
17-Mar-000.760.76 
24-Mar-000.84 0.84
31-Mar-000.88  
7-Apr-000.9 0.9
14-Apr-000.87  
21-Apr-00   
28-Apr-000.9 0.9
5-May-000.84 0.84
12-May-000.83 0.83
19-May-000.84 0.84
26-May-000.83 0.83
2-Jun-000.82 0.82
9-Jun-000.82 0.82
16-Jun-000.770.77 
23-Jun-000.810.81 
30-Jun-000.810.81 
7-Jul-000.83 0.83
14-Jul-000.840.84 
21-Jul-000.90.9 
28-Jul-000.92 0.92
4-Aug-000.870.87 
11-Aug-000.840.84 
18-Aug-000.840.84 
25-Aug-000.850.85 
1-Sep-000.830.83 
8-Sep-000.830.83 
15-Sep-000.82  
22-Sep-000.880.88 
29-Sep-000.920.92 
6-Oct-000.930.93 
13-Oct-000.830.83 
20-Oct-000.840.84 
27-Oct-000.830.83 
3-Nov-000.810.81 
10-Nov-000.80.8 
17-Nov-000.780.78 
24-Nov-00   
1-Dec-000.810.81 
8-Dec-000.890.89 
15-Dec-000.860.86 
22-Dec-000.910.91 
29-Dec-000.90.9 
5-Jan-010.860.86 
12-Jan-010.830.83 
19-Jan-010.790.79 
26-Jan-010.840.84 
2-Feb-010.830.83 
9-Feb-010.85  
16-Feb-010.88  
23-Feb-010.880.88 
2-Mar-010.910.91 
9-Mar-010.930.93 
16-Mar-010.950.95 
23-Mar-010.930.93 
30-Mar-01   
6-Apr-010.93 0.93
13-Apr-01   
20-Apr-010.950.95 
27-Apr-010.940.94 
4-May-010.920.92 
11-May-010.92 0.92
18-May-010.90.9 
25-May-010.920.92 
1-Jun-010.930.93 
8-Jun-010.930.93 
15-Jun-010.910.91 
22-Jun-010.940.94 
29-Jun-010.96 0.96
6-Jul-010.9  
13-Jul-010.93 0.93
20-Jul-010.96 0.96
27-Jul-010.91 0.91
3-Aug-010.9 0.9
10-Aug-010.89 0.89
17-Aug-010.9 0.9
24-Aug-010.92 0.92
31-Aug-010.92 0.92
7-Sep-010.9 0.9
14-Sep-01   
21-Sep-010.93 0.93
28-Sep-011 1
5-Oct-011.011.01 
12-Oct-011 1
19-Oct-011.021.02 
26-Oct-0111 
2-Nov-011.041.04 
9-Nov-010.99 0.99
16-Nov-011.11.1 
23-Nov-01   
30-Nov-011.06  
7-Dec-011.091.09 
14-Dec-011.071.07 
21-Dec-011.051.05 
28-Dec-011.041.04 
4-Jan-021.011.01 
11-Jan-021.061.06 
18-Jan-021.111.11 
25-Jan-021.031.03 
1-Feb-021.031.03 
8-Feb-02   
15-Feb-02   
22-Feb-021 1
1-Mar-020.99 0.99
8-Mar-020.98 0.98
15-Mar-020.96 0.96
22-Mar-020.95 0.95
29-Mar-02   
5-Apr-020.91 0.91
12-Apr-020.95 0.95
19-Apr-020.91  
26-Apr-020.91 0.91
3-May-020.91 0.91
10-May-020.89 0.89
17-May-020.89 0.89
24-May-020.95 0.95
31-May-020.95 0.95
7-Jun-020.97 0.97
14-Jun-020.95 0.95
21-Jun-020.95 0.95
28-Jun-020.92 0.92
5-Jul-02   
12-Jul-020.91 0.91
19-Jul-020.91 0.91
26-Jul-020.92 0.92
2-Aug-020.91 0.91
9-Aug-020.91 0.91
16-Aug-020.87  
23-Aug-020.89 0.89
30-Aug-020.89 0.89
6-Sep-020.87 0.87
13-Sep-020.86 0.86
20-Sep-020.84  
27-Sep-020.82 0.82
4-Oct-020.84 0.84
11-Oct-020.85 0.85
18-Oct-020.85 0.85
25-Oct-020.89 0.89
1-Nov-020.88 0.88
8-Nov-020.9 0.9
15-Nov-020.92 0.92
22-Nov-020.91 0.91
29-Nov-02   
6-Dec-020.9 0.9
13-Dec-020.86 0.86
20-Dec-020.82 0.82
27-Dec-020.77  
3-Jan-030.75  
10-Jan-030.78 0.78
17-Jan-030.76 0.76
24-Jan-030.79 0.79
31-Jan-030.8 0.8
7-Feb-030.78 0.78
14-Feb-030.74 0.74
21-Feb-030.77 0.77
28-Feb-030.75 0.75
7-Mar-030.74 0.74
14-Mar-030.77 0.77
21-Mar-030.91 0.91
28-Mar-030.83 0.83
4-Apr-030.86 0.86
11-Apr-030.9  
18-Apr-03   
25-Apr-030.94 0.94
2-May-030.95 0.95
9-May-030.91 0.91
16-May-030.87 0.87
23-May-030.87 0.87
30-May-030.86 0.86
6-Jun-030.82 0.82
13-Jun-030.82  
20-Jun-030.83 0.83
27-Jun-030.88 0.88
4-Jul-03   
11-Jul-030.85 0.85
18-Jul-030.83 0.83
25-Jul-030.88 0.88
1-Aug-030.84 0.84
8-Aug-030.85 0.85
15-Aug-03   
22-Aug-030.86 0.86
29-Aug-030.86 0.86
5-Sep-030.9 0.9
12-Sep-030.92 0.92
19-Sep-03   
26-Sep-030.92 0.92
3-Oct-030.87 0.87
10-Oct-030.86  
17-Oct-030.88 0.88
24-Oct-030.89 0.89
31-Oct-030.91 0.91
7-Nov-030.88 0.88
14-Nov-030.85 0.85
21-Nov-030.86 0.86
28-Nov-03   
5-Dec-030.89 0.89
12-Dec-030.87 0.87
19-Dec-030.86 0.86
26-Dec-03   
2-Jan-04   
9-Jan-040.86 0.86
16-Jan-040.85 0.85
23-Jan-040.86 0.86
30-Jan-040.87 0.87
6-Feb-040.88 0.88
13-Feb-040.87 0.87
20-Feb-040.84 0.84
27-Feb-040.86 0.86
5-Mar-040.85 0.85
12-Mar-040.87 0.87
19-Mar-040.86 0.86
26-Mar-040.88  
2-Apr-040.9 0.9
9-Apr-04   
16-Apr-040.87 0.87
23-Apr-040.9 0.9
30-Apr-040.89 0.89
7-May-040.87 0.87
14-May-040.86 0.86
21-May-040.88 0.88
28-May-040.89 0.89
4-Jun-040.91 0.91
11-Jun-04   
18-Jun-040.92 0.92
25-Jun-040.93 0.93
2-Jul-040.93 0.93
9-Jul-040.9 0.9
16-Jul-040.9 0.9
23-Jul-040.9 0.9
30-Jul-040.9 0.9
6-Aug-040.89 0.89
13-Aug-040.89 0.89
20-Aug-040.87 0.87
27-Aug-040.92 0.92
3-Sep-040.91 0.91
10-Sep-040.91 0.91
17-Sep-040.89 0.89
24-Sep-040.87 0.87
1-Oct-040.87 0.87
8-Oct-04   
15-Oct-040.86 0.86
22-Oct-040.88 0.88
29-Oct-040.92 0.92
5-Nov-040.92 0.92
12-Nov-040.93 0.93
19-Nov-040.93 0.93
26-Nov-04   
3-Dec-040.97 0.97
10-Dec-040.99 0.99
17-Dec-040.95 0.95
24-Dec-04   
31-Dec-04   
7-Jan-050.94 0.94
14-Jan-050.93 0.93
21-Jan-050.94 0.94
28-Jan-050.96 0.96
4-Feb-050.97 0.97
11-Feb-050.96 0.96
18-Feb-050.96 0.96
25-Feb-050.95 0.95
4-Mar-050.95 0.95
11-Mar-050.97 0.97
18-Mar-051 1
25-Mar-05   
1-Apr-0511 
8-Apr-051.021.02 
15-Apr-051.04  
22-Apr-051.011.01 
29-Apr-051.061.06 
6-May-051.041.04 
13-May-051.061.06 
20-May-051.091.09 
27-May-051.021.02 
3-Jun-051.031.03 
10-Jun-051.051.05 
17-Jun-051.021.02 
24-Jun-051.011.01 
1-Jul-051.031.03 
8-Jul-051.031.03 
15-Jul-051.031.03 
22-Jul-051.031.03 
29-Jul-051.041.04 
5-Aug-051.041.04 
12-Aug-050.99 0.99
19-Aug-051.011.01 
26-Aug-051.021.02 
2-Sep-051.011.01 
9-Sep-051.031.03 
16-Sep-051.03 1.03
23-Sep-051.02 1.02
30-Sep-051.01 1.01
7-Oct-051.02 1.02
14-Oct-0511 
21-Oct-051.01 1.01
28-Oct-051.01 1.01
4-Nov-051.03 1.03
11-Nov-051.041.04 
18-Nov-051.06 1.06
25-Nov-051.03 1.03
2-Dec-051.051.05 
9-Dec-051.061.06 
16-Dec-051.061.06 
23-Dec-051.051.05 
30-Dec-051.05 1.05
6-Jan-061.04 1.04
13-Jan-061.05 1.05
20-Jan-061.03 1.03
27-Jan-061.04 1.04
3-Feb-061.06 1.06
10-Feb-061.08 1.08
17-Feb-061.1 1.1
24-Feb-061.08 1.08
3-Mar-061.09 1.09
10-Mar-061.09 1.09
17-Mar-061.07 1.07
24-Mar-061.05 1.05
31-Mar-061.05 1.05
7-Apr-061.05  
14-Apr-06   
21-Apr-061.02 1.02
28-Apr-061.05 1.05
5-May-061.06 1.06
12-May-061.05 1.05
19-May-061.07 1.07
26-May-061.04 1.04
2-Jun-061.04 1.04
9-Jun-061.05 1.05
16-Jun-061.04 1.04
23-Jun-061.04 1.04
30-Jun-061.03 1.03
7-Jul-061.04 1.04
14-Jul-061.04 1.04
21-Jul-061.03 1.03
28-Jul-061.051.05 
4-Aug-061.06 1.06
11-Aug-061.06 1.06
18-Aug-061.07 1.07
25-Aug-061.05 1.05
1-Sep-061.071.07 
8-Sep-061.091.09 
15-Sep-061.11.1 
22-Sep-061.091.09 
29-Sep-061.091.09 
6-Oct-061.111.11 
13-Oct-061.131.13 
20-Oct-061.171.17 
27-Oct-061.121.12 
3-Nov-061.131.13 
10-Nov-061.131.13 
17-Nov-061.191.19 
24-Nov-061.131.13 
1-Dec-061.11.1 
8-Dec-061.091.09 
15-Dec-061.081.08 
22-Dec-061.091.09 
29-Dec-061.091.09 
5-Jan-071.121.12 
12-Jan-071.11.1 
19-Jan-071.131.13 
26-Jan-071.091.09 
2-Feb-071.091.09 
9-Feb-071.081.08 
16-Feb-071.071.07 
23-Feb-071.091.09 
2-Mar-071.091.09 
9-Mar-071.11.1 
16-Mar-071.141.14 
23-Mar-071.08  
30-Mar-071.061.06 
6-Apr-07   
13-Apr-071.121.12 
20-Apr-071.091.09 
27-Apr-071.081.08 
4-May-071.121.12 
11-May-071.111.11 
18-May-071.091.09 
25-May-071.091.09 
1-Jun-071.081.08 
8-Jun-071.071.07 
15-Jun-071.061.06 
22-Jun-071.051.05 
29-Jun-071.021.02 
6-Jul-071.01  
13-Jul-071 1
20-Jul-070.97 0.97
27-Jul-070.95 0.95
3-Aug-070.97 0.97
10-Aug-070.97 0.97
17-Aug-070.96 0.96
24-Aug-070.97 0.97
31-Aug-070.95 0.95
7-Sep-070.93 0.93
14-Sep-070.93 0.93
21-Sep-070.94 0.94
28-Sep-070.93 0.93
5-Oct-070.94 0.94
12-Oct-070.930.93 
19-Oct-070.910.91 
26-Oct-070.910.91 
2-Nov-070.90.9 
9-Nov-070.920.92 
16-Nov-070.910.91 
23-Nov-070.920.92 
30-Nov-070.960.96 
7-Dec-070.970.97 
14-Dec-070.970.97 
21-Dec-070.960.96 
28-Dec-070.950.95 
4-Jan-080.960.96 
11-Jan-080.960.96 
18-Jan-080.960.96 
25-Jan-080.970.97 
1-Feb-080.990.99 
8-Feb-080.980.98 
15-Feb-080.970.97 
22-Feb-080.970.97 
29-Feb-080.970.97 
7-Mar-080.940.94 
14-Mar-080.930.93 
21-Mar-08   
28-Mar-080.950.95 
4-Apr-080.950.95 
11-Apr-080.95  
18-Apr-080.950.95 
25-Apr-080.950.95 
2-May-080.950.95 
9-May-080.970.97 
16-May-080.990.99 
23-May-080.990.99 
30-May-080.990.99 
6-Jun-080.980.98 
13-Jun-081 1
20-Jun-081 1
27-Jun-081 1
4-Jul-08   
11-Jul-081 1
18-Jul-081.02 1.02
25-Jul-081.01 1.01
1-Aug-081.01 1.01
8-Aug-081.01 1.01
15-Aug-081.01 1.01
22-Aug-081.02 1.02
29-Aug-081.02 1.02
5-Sep-081.03 1.03
12-Sep-081.03 1.03
19-Sep-080.990.99 
26-Sep-081.01 1.01
3-Oct-081.01 1.01
10-Oct-081.06 1.06
17-Oct-081.071.07 
24-Oct-081.081.08 
31-Oct-081.091.09 
7-Nov-081.161.16 
14-Nov-081.161.16 
21-Nov-081.191.19 
28-Nov-081.191.19 
5-Dec-081.341.34 
12-Dec-081.271.27 
19-Dec-081.631.63 
26-Dec-081.36  
2-Jan-091.32  
9-Jan-091.461.46 
16-Jan-091.61.6 
23-Jan-091.231.23 
30-Jan-091.331.33 
6-Feb-091.411.41 
13-Feb-091.441.44 
20-Feb-091.291.29 
27-Feb-091.21.2 
6-Mar-091.171.17 
13-Mar-091.161.16 
20-Mar-091.211.21 
27-Mar-091.191.19 
3-Apr-091.221.22 
10-Apr-09   
17-Apr-091.241.24 
24-Apr-091.171.17 
1-May-091.191.19 
8-May-091.131.13 
15-May-091.131.13 
22-May-091.091.09 
29-May-091.071.07 
5-Jun-091.11 1.11
12-Jun-091.08 1.08
19-Jun-091.081.08 
26-Jun-091.071.07 
3-Jul-09   
10-Jul-091.131.13 
17-Jul-091.131.13 
24-Jul-091.131.13 
31-Jul-091.121.12 
7-Aug-091.121.12 
14-Aug-091.131.13 
21-Aug-091.07 1.07
28-Aug-091.07 1.07
4-Sep-091.071.07 
11-Sep-091.071.07 
18-Sep-091.07 1.07
25-Sep-091.081.08 
2-Oct-091.071.07 
9-Oct-091.071.07 
16-Oct-091.051.05 
23-Oct-091.06 1.06
30-Oct-091.061.06 
6-Nov-091.071.07 
13-Nov-091.081.08 
20-Nov-091.091.09 
27-Nov-091.11.1 
4-Dec-091.121.12 
11-Dec-091.131.13 
18-Dec-091.11.1 
25-Dec-09   
1-Jan-10   
8-Jan-101.061.06 
15-Jan-101.071.07 
22-Jan-101.071.07 
29-Jan-101.071.07 
5-Feb-101.071.07 
12-Feb-101.071.07 
19-Feb-101.041.04 
26-Feb-101.041.04 
5-Mar-101.041.04 
12-Mar-101.041.04 
19-Mar-101.031.03 
26-Mar-101.031.03 
2-Apr-101.121.12 
9-Apr-101.051.05 
16-Apr-101.081.08 
23-Apr-101.08  
30-Apr-101.071.07 
7-May-101.131.13 
14-May-101.161.16 
21-May-101.091.09 
28-May-101.081.08 
4-Jun-101.11.1 
11-Jun-101.11.1 
18-Jun-101.081.08 
25-Jun-101.051.05 
2-Jul-101.061.06 
9-Jul-101.061.06 
16-Jul-101.061.06 
23-Jul-101.05  
30-Jul-101.06  
6-Aug-101.06  
13-Aug-101.06  
20-Aug-101.07  
27-Aug-101.08  
3-Sep-101.1  
10-Sep-101.08  
17-Sep-101.12  
24-Sep-101.08  
1-Oct-101.06  
8-Oct-101.06  
15-Oct-101.06  
22-Oct-101.05  
29-Oct-101.05  
5-Nov-101.04  
12-Nov-101.04  
19-Nov-101.04  
26-Nov-101.04  
3-Dec-101.01  
10-Dec-101.02  
17-Dec-101.04  
24-Dec-10   
31-Dec-101.03  
7-Jan-111.06  
14-Jan-111.06  
21-Jan-111.07  
28-Jan-111.1  
4-Feb-111.11  
11-Feb-111.15  
18-Feb-111.14  
25-Feb-111.04  
4-Mar-111.01  
11-Mar-111.03  
18-Mar-111.02  
25-Mar-111.01  
1-Apr-111  
8-Apr-111  
15-Apr-111.01  
22-Apr-11   
29-Apr-111  
6-May-111.01  
13-May-111.01  
20-May-111.02  
27-May-111.03  
3-Jun-111.03  
10-Jun-111.03  

Figure 5. Net Long Futures Positioins for Producers/Users

Data for Figure 5 immediately follows.

Source: Commodity Futures Trading Commission, Commitments of Traders.

Data for Figure 5

DATESCOPNETLPMCRNNETLPMNGNETLPMSOYNETLPMWTINETLPMWHTNETLPMCOTNETLPMSUGNETLPM
2-Jan-06NANANANANANANANA
3-Jan-06NANANANANANANANA
4-Jan-06NANANANANANANANA
5-Jan-06NANANANANANANANA
6-Jan-06NANANANANANANANA
9-Jan-06NANANANANANANANA
10-Jan-06NANANANANANANANA
11-Jan-06NANANANANANANANA
12-Jan-06NANANANANANANANA
13-Jan-06NANANANANANANANA
16-Jan-06NANANANANANANANA
17-Jan-06NANANANANANANANA
18-Jan-06NANANANANANANANA
19-Jan-06NANANANANANANANA
20-Jan-06NANANANANANANANA
23-Jan-06NANANANANANANANA
24-Jan-06NANANANANANANANA
25-Jan-06NANANANANANANANA
26-Jan-06NANANANANANANANA
27-Jan-06NANANANANANANANA
30-Jan-06NANANANANANANANA
31-Jan-06NANANANANANANANA
1-Feb-06NANANANANANANANA
2-Feb-06NANANANANANANANA
3-Feb-06NANANANANANANANA
6-Feb-06NANANANANANANANA
7-Feb-06NANANANANANANANA
8-Feb-06NANANANANANANANA
9-Feb-06NANANANANANANANA
10-Feb-06NANANANANANANANA
13-Feb-06NANANANANANANANA
14-Feb-06NANANANANANANANA
15-Feb-06NANANANANANANANA
16-Feb-06NANANANANANANANA
17-Feb-06NANANANANANANANA
20-Feb-06NANANANANANANANA
21-Feb-06NANANANANANANANA
22-Feb-06NANANANANANANANA
23-Feb-06NANANANANANANANA
24-Feb-06NANANANANANANANA
27-Feb-06NANANANANANANANA
28-Feb-06NANANANANANANANA
1-Mar-06NANANANANANANANA
2-Mar-06NANANANANANANANA
3-Mar-06NANANANANANANANA
6-Mar-06NANANANANANANANA
7-Mar-06NANANANANANANANA
8-Mar-06NANANANANANANANA
9-Mar-06NANANANANANANANA
10-Mar-06NANANANANANANANA
13-Mar-06NANANANANANANANA
14-Mar-06NANANANANANANANA
15-Mar-06NANANANANANANANA
16-Mar-06NANANANANANANANA
17-Mar-06NANANANANANANANA
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27-Jan-11NANANANANANANANA
28-Jan-11NANANANANANANANA
31-Jan-11NANANANANANANANA
1-Feb-11-0.41-0.4-0.05-0.46-0.11-0.36-0.32-0.34
2-Feb-11NANANANANANANANA
3-Feb-11NANANANANANANANA
4-Feb-11NANANANANANANANA
7-Feb-11NANANANANANANANA
8-Feb-11-0.43-0.39-0.04-0.45-0.12-0.37-0.27-0.3
9-Feb-11NANANANANANANANA
10-Feb-11NANANANANANANANA
11-Feb-11NANANANANANANANA
14-Feb-11NANANANANANANANA
15-Feb-11-0.43-0.38-0.03-0.41-0.13-0.36-0.33-0.3
16-Feb-11NANANANANANANANA
17-Feb-11NANANANANANANANA
18-Feb-11NANANANANANANANA
21-Feb-11NANANANANANANANA
22-Feb-11-0.44-0.39-0.03-0.39-0.14-0.35-0.4-0.33
23-Feb-11NANANANANANANANA
24-Feb-11NANANANANANANANA
25-Feb-11NANANANANANANANA
28-Feb-11NANANANANANANANA
1-Mar-11-0.44-0.41-0.03-0.39-0.16-0.38-0.36-0.34
2-Mar-11NANANANANANANANA
3-Mar-11NANANANANANANANA
4-Mar-11NANANANANANANANA
7-Mar-11NANANANANANANANA
8-Mar-11-0.45-0.4-0.03-0.41-0.16-0.37-0.35-0.37
9-Mar-11NANANANANANANANA
10-Mar-11NANANANANANANANA
11-Mar-11NANANANANANANANA
14-Mar-11NANANANANANANANA
15-Mar-11-0.44-0.36-0.04-0.37-0.15-0.35-0.3-0.32
16-Mar-11NANANANANANANANA
17-Mar-11NANANANANANANANA
18-Mar-11NANANANANANANANA
21-Mar-11NANANANANANANANA
22-Mar-11-0.45-0.35-0.05-0.39-0.16-0.34-0.29-0.3
23-Mar-11NANANANANANANANA
24-Mar-11NANANANANANANANA
25-Mar-11NANANANANANANANA
28-Mar-11NANANANANANANANA
29-Mar-11-0.48-0.36-0.07-0.38-0.15-0.35-0.27-0.32
30-Mar-11NANANANANANANANA
31-Mar-11NANANANANANANANA
1-Apr-11NANANANANANANANA
4-Apr-11NANANANANANANANA
5-Apr-11-0.48-0.36-0.07-0.38-0.14-0.36-0.26-0.3
6-Apr-11NANANANANANANANA
7-Apr-11NANANANANANANANA
8-Apr-11NANANANANANANANA
11-Apr-11NANANANANANANANA
12-Apr-11-0.49-0.36-0.06-0.34-0.13-0.36-0.27-0.27
13-Apr-11NANANANANANANANA
14-Apr-11NANANANANANANANA
15-Apr-11NANANANANANANANA
18-Apr-11NANANANANANANANA
19-Apr-11-0.46-0.37-0.05-0.32-0.14-0.35-0.31-0.31
20-Apr-11NANANANANANANANA
21-Apr-11NANANANANANANANA
22-Apr-11NANANANANANANANA
25-Apr-11NANANANANANANANA
26-Apr-11-0.45-0.4-0.06-0.35-0.13-0.37-0.36-0.32
27-Apr-11NANANANANANANANA
28-Apr-11NANANANANANANANA
29-Apr-11NANANANANANANANA
2-May-11NANANANANANANANA
3-May-11-0.43-0.4-0.06-0.36-0.12-0.35-0.38-0.32
4-May-11NANANANANANANANA
5-May-11NANANANANANANANA
6-May-11NANANANANANANANA
9-May-11NANANANANANANANA
10-May-11-0.39-0.39-0.05-0.33-0.12-0.33-0.4-0.31
11-May-11NANANANANANANANA
12-May-11NANANANANANANANA
13-May-11NANANANANANANANA
16-May-11NANANANANANANANA
17-May-11-0.35-0.38-0.05-0.32-0.13-0.29-0.4-0.27
18-May-11NANANANANANANANA
19-May-11NANANANANANANANA
20-May-11NANANANANANANANA
23-May-11NANANANANANANANA
24-May-11-0.36-0.4-0.06-0.34-0.14-0.33-0.4-0.27
25-May-11NANANANANANANANA
26-May-11NANANANANANANANA
27-May-11NANANANANANANANA
30-May-11NANANANANANANANA
31-May-11-0.37-0.4-0.07-0.34-0.13-0.33-0.4-0.27
1-Jun-11NANANANANANANANA
2-Jun-11NANANANANANANANA
3-Jun-11NANANANANANANANA
6-Jun-11NANANANANANANANA
7-Jun-11-0.38-0.39-0.08-0.35-0.13-0.32-0.38-0.27
8-Jun-11NANANANANANANANA
9-Jun-11NANANANANANANANA
10-Jun-11NANANANANANANANA
13-Jun-11NANANANANANANANA
14-Jun-11-0.37-0.38-0.07-0.32-0.11-0.31-0.43-0.3
15-Jun-11NANANANANANANANA
16-Jun-11NANANANANANANANA
17-Jun-11NANANANANANANANA
20-Jun-11NANANANANANANANA
21-Jun-11-0.34-0.35-0.07-0.29-0.12-0.28-0.43-0.38
22-Jun-11NANANANANANANANA
23-Jun-11NANANANANANANANA
24-Jun-11NANANANANANANANA
27-Jun-11NANANANANANANANA
28-Jun-11-0.36-0.37-0.06-0.31-0.12-0.3-0.43-0.39
29-Jun-11NANANANANANANANA
30-Jun-11NANANANANANANANA
1-Jul-11NANANANANANANANA
4-Jul-11NANANANANANANANA
5-Jul-11-0.39-0.35-0.06-0.31-0.11-0.29-0.41-0.41
6-Jul-11NANANANANANANANA
7-Jul-11NANANANANANANANA
8-Jul-11NANANANANANANANA
11-Jul-11NANANANANANANANA
12-Jul-11-0.4-0.36-0.05-0.35-0.11-0.3-0.41-0.43

 


Footnotes

1.   The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System, any other person associated with the Federal Reserve System. Return to text

2.   Comments and suggestions can be directed to robert.j.vigfusson@frb.gov. Return to text

3.   Developments of these relationships can be found in standard textbooks including Hull (2002) and also in articles such as Pindyck (2001). Return to text

4.   In this example, the storage cost C and convenience yield Y are assumed to be proportionate to the price of the commodity S. Alternatively, we could have specified the cost in per physical unit terms, so (1+R)S + C-Y $\leq $ F. Return to text

5.   Because not all futures markets have contracts for every month, defining the year-ahead futures price is not straightforward. To maximize our sample, in this memo we use 12-month ahead futures for energy, 8-month ahead futures for agricultural commodities, and 15-month ahead forwards for metals. Return to text

6.   For metals, the London Metals Exchange reports maximum daily warehouse storage rates of roughly 40 cents per ton, which at current commodity prices would amount to roughly 1.6 percent a year for copper, 0.7 percent a year for nickel, and 6.5 percent a year for zinc. (These rates vary somewhat by metal and by location.) Warehouses can and do offer discounts to preferred customers. Additional charges are associated with removing the metals from the warehouses, which can be a substantial source of revenue for the warehouses. Return to text

7.   With the year-ahead as defined in Footnote 3. Return to text

8.   An additional constraint on the risk premium is that commodity producers and users have the alternative of hedging by adjusting their inventory positions. If a user wants to guarantee his price, then he could buy the product today and just hold it in inventory. Likewise, if a producer wants to insure the price received, he could either sell out of existing inventory or else speed up extraction (which, in the near term, may be more feasible for metals than for agricultural goods). Hence, the cost of using futures to hedge (the risk premium) should not be much larger than the costs of hedging through physical holdings. Return to text

9.   See the discussion in Chernenko et al (2004) and Chinn et al. (2005).  Return to text


This version is optimized for use by screen readers. Descriptions for all mathematical expressions are provided in LaTex format. A printable pdf version is available. Return to text

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