Review of Agricultural Economics--Volume 19, Number 1--Pages 23-44

C o m m o d i t y F u t u r e s P r i c e s as
Forecasts

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William G. Tomek

Futures markets provide contemporaneous price quotations for a constellation of con-

tracts with maturities thirty or more months in the future, a n d a large literature exists
about interpreting these prices as forecasts. Futures markets simultaneously determine a
price level and price differences appropriate to contract temporal definitions. Futures prices
can efficiently reflect a complex set of factors but still provide poor forecasts. Forecasts
based on quantitative models cannot, however, improve on efficient futures prices as fore-
casting agents; empirical models provide as poor, if not poorer, forecasts. I discuss analo-
gous ideas for basis forecasts.

~ conomists have long thought that forecasts are potentially useful as decision-
pmaking aids, and agricultural economists have devoted considerable effort
to developing and analyzing forecasting methods (Allen). One source of price fore-
casts for major commodities is the current price of a contract for future delivery,
and debate about the interpretation of futures contract prices as forecasts of matu-
rity-month prices has continued for more than fifty years. For example, is the cur-
rent price of the December 1998 com contract an unbiased forecast of the price
that will prevail in December 1998? Is it possible to find other forecasts that are
better? The proliferation of the literature on this topic suggests a need to take
stock. Thus, a primary objective of this paper is to draw out implications of past
research about futures markets as forecasting agencies.
The context for this paper begins in the 1920s and 1930s. Then, analysts viewed
futures and cash prices as being determined by separate factors--cash prices by
current economic conditions and futures prices by expected economic conditions.
Futures prices were treated as independent forecasts. Working (1942) pointed out,
however, that current cash prices are closely linked to quotes for futures contracts
in the grain markets. This link is created by carrying inventories and the associ-
ated prices of storage provided by the constellation of prices for different matu-

9 William G. Tomek is professor ofagricultural economics at Cornell University.

24 Review of Agricultural Economics

rity dates. Thus, Working focused on explaining the price differences and the link
among all the prices for different maturity dates, and he was reluctant to view
futures price quotes as forecasts.
Subsequently, Tomek and Gray suggested that futures markets played both re-
source-allocation and forecasting roles. The overall price level a n d a set of price
differences are indeed determined simultaneously in commodity markets, as
Working (1942, 1949) argued. A com futures market, for example, is providing
incentives or disincentives for carrying inventories. But these prices can also be
interpreted as forecasts. Since the publication of Tomek and Gray; numerous em-
pirical analyses of the forecasting performance of futures markets have been made,

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sometimes with conflicting interpretations (for example, Kenyon, Jones, and
McGuirk versus Zulauf et al.); survey articles have been published (Blank, Kamara);
and the conceptual model has been formalized and extended (for example, French).
The literature on futures prices as forecasts is closely allied with the literature
on the efficient market hypothesis. A price forecast is conditioned by the infor-
mation available at the time the forecast is made, and the concept of pricing effi-
ciency relates to the question of how well a market uses current information to
determine prices. A futures market is defined as being weak forro efficient if the
current price (which can be viewed asa forecast) reflects all the information avail-
able in past prices (Fama). That is, competitive arbitrage eliminates profit oppor-
tunities based on information contained in the prices available to all market trad-
ers.
Thus, many of the papers about the forecasting performance of futures mar-
kets have centered on the issue of the efficiency of the markets. While the small,
marginal contributions of some articles on this topic is unfortunate, it is an im-
portant issue and remains so, notwithstanding the trend toward more industrial-
ized agriculture. Futures markets are an important pricing institution for many
agricultural commodities, and cash transactions often use the nearby futures price
asa reference price. It is uncertain whether futures markets wiU become more or
less important as pricing institutions for agricultural commodities (Tomek 1993),
but whatever the future may hold, we must better understand market behavior
and identify sources of market failure in an increasingly complex economy. Be-
cause most buying and selling of goods and services involves dealing in con-
tracts (either implicit or explicit), this understanding depends on identifying the
goods being bought and sold, the transaction terms, and the possible arbitrage
barriers (Paul). Lack of competition can be defined in terms of arbitrage opportu-
nifies.
The preponderance of evidence suggests that futures markets typically are
weak form efficient. Thus, other, publicly available forecasts cannot improve on
futures quotes forecasts. This does not mean, however, that futures quotes (or
other forecasts) have a high degree of accuracy. In this paper, I elaborate on this
and other, related points.
The paper is organized as follows:

(a) I begin with a formal model of price level and basis (price difference)behav-
ior for a grain to clarify Working's original argument (perhaps best stated in
its 1949 version) about forecasting price levels. The model includes a basis
 Commodity Futures Prices as Forecasts 25

equation because the basis is simultaneously determined with the price level.
(b) The second section draws implications from the model, including a discus-
sion of the emphasis in the current literature on econometric technique and
detail. My concem is that the emphasis on statistical methods, while impor-
tant, misses the big picture of futures prices analyses.
(c) Because Working's (1949) model was intended for an annuaUy produced com-
modity with storage, like com, I discuss the issue of extending concepts to
other types of commodities in a subsequent section.
(d) The final section brings the conclusions together.

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A Model
I assume, as is common in the literature, that current commodity production
is predetermined by farmers' prior decisions. The commodity can be used for
current consumption or stored from one period to the next. We are interested in
determining the consumption in each period and the inventory that will be car-
ried from one period to the next. Thus, the current cash price and the future
delivery price are also important. The model emphasizes the cash price and price
difference. For simplicity, I consider only a two-period model (for a more general
discussion, refer to Williams and Wright). These periods can be considered as
intrayear months with production occurring only in period one, or the two peri-
ods can be treated as two years with production occurring in both. For the case of
production occurring only in period one, the model determines current consump-
tion, future consumption (inventory), the current cash price, and the current fu-
tures price (or, more commonly, the difference in the two prices).

Supply of Storage
A key model component is the profit function for the farmer or grain merchant
who is considering storing grain. Profit is the difference between the revenue
obtained from storing the commodity and the storage cost. In this model, costs
are the sum of three items:

(a) Opportunity cost of carrying inventory from one period to the next;
(b) Cost of other inputs involved in storage, such as wages and energy prices;
(c) Convenience yield (see below).

Costs also could include a risk premium if inventory holders are assumed
risk-averse and if period two prices are treated as uncertain. The empirical evi-
dence suggests that if risk premiums exist, they are tiny (Kamara), and their pres-
ence is not important for this paper.
Opportunity cost is separated from other costs to emphasize its dependence
on price level (and interest rates). Because commodity prices are volatile, the
opportunity cost is also potentially variable; the higher the price of the commod-
ity, the higher the opportunity cost of storing grain.
When profits are defined in terms of conventional costs, an implicit assump-
tion is that inventories are carried for only speculative purposes. That is, invento-
ries are held only if the expected price increase over the storage interval equals the
26 Review of Agricultural Economics

expected carrying costs. It is clear, however, that some inventories are carried when
the expected storage price does not cover conventional costs. Hence, we add con-
venience yield a s a cost component that derives from the benefit (viewed a s a
negative cost) of having working inventories. For example, a grain merchant per-
ceives a benefit from having a stock to meet unexpected commodity demand, or
the flour miller obtains a benefit from having wheat on hand to provide for con-
tinuous mill operation.
Like owning an option, holding an inventory gives the holder flexibility that
the firm otherwise would not have. This benefit is presumably large when total
inventory is small, but decreases as inventories increase. Because marginal con-

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venience yield decreases as i n v e n t o r y increases, this concept i n t r o d u c e s
nonlinearity into the cost function. This nonlinearity is consistent with the fact
that inventories are carried when the storage price is negative. That is, positive
inventories exist when the price for future delivery is well below the current cash
price, and this reality must be modeled.
The short-run profit equation (ignoring fixed costs) for a representative firm is
written as

Ra= F 1I1- Pi 11- c(I, ) (1)

where
C(I1) = cost function defined in equation (2),
F1 = period one price for delivery in period two,
11 = inventory,
P1 = current cash price,
R 2 = revenue realized in period two.

Thus, firms carrying inventory can buy inventory and simultaneously s e l l a

forward contract at the respective prices. The storer realizes the revenue in period
two.
As noted above, the cost function is assumed to have three components.

C(I1 ) = iP~ I1 + di1- vlnI1 (2)

where
d = cost per unit of I of conventional inputs, such as labor,
i = interest rate,
n = number of identical firms,
v = parameter.

The first component represents the opportunity cost of carrying inventory from
one period to the next, based on an interest rate, i, and price level, P. The second
component assumes that other short-run costs are a linear function of the inven-
tory level. These two terms are combined as m below. Convenience yield is speci-
fied a s a logarithmic function of I; which is one way to allow for a nonlinear ben-
efit; it permits the marginal convenience to decline as I increases.
Substituting the cost function into the profit function, taking the derivative of
 Commodity Futures Prices as Forecasts 27

profits with respect to/, and solving this first-order condition gives a supply of
storage equation, commonly written in inverse formas

F 1 - P~ = (iP~ + d) - v / I ~ = m - v / I 1 (3)

where
m = iP~ + d.

This equation is a specific forro of the profit maximization rule that marginal
revenue equals marginal cost, and, in principle, it applies to an individual firm.

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The usual approach to aggregation is to assume that this equation applies to n
identical firms. If so, total inventory equals/1 multiplied by n. To simplify the
notation, I treat the foregoing equation as the market supply function.
In this model, the marginal costs depend on the storage opportunity cost,
the direct storage costs, and convenience yield. The left side of the equation is
a basis o r a storage price, which can be denoted B~. The storage price can be
negative with positive, but small inventories. As inventories increase, the stor-
age price increases, but in this specification reaches an asymptote, m. The as-
ymptote depends on, among other things, the price level and, in this sense, is
n o t a constant.

Demand for Storage

The development of a demand for storage equation has been more problematic
in the literature (Telser, Peck). An approach that provides useful insights is to con-
sider period one and period two demand for current consumption. In the follow-
ing notation, the level of demand (intercept) differs in the two periods and they
have a common slope coefficient, b < O.

Q1 = al + bP1, (4)

and

Q2 = a2+ bF 1 (5)

where
a = intercept coefficient,
b = slope coefficient,
Q = current consumption,
= period one,
2 = period two.

If there is no production in period two, then the following simple identity holds:

Si = Q1 + Q2, and Q2 = 11 (6)

where
S1 = predetermined production in period one.
28 Review of Agricultural Economics

Setting Q1 = S~ - I~ and Q2 = I~, substituting the Q's out of the demand equa-
tions, and subtracting equation (4) from equation (5), gives

I1 = (~ al ) + (b/2)(F~- PI). (7)

In this simplest case, the inventory demand depends only on expected future de-
mand relative to current demand.
We can modify equation (6) to allow for more than two periods by having be-
ginning inventory and assuming production occurs in each period. In this case,
the following identity ties the periods together:

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I~ = $1 + I0- Q~ (6')

where
lo = beginning inventory, and inventory 12is not modeled (that is, omitted).

Equation (7) then is modified so that the demand for inventory also depends
on past inventory and expected future production. That is,

I~ = f (B~, SI + Io, $2, a2, al ) (7')

where
B1 = storage price = F 1- P~,
f = general "function" of notation.

Mor Interpretation
In sum, equations (3), (4), (6) or (6'), and (7) or (7') determine the current cash
price, P1; the current consumption, Q1; the carryover, I1; and the current price for
future deliver}~ F~; or, equivalently, the storage price, B~. A more complete specifi-
cation would include specific demand determinants and a specification of a sup-
ply equation for S. However, current S depends, among other things, on the F
level in the prior period; that is, F 0 can be treated as the expected price for Sv Thus,
while the model does not explain how expectations are formed about the demand
level for consumption in subsequent periods, the futures prices, F, are treated as
the expected P levels in the next period. The model specifies the information set
at time I (more generally, at time t) that determines F~, and this price can be viewed
asa forecast of P2"
While we can view the m o d e l a s explaining the two price levels, F a n d P, the
specification is in terms of the simultaneously determined price level, P, and the
storage price, B (basis). The model has two pieces of information about prices,
not three. Specifying the modelas determining a price level a n d a price difference
is consistent with Working's (1942, 1949) view of futures markets as establishing a
price level and storage prices, which relate to various maturities of futures con-
tracts. Futures prices for storables are not independently established forecasts for
various maturity months but are linked to each other and to cash prices.
It is in this context that Tomek and Gray (p. 373) emphasized that futures prices
reflect "no prophecy that is not reflected in the cash price and is in this sense
 Commodity Futures Prices as Forecasts 29

F i g u r e 1. M a y - D e c e m b e r spread and July price level for com, Chicago

B o a r d o f T r a d e , J u n e 19 t h r o u g h J u l y 17, 1995

300
14
13 290
,, ..... ~176176

12 .... 9 ~176176 280

11 ~

270
10

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,i

'~ 9
260 ~
m 8 250 ~
7
240
6
230
5
I I I I I, I I I I I I I I I I I I I 220
1 3 5 7 9 11 13 15 17 19
Days
{ B . . . . . . JF]

already fulfilled." The two price levels depend on precisely the same set of ex-
planatory variables. They differ by the basis, which reflects the temporal differ-
ences in delivery time, but their changes depend on the same factors (the reduced
form equation variables).
To further set ideas, figure I illustrates a price difference and a price level for
com for twenty trading days June through July 1995. The example is arbitrary in
that the prices were those occurring when I wrote the first draft of this paper, but
it is a good example because changes in expected supply are quite likely to be a
relatively important influence on prices in this period. The July futures price, ob-
served just before contract maturity, can be treated as the spot price, and the dif-
ferences between the prices of the May 1996 and December 1995 futures, observed
in summer 1995, measure a price of storage for the coming crop year.
Figure I suggests a plausible inverse relationship between the simultaneously
determined prices. Each series is observed near the end of the 1994-95 crop year,
hence during the growing season for the new crop to be harvested in fall 1995. If
the main factor affecting prices in July is changes in the expected harvest, increases
in price levels are associated with decreases in expected production. At the same
time, a smaller crop implies a smaller expected storage demand during the next
year, hence, other factors held constant, a smaller storage price. The price level
and difference, for intrayear storage are inversely related even though the three
measures of price level (Jul391December, and May futures) are highly positively
correlated (refer to the appendix).
The July price of the May futures reflects expectations about, among other
things, production and the amount expected to be stored until May. In this sense,
the July 1995 quote of the May 1996 futures price is a forecast, but it can only
30 Review of Agricultural Economics

Figure 2. Storage supply and demand

Basis

m
..... ~ ............................................................. " ..... "S .....

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1 >

J Inventory
D2

summarize information available in July. If realized production or other factors

differ from July expectations, as they most likely will, then the realized May price
will differ from the July market forecast. Indeed, the price of May futures on May
15, 1996, was about $5 a bushel. The market seriously underestimated the matu-
rity price of the May futures contract during the previous summer. Assuming the
corn market is efficient, it incorporated all of the information available in July,
but this did not guarantee an accurate forecast for the subsequent May.
In sum, we can view F1as an expected cash price at contract maturity. But F 1is
based on the same information set that determines P1 and on information that
determines the storage price. Depending on inventory size, the storage price can
be negative or positive. Typically, the price-level changes are larger than price-
difference changes.
Tomek and Gray (1970, pp. 378)9 stated that, because of the correlation between
cash and futures prices, routine annual hedging in futures may not stabilize rev-
enue; the price of the harvest futures at planting time can be, they argued, justas
variable as the harvest price. The foregoing model suggests, however, that this
argument is wrong, or at least exaggerated. For example, in figure 2, shifts in the
storage demand are shown along a static supply of storage function. For large
inventories, F 1is constrained to a constant difference above P~ by the nature of the
marginal costs of storage (and by arbitrage which equates the price difference to
the marginal storage cost). Thus, for large levels of/, cash prices and futures prices
change by about the same amounts. If demand shifted, price level would change,
but price differences would not.
This is not true, however, when inventories are small. In times of scarcity, such
as the com and wheat markets in spring 1996, the current cash price can be much
 Commodity Futures Prices as Forecasts 31

higher than prices for distant futures. When cash com was $5 a bushel in May
1996, the price for December 1996 delivery was about $3.60 a bushel, and the price
for May 1997 delivery was approximately $3.65 a bushel. With small stocks, a
demand shift causes the price level and price differences to change.
The nature of these changes is such that the price of the distant future varies
less from year to year than do cash prices. When inventories are large, the amount
that the futures price can exceed the cash price is limited; this limit is determined
by the d and iP terms in the storage cost function. When inventories are small,
cash prices can be high relative to futures prices, and the limit on this relation-
ship is the nature of the stock convenience yield. Experience indicates that cash

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prices can be extremely large relative to distant futures. Samuelson 1965 and
others suggest that futures prices become more volatile as the maturity date ap-
proaches; that is, intrayear volatility also varies over the contract life. But this
notion can be separated from differences in annual variability.
Consequently, with a sufficiently long sample, one should observe for grain
markets that current prices of distant futures are less variable than subsequent
cash prices, and, hence, that routine hedges should reduce the variability of an-
nual revenue. In Tomek and Gray~ the va¡ of futures prices at planting time
was only slightly smaller than the variance at harvest for soybeans and com based
on a 1952-68 sample period. This was a period of generally large stocks. Using
1974-95 price data for the December com contract, Zulauf et al. found that the
standard deviation was 38 cents a bushel on May 1 and 54.7 cents a bushel on
December 1. For November soybean prices, the standard deviation was 83.7 cents
a bushel on May 1 and 115 cents a bushel on November 1. For the more recent
sample, the price at planting of the harvest futures is less variable than the p¡ at
harvest.

Implications

Price Level Forecasting

This subsection discusses three topics:

(a) Relationship of prices generated by efficient/inefficient markets to forecasts

generated by quantitative models,
(b) Implications of the literature for differences in forecasting ability of efficient
futures markets for different commodities,
(c) Technical econometric issues.

Market-Based Versus Model-Based Forecasts. If the foregoing model is a rea-

sonable representation of a commodity (grain) market and if the market is effi-
cient (Fama), then current (time t) prices reflect known information about all the
variables determining prices, including traders' expectations. In this case, a fore-
cast from a correcfly specified econometric model should not be able to improve
on the market's price estimate. Both, by definition, incorporate the available infor-
mation that conditions the price forecast.
Ir ah econometric model outperforms the market (or vice versa), three interpre-
tations are possible:
32 Review of Agricultural Economics

(a) O n e is merely that both are correct, that the differences reflect sampling error,
and that if a sufficiently large sample is analyzed, no significant difference in
forecasting performance would exist.
(b) T h e second interpretation is that one or the other is wrong. If the market
outperforms the model, the model is erroneously specified, or if the model
outperforms the market, the market is inefficient. Just and Rausser's (1981)
and Rausser and Carter's (1983) results are consistent with these explana-
tions.
It is unlikely that econometric models, at least those in the public domain,
can consistently outperform markets (for example, Just and Rausser 1981).

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Some evidence of mean-reverting behavior exists for futures prices, suggest-
ing the possibility of developing models that outperform the market. A recent
paper by Irwin, Zulauf, and Jackson (1996), however, raises questions about
the validity of empirical studies that have found mean-reverting behavior in
futures prices. Moreover, even if futures prices in a market were mean-revert-
ing in the past, it is unclear whether this information could be used to make
useful ex a n t e forecasts (but for evidence that an expert outperformed a fu-
tutes market, refer to Bessler and Brandt 1992).
(c) A third possibility is that the market is weak form efficient, but not strong
form efficient. Strong forro inefficiency implies that one or more analysts have
private information that is superior to the market's: a superior econometric
model and/or superior ancillary estimates of the variables used to make the
forecasts. Thus, it is possible for this analyst to make forecasts that outper-
form the market. Assuming these forecasts can be used to make profitable
decisions, the analyst is paid for this better information.

In comparing forecasts, it is important to remember that a model can have su-

perior forecasting performance in a statistical sense, but that this information is
not sufficient to provide profitable trades; that is, the information does not have
economic significance (Rausser and Carter). Forecasts require resources, and trades
to take advantage of the information in forecasts have transactions costs. Hence,
the costs of making and using forecasts may exceed the benefits of using them.
Nonetheless, the most common model used to appraise the forecasting (effi-
ciency) performance of futures markets has been

Ft§ i = a + bF t + et§ i (8)

where
et+ i - error term,
-

Ft = forecast,
Ft§ i = actual price realization,

or, altematively,

Ft +i --Ft = a + (b - 1)F t + e t +i" (9)

In early work, such as Tomek and Gray3 Ft+i w a s observed at or near contract ma-
turity; subsequent research has used a variety of definitions of i, hence, of the
 C o m m o d i t y F u t u r e s Prices as Forecasts 33

price being forecast (more on this below). In any case, this equation can be inter-
preted as a forecast evaluation tool, as Theil used it.
The second variant emphasizes that in a weak forro efficient market, the cur-
rent price level has no significant ability to forecast a price change, that is, a = b - 1
= 0. The two variants are equivalent statements; the current price is the best esti-
mate of the coming price and has no ability to forecast changes. To compare with
other forecasts, the market quote F t is replaced with the alternative forecast.
Thus, in saying that one forecast is better than another, the emphasis has been
on the coefficients a and b. In commenting on an earlier draft, David Bessler
reminded me that alternative forecasts can be unbiased, but have different fore-

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cast error variances. A plausible hypothesis is that futures markets have more
noise than alternative forecasting methods, such as an econometric model. Infor-
mation is costly, and learning by traders in markets may be complex (Grossman
and Stiglitz 1980). Not all traders are equally well-informed and some traders are
uninformed. Uninformed traders can contribute to random noise in observed
prices. That is, the price variance increases, other things being the same, as the
number of irrational traders increases (Stein, p. 229). In this context, statistical
model forecasts could contribute to learning and to improved social welfare (Irwin
1994).
The longer the lag between t and t + i (the larger i is), the larger the scope for
changes in the variables explaining price level. It is possible and even likely that
with the passage of time, significant changes in information will occur. Markets
do not have perfect foresight. Consequently; the current price quote for a distant
maturity month can be a poor forecast of the realized price simply because so
many unforeseeable events can occur in the interim. The best available forecast
today can be a poor one. Leuthold, Junkus, and Cordier (p. 108) summarize this
point in their textbook, and French discusses it, but it is sometimes ignored in
research articles on the topic.
In their discussion of futures as forecasting agents, Fama and French suggest
an evaluation equation, which makes the change in the cash price a function of the
basis at the time of the forecast. Namely, letting P be the cash price, they use the
model

Pt§ - P t = a + b ( F t - P t ) + et" (10)

This equation equals

Pt+l = a + b F t + c P t + e t (11)

when the parameters in equation (10) are constrained so that c = 1 - b. Heifner

fitted the same model to com data for Michigan in 1966.
This equation is another way of looking at the arguments Working (1953) de-
veloped. For storables, the structural model discussed in the previous section im-
plies that the two price levels should be highly correlated, and if the null hypoth-
esis that b = 1 cannot be rejected, this is the same as saying that F (or equivalentl~
P) contains all the information available at time t. Thus, an evaluation equation
specified in levels can have a large simple coefficient of determination, r 2, but will
have little or no ability to forecast price changes. Likewise, the basis at time t is
34 Review of Agricultural Economics

unlikely to have significant ability to forecast price changes, but this does not ob-
viate the fact that the current quote in a futures market can be the best (at least
unbiased) forecast of the maturity-fime price.
Forecasting Performance for Different Commodities. The literature makes an-
other point: The forecasting ability of futures markets can vary by commodity.
For example, Working (1953, footnote 5) stated that "perishability of a product
favors predictability of price change because it tends to eliminate expectations
regarding subsequent prices as current price influences." This seems to have been
an off-hand thought, which, in light of subsequent models, is not true. The hy-
potheses in this literature derive, however, from the basic economics of alterna-

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tive markets, not from differences in market efficiency.
Working (1949), Tomek and Gray, and French use a similar model for com-
modities with continuous inventories. As previously noted, changes in expecta-
tions about economic conditions in future periods affect current cash and futures
prices. The strength of this link, however, is related to the size of inventories: When
inventories are large, the basis is relatively constant; when inventories are small,
the basis is variable; that is, changes in future delivery prices are less closely re-
lated to current cash prices.
In this context, French conjectures that metals futures prices will have less pre-
dictive power than those for seasonally produced, continuously stored agricul-
tural products. This hypothesis relates to the intrayear and interyear seasonality
of agricultural prices. Within ayear, futures prices are anticipating the seasonal
increase in price. Between years, the current price of new crop futures relafive to
the current cash price provides incentives or disincentives for carrying stocks into
the new crop year. Tomek and Gray make a similar conjecture, but as previously
noted, this informafion content can be small relafive to changes in expectations
that can occur before the new crop futures contract matures.
The conceptual model in this paper or in French is not really applicable to com-
modities with discontinuous inventories between growing seasons, such as pota-
toes, onions, and apples; discontinuous inventories are equal to infinite storage
costs between crop years. For such commodities, Tomek and Gray hypothesized
that price at planting of the harvest futures would be a poor forecast of the real-
ized harvest price. At planting time, the harvest futures price is not linked to the
current cash price, and the basis reflects no information about inventories to be
carried to the next year. Moreover, little information exists at planting time about
expected demand or supply changes for commodities such as potatoes. Thus, F t a t
planting time varies little from year to year.
French's equation (7) helps elucidate the Tomek and Gray hypothesis. This equa-
tion can be written as

R = var[F t - P t ]/ var[Pt§ - Pt] (12)

where
Ft = price at planting of the harvest futures,
P.,
ti
= price at time t + j.
The numerator is the variance of the planting basis. A small ratio is the same as
saying that relafively little information is available at time t about the prices that
 Commodity Futures Prices as Forecasts 35

prevail at time t + j. In French's terms, the numerator variance is small relative to

the denominator variance. Indeed, Tomek and Gray found that the price at plant-
ing of the harvest futures for potatoes had no predictive power.
French and Fama and French try to extend arguments based on storage costs to
animal-product markets, but as discussed in a separate section, that requires a
more-complex model. Covey and Bessler discuss whether futures markets add
information to that contained in cash prices, and, hence, whether futures markets
improve on the predictive power of cash-price, time-series models. They hypoth-
esize that futures markets for livestock should provide additional information that
is not provided by grain markets.

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As discussed previously, a quantitative model--structural or time-series--
should not be able to provide better forecasts than price quotes from an efficient
futures market. I interpret the Covey and Bessler hypothesis as exploring the mar-
ginal improvement that futures quotes might provide relative to cash-price mod-
els and whether such improvements differ by commodity type. In practice, how-
ever, this idea is difficult to test. Building good quantitative models for different
commodities is not easy. Comparisons are difficult because of the lack of high-
quality price series for cash commodities, including a lack of comparable, syn-
chronous observations on cash and futures prices for agricultural commodities.
What is true, however, is that markets can differ in the kinds and amounts of
information available about factors affecting prices. Also, the availability of in-
ventories can help to adjust to changes in expectations. In addition, markets may
differ in efficiency, that is, in their ability to adjust to information changes.
It is important to keep in mind that numerous variables influence all commod-
ity prices. The fact that com prices in April include information about inventories
does not mean that the April price of December corn will be a precise forecast of
the subsequent December price. Much can change between April and December.
Technical Issues. Much of the agricultural economics literature in this area has
been concerned with modeling and estimation issues. These issues include

(a) the possibility of appraising the efficiency of different maturity months sepa-
rately (versus appraising the efficiency of all contracts by pooling data in one
equation);
(b) the effects of outliers;
(c) the nature of the price distributions, including the possibility of nonstationary
series;
(d) the possible bias of the ordinary least squares (OLS) estimator in fitting mod-
els with a lagged endogenous variable (for example, Elam and Dixon, Kahl
and Tomek, Koppenhaver, and Zulauf et al.).

This literature has been motivated by the fact that estimates of b in the price-
forecast evaluation equation [equation (8)] are sometimes less than one, implying
biased forecasts.
We can understand many technical issues by referring to the forecast evalua-
tion equation. Consequentl~ I use it as a framework. It is convenient, however, to
simplify the notation to
36 Review of Agricultural Economics

A t = maturity-month prices (the series to be forecast)

and

Ft = the prior futures prices (the forecasts).

For evaluating forecasts for a single contract's price, just one observation each
year is to be forecast with one corresponding forecast, although with the passage
of time, we can view F t a s a series of intrayear forecasts for a given A t . A typical
evaluation, however, would define F t for a fixed time before maturity, so that the

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forecast is i months before maturity. For example, A t might be the price at or near
maturity of December com, while F t is the price of December com on April 15,
which is interpreted as i = 8 months ahead forecast.
Recall, we assume the futures price reflects information available at time t, for
example April 15, as conceptualized in the model in the first section. While the t
subscript refers to years, A and F are observed at different times in the year. The
forecast error is thus defined as

e t = A t - F t. (13)

This implies that a = 0 and b = 1 in

A t = a + b F t + e t. (14)

Optimal forecasts typically are defined as those that minimize the expected
squared errors, defined as

E(et)2 = E ( A t - Ft)2. (15)

where
E = expectation operator.

An implicit assumption in the definifion of mean squared error is that the se-
ries being forecast, A, has a fixed mean and variance, that is, it is stationary (Granger
and Newbold, p. 283). The conceptual model in this paper cannot give a definitive
answer about whether a price in a series is stationary, but the model permits cash
prices to be high relative to futures prices--a large negative price of storage
when inventories are relatively small. Thus, commodity prices can have occasional
spikes or temporary shifts in the mean. Prices also could trend, although this is
not required by the model. Ultimately, whether prices are stationary is an empiri-
cal question, but if the analyst is using a long time series in the analysis, the prices
may not have a constant mean and variance.
Assuming a stationary time series, an optimal forecast requires that the error
series have mean zero and be uncorrelated with the forecast series. This means
that E ( A t ) = E(F t ) and that the var(A t ) = var(F t ) + var(e t ). The variance equation
implies that var(F t ) < var(A/), and the conceptual model of price behavior, dis-
cussed earlier, suggests that this indeed should be true in an efficient market. Also,
given a stationary series, the optimal forecast requires that the correlation, r, be-
 Commodity Futures Prices as Forecasts 37

tween A t a n d F t be as large as possible, that the mean of A t equal the mean of F e

and that sF = rs A, where s represents standard deviations (Granger and Newbold,
p. 284). If the true means, variances, and correlations are as defined, then a = 0 and
b=l.
In this context, various explanations of estimated b < 1 are plausible. One is that
the error series is correlated with the forecast, which is technically true because
the futures price is like a lagged endogenous variable. Thus, the OLS estimator
gives biased estimates of the parameters a and b. However, a common result is
that the bias increases as the time lag, i, between observing F and A increases: a
becomes a larger positive number and b decreases below one (for example, Bigman,

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Goldfarb, and Schechtman, Kahl and Tomek). This seems inconsistent with a bias
related to a correlation between F and the error series because this correlation
should decrease as the lag between F and A increases. In other words, the longer
the time between observing F and realizing A, the smaller the correlation between
F a n d e is likely to be.
The pattern of results, alluded to in the prior paragraph, is consistent with the
mean of A differing from the mean of F when long lags exist between F and A, but
as the lag decreases, the two means become similar, and the error variance de-
clines. (By definition, the two variables are identical at maturity.) This difference
in means, in turn, could be related to nonstationary data a n d / o r an inefficient
market in which F has a persistent bias in interpreting the information available at
time t. Also, the fact that var (F t ) < var ( A t ) implies that a single, short sample
could produce quite different means for the two variables; a particular pair of
observations in the sample may appear as an outlier if events result in a large
price change in a year.
Brenner and Kroner suggest that the data-generating process for commodity
futures could be such that the hypothesis about being unbiased cannot hold. This
would require, as I understand their argument, that a component of the carrying
cost, like interest rates or convenience yield, has a stochastic trend, that is, it is not
stationary. While this is possible, it certainly is not required by the conceptual
model in this paper, which defines the interest rateas exogenous. This model and
empirical observation suggest, as already noted, that commodity prices can move
from regimes with relatively little variability to regimes with great variability and
possibly with large price spikes. Thus, either the market or analysts using quanti-
tative models can have problems making ancillary forecasts of the factors that
influence prices. These factors could indude temporary or permanent regime shifts
(structural change). But these arguments do not preclude possible stochastic trends
in the data-generating process.
In this context, it is difficult to discriminate between the alternative explana-
tions for futures price behavior. As mentioned earlier, prices for the May 1996 com
futures contract observed in July 1995 vastly underestimated the actual 1996 price.
The July prices, however, can be viewed as reflecting the then-existing informa-
tion; to show that the com market was inefficient in July, we must demonstrate
that market participants ignored information available in July. Market participants
surely know that a highly nonlinear relationship exists between prices and the
stocks-to-use ratio. When demand is large relative to stocks, prices increase dra-
matically. The problem for the market (or those using quantitative models) is fore-
casting when the stocks-to-use ratio is small. Consequently, forecast errors may be
38 Review of Agricultural Economics

asymmetric because F t does not fully anticipate occasional spikes in A c The same
is true for other forecasts.
The statistical evaluation of pricing efficiency most likely is complicated by the
availability of data from one regime. The evaluation of one contract at one time
lag provides only one pair of observations each year, and the analyst may use
many years to provide degrees of freedom. But in this case, the prices quite likely
were generated by more than one regime, and/or a stochastic trend exists. If a
regime shift has occurred, then the analysis must be limited to a period with con-
stant structure and, hence, few data points, or the change in structure must be
explicitly modeled. A common recommendation in evaluation forecasts is to use

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first differences (Granger and Newbold, p. 283).
Some analysts have tried to overcome the degrees of freedom problem by pool-
ing data for more than one contract, for example, analyzing i months ahead fore-
casts for five different maturity months in one equation. As Kahl and Tomek point
out, however, pooling observations to increase the number of observations cre-
ates other statistical issues. It is important to emphasize that this paper is about
making forecasts i months in advance for prices on fixed expiration dates. Often,
in the empirical analyses of market efficiency or in estimating optimal hedge ra-
tios, a variety of lags, i, is used, and the terminal month is not necessarily fixed.
This creates a number of subtle issues in the analyses (refer to Brenner and Kro-
ner).
The bottom line of the foregoing discussion is that it is difficult to obtain defini-
tive appraisals about the forecasting ability of futures markets. This is also true for
other forecasting methods. Thus, the empirical results can be interpreted as defin-
ing the difficulty of making accurate forecasts of commodity prices more than two
to four months in advance by any method.

Forecasting the Basis

Considerable research has been done on modeling basis behavior (Hauser,
Garcia, and Tumblin; Kahl and Curtis; Leuthold and Peterson; Taylor and Tomek).
The number of forecasting analyses is small, however, and much less research has
been done on basis behavior than on the pricing efficiency of futures markets.
Basis forecasts are potentially valuable because they can help support hedging
decisions. This value arises because the return from a hedge is defined by the
futures price at the time the hedge is placed plus or minus the basis. Because we
know the current futures price, a forecast of the basis provides an estimate of the
purchase or sale price the hedge locks in.
Because of the large number of basis relationships and possible kinds of hedges,
it is important to be precise about the definition of the particular basis being mod-
eled. My comments are limited to two types of models:

(a) One relates to inventories carried from one crop year to the next and related
bases.
(b) The other relates to intrayear inventories.

Models for interyear relationships use cash prices that pertain to a period near
the end of the current crop year and futures quotes for the first contract in the new
 Commodity Futures Prices as Forecasts 39

crop year. This basis measures the magnitude of the incentive for carrying stocks
from one year to the next.
A model like the one above is intended to explain the variability of this basis
and other endogenous variables. If expected production for next year is small,
then all other things being equal, the basis will provide incentives to carry stocks
into the new crop year. Clearl3r the size of inventory carried into the next year--
and, hence, its effect on the price levelmis conditioned by many variables, in-
cluding the size of the previous crop. But this does not invalidate the concept of
the basis providing incentives, or disincentives, for carrying stocks from one year
to the next and therefore simultaneously influencing the price level.

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A variant of this model considers, for example, the harvest cash price and the
harvest quote of the nearby futures contract. A local basis forecast can help farm-
ers who are considering anticipatory hedges of a growing crop. The conceptual
model, discussed above, implies that this basis will vary from year to year and
that explaining this variability is potentially difficult. Hence, obtaining useful
forecasts may be difficult. Among other things, they depend on the expected
values of variables, which are often difficult to measure. Because of the difficulty
of making ancillary forecasts of explanatory variables in structural models, it is
not surprising that basis forecasts often have been made from simple time-series
or naive models.
The second kind of basis model relates to intrayear basis changes, that is, changes
over a storage interval. The profit or revenue function for the potential inventory
holder again provides a useful frame of reference. Here, define R to be the rev-
enue obtained from hedged inventory.

R = ( P t q - P, )Ir + ( F t - F,§ (16)

where
Ir -- inventory bought,
R = revenue obtained from hedged inventory,
t + j " - expected delivery time,

X t = futures contracts sold at time t,

We use this notation to emphasize that the time of inventory sale is variable. A
common application is to think of tas representing harvest and t + j a s a time in
the storage period. The signs assume that the inventory is sold and the futures
position offset at t + j.
We can rewrite this revenue equation to emphasize that with a hedge, the in-
ventory holder earns the change in the basis, or basis convergence. Let

B t = F, - P t (17)

and

B,§ = Ftq - Pt*i" (18)

then solve each for the respective P's and substitute the P's out of the revenue
equation to give
40 Review of Agricultural Economics

R = (Ft.s - F, )Qt + (Bt - Bt§ + (Fe - F,+j)Xc (19)

Working (1953) emphasized that if X = Q (the short futures position equals the
long cash position), then the hedger earns exactly the basis change (convergence).
If expected convergence equals the expected marginal storage cost, the firm should
store and hedge. In a perfect market, basis at contract maturity would be zero.
Thus, basis convergence is exactly Bt, t h e initial basis.
In reality, convergence is not exact, but as Working (1953) suggested, the degree
of convergence can be forecast using the initial basis as the explanatory variable.
The simple model, which Working (1953) suggested and Heifner, Tomek (1978),

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and others used, rnakes the basis change over a storage interval a function of the
initial basis.

B t - Bt§ j = c + dB t + uf§ j (20)

where
u t § = error term.

In a perfect market, the equation would merely state the idenfity that the de-
crease in basis must equal the inifial basis (c = 0, d = 1, and the errors ate zero).
In practice, equafion (20) is a classic forecasting model. It can be fitted to his-
torical data. For forecasting, the basis at time t is observable; it can be inserted into
the esfimated equafion to compute the point forecast. Moreover, we can estimate
the standard deviafion of forecast error, which is a measure of basis risk. This is a
potenfiaUy useful decision tool for firms considering carrying and hedging inven-
tories, and limited evŸ suggests that such equations for the grains have con-
siderable predictive ability. In contrast, Working (1953) and Heifner argued in the
context of grain markets that the basis has relatively little ability to forecast p¡
changes, which is consistent with arguments made in a previous section.
Given basis risk, we can modify the revenue or objective function to allow for
risk. In an optimal hedge, the quantity in the futures position will not exactly
equal the inventory quantity, but this is a topic of a large literature outside the
scope of this paper. Instead, the point here is that forecasting basis change is im-
portant w h e n making a storage and hedging decision.
One question, in light of the discussion of forecasting price levels, is whether
an analyst can improve on the simple basis convergence model. Does the basis at
time t contain all the relevant information for estimating the basis change? If it
does not, does this mean that markets are inefficient?
If markets are assumed efficient in the sense of incorporating all avaflable in-
formation, then, as noted, an econometric model cannot improve on the market's
estimates. But this answer may need to be modified in specific applications. Gen-
eral models of basis and price-level behavior use representative cash prices, which
sometimes are just the prices of futures contracts at maturity. Basis convergence
models typically a_re for particular locations; they involve specific local, spot mar-
kets. It may be that such a model must include variables specific to that location
(and its cash price) a n d / o r relate to differing convergence rates from year to year.
It is also plausible that a cash market is less efficient than a futures market. Thus,
 Commodity Futures Prices as Forecasts 41

when specific cash prices or bases are forecast, a quantitative model may be valu-
able. 1
Adam, Tilley, and Olbert specify and estimate a model for wheat in the spirit of
the model in this paper. They consider the basis change from June 20 to November
30 using Gulf Coast cash prices a s a function of the basis on June 20. Their model
also includes such predetermined variables as carrying charges over the storage
interval, production from June I to December I (like expected production), fore-
cast consumption from December I to March I (like a proxy for expected demand),
and a stocks ratio on December 1. While these variables are observable ex post,
they must be estimated for ex ante forecasts. They use the model to study the ef-

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fects of government programs on wheat stocks, and although the predetermined
variables are statistically important in the simultaneous equations model, it is
unclear whether they would improve ex ante forecasts. This is perhaps a fruitful
area for further research.

E x t e n s i o n s to L i v e s t o c k F u t u r e s
The model in this essay is specified from the viewpoint of a grain market. Clearly,
ir must be modified for livestock markets, for example, the live cattle market. While
inventories are relatively unimportant in explaining basis behavior for livestock
commodities, p¡ have temporal links. Prices in the temporal constellation are
less strongly correlated for livestock futures than for grains, but livestock rela-
tions are more complex. They depend partly on the array of alternatives that pro-
ducers face in the animal life cycle. For example, producers make choices about
using heifers as replacements in the breeding herd versus feeding them for slaugh-
ter, and the choices made a t a particular time subsequently influence outcomes.
Presumably, the basis at the current time t, using the current quote of a futures
contract maturing at a future time t + i, reflects existing information about the
complex array of factors expected to influence the price change from t to t + i. That
is, the current price of a distant future presumably reflects expectations about fu-
ture economic conditions. The (implicit) underlying model for livestock products,
however, is more complex than the storage model in this paper or in French or
Covey and Bessler. Whether the time t basis for livestock products has more or
less predictive power than the comparable basis for grains appears to be an em-
pirical question. The evidence Fama and French presented is not definitive on this
issue.
One last concem is the quality of cash-price observations in the analysis of any
agricultural commodity. The changing nature of cash markets is making ir more
difficult to observe a consistent series of cash prices through time. Also, local
cash markets may be relatively less efficient than futures markets, and the quality
of prices depends partly on resources devoted to eliciting and compiling data.

1Notethat basis variabilityassociatedwith an efficientcash marketis not alwaysbad. A good manager

may be able to completea hedge with a relativelyfavorablebasis change.
42 Review of Agricultural Economics

Conclusions
The following conclusions or hypotheses may be drawn:

(a) Futures prices can be viewed as forecasts of maturity-month prices, and the
evidence suggests that it is difficult for structural or time-series econometric
models to improve on forecasts futures markets provide. We should not be
surprised, however, that act:urate price forecasts are difficult to make, par-
ticularly when the forecast is for a distant time. Prices are influenced by a
complex array of forces, and the information available can change dramati-
cally over time. The precision of futures quote forecasts seems to decline

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rapidly for forecasts made more than three or four months in advance. Thus,
even if a futures price is an unbiased forecast, a large variance of forecast
error should not be surprising.
(b) Second, markets differ in their forecasting ability, for any given time horizon,
i, because the information available in markets differs. That is, viewing a
futures price as an expected spot price, the expectation is based on different
conditioning information in different markets. Markets with continuous in-
ventories, such as corn, have more information available at planting than do
markets with discontinuous inventories, such as potatoes. The evidence also
implies that grain markets with large inventories are most likely to provide
more accurate forecasts than those with small inventories. This is partly re-
lated, however, to the fact that prices are more likely to be less variable when
inventories are large. Markets also may differ in their pricing efficiency, al-
though it is difficult to see why profitable arbitrage opportunities would not
be used. Assuming markets are efficient, it does not seem possible to judge,
based purely on conceptual models, whether markets for livestock are more
likely to provide more- or less-accurate forecasts than those for grain mar-
kets. This question must be answered empirically.
(c) A third point is that the nature of the data-generating processes for commod-
ity prices is such that it will always be difficult to evaluate the efficiency of
commodity futures markets. The data are probably no t adequate to discrimi-
nate among competing hypotheses about market performance. I think that
additional conventional tests of market efficiency are a waste of research re-
sources. If analysts continue to perform these types of studies, however, they
must be cognizant of possible structural change (regime shifts), outliers and
nonstationary price series, and the question of adequate sample size.
(d) Finally, this essay should not be interpreted as meaning that econometric
analyses have no value. Some firms may be able to develop superior private
information. And even if no differences exist between econometric models
and futures price quotes in terms of bias, composite forecasts may have smaller
forecast error variances. In any case, academics still want to understand the
general forces affecting prices. As academics, however, we must be realistic
about what forecasting models can accomplish. In my view, most price ana-
lysts' models cannot improve on futures markets as forecasting agents, and if
so, we must exercise great care in providing marketing advice based on such
models.
 Commodity Futures Prices as Forecasts 43

Acknowledgments
David Bessler, David Debertin, Jana Hranaiova, Kandice Kahl, Raymond Leuthold, Anne Peck,
B.F. Stanton, and an anonymous referee provided helpful comments.

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Appendix
The correlation coefficients among the three price levels used in this paper exceed 0.93. In July
1995, prices were available for eight com futures contracts (through December 1996 delivery), and the
Chicago Board of Trade was listing contracts (with occasional transactions) through December 1997.
In effect, we could price com for three different crop years in late spring and summer 1995. Thus, the
three prices used in this paper are only illustrative of a richer data set. In using daily prices, however,
I d o not intend to imply that one could fit a structural model to them. Clearl3~ daily observations ate
unavailable for the changing expectations affecting prices, and July prices ranged between 263.5 and
294.5 cents a bushel in the twenty sample days, implying considerable changes in the factors affecting
prices. Also, while perhaps not obvious from figure 1, the basis was on a trend. A descriptive regres-
sion equation for the data is

B = 48.2 - 0.147JF + 0.163TRD (Al)

and

Ra = 0.83, D W = 1.85 (A2)

where
B = basis, in cents per bushel;
JF = July futures price level, in cents per bushel;
TRD = linear trend variable, changing one unit each day.

The t-ratios are 7.4 or larger, but recalling the simultaneity in prices and given other possible econo-
metric problems, the equation merely emphasizes that other factors can influence the basis even over
a short time. This reinforces a general point of this paper, namely that the constellation of futures
prices at any time are reflecting many economic forces.