Facts and Fantasies
about Commodity Futures*
The Wharton School, University of Pennsylvania
and National Bureau of Economic Research
and K. Geert Rouwenhorst
School of Management, Yale University This Draft: June 14, 2004 Abstract
We construct an equally-weighted index of commodity
futures monthly returns over the period between July of 1959 and March
of 2004 in order to study simple properties of commodity futures as an
asset class. Fully-collateralized commodity futures have historically
offered the same return and Sharpe ratio as equities. While the risk premium
on commodity futures is essentially the same as equities, commodity futures
returns are negatively correlated with equity returns and bond returns.
The negative correlation between commodity futures and the other asset
classes is due, in significant part, to different behavior over the business
cycle. In addition, commodity futures are positively correlated with inflation,
unexpected inflation, and changes in expected inflation.
*We thank Dimitry Gupalo and Missaka Warusawitharana for research
assistance, AIG Financial Products for financial support, Michael
Crowe of the London Metals Exchange for assistance with data, Chris
Lown of the Commodities Research Bureau (CRB) for assistance with
the CRB data, and Frank Strohm and Amir Yaron for comments and suggestions.
Commodity futures are still a relatively unknown
asset class, despite being traded in the U.S. for over 100 years and
elsewhere for even longer. This may be because commodity futures are
strikingly different from stocks, bonds, and other conventional assets.
Among these differences are: (1) commodity futures are derivative securities;
they are not claims on long-lived corporations; (2) they are short maturity
claims on real assets; (3) unlike financial assets, many commodities
have pronounced seasonality in price levels and volatilities. Another
reason that commodity futures are relatively unknown may be more prosaic,
namely, there is a paucity of data.2
The economic function of corporate securities such as
stocks and bonds, that is, liabilities of firms, is to raise external
resources for the firm. Investors are bearing the risk that the future
cash flows of the firm may be low and may occur during bad times, like
recessions. These claims represent the discounted value of cash flows
over very long horizons. Their value depends on decisions of management.
Investors are compensated for these risks. Commodity futures are quite
different; they do not raise resources for firms to invest. Rather,
commodity futures allow firms to obtain insurance for the future value
of their outputs (or inputs). Investors in commodity futures receive
compensation for bearing the risk of short-term commodity price fluctuations.
Commodity futures do not represent direct exposures to
actual commodities. Futures prices represent bets on the expected future
spot price. Inventory decisions link current and future scarcity of
the commodity and consequently provide a connection between the spot
price and the expected future spot price. But commodities, and hence
commodity futures, display many differences. Some commodities are storable
and some are not; some are input goods and some are intermediate goods.
In this paper we produce some stylized facts about
commodity futures and address some commonly raised questions: Can an investment
in commodity futures earn a positive return when spot commodity prices
are falling? How do spot and futures returns compare? What are the returns
to investing in commodity futures, and how do these returns compare to
investing in stocks and bonds? Are commodity futures riskier than stocks?
Do commodity futures provide a hedge against inflation? Can commodity
futures provide diversification to other asset classes? Many of these
questions have been investigated by others but in large part with short
data series applying to only a small number of commodities.3
An exception is Bodie and Rosansky (1980), who studied commodity futures
over the period 1950 to 1976, using quarterly data.4
futures markets appear to have their origin in Japanese rice futures,
which were traded in Osaka starting in the early 18th century; see
Anderson, et al. (2001). 2 For example, the University
of Chicago Center for Research in Security Prices has no commodity
futures data, nor does Ibbotson Associates. In addition, the well-known
commodity futures indices either do not extend back very far or
cannot be reproduced for various reasons. 3 There
is a very large literature on commodity futures. For example, see
the papers collected in Telser (2000). 4 Bodie and
Rosansky (1980) obtained their data from a U.S. Department of Agriculture
publication called Commodities Futures Statistics and from
the Journal of Commerce.
In this primer we construct a monthly time series
of an equally-weighted index of commodity futures prices starting in
1959. We focus on an index because we want to address the above questions
with respect to this asset class as a whole, rather than with respect
to individual commodity futures. We produce some stylized facts to characterize
2. The Mechanics of an Investment in Commodity
A commodity futures contract is an agreement to buy (or
sell) a specified quantity of a commodity at a future date, at a price
agreed upon when entering into the contract - the futures price. The
futures price is different from the value of a futures contract. Upon
entering a futures contract, no cash changes hands between buyers and
sellers - and hence the value of the contract is zero at its inception.5
How then is the futures price determined? Think of the
alternative to obtaining the commodity in the future: simply wait and
purchase the commodity in the future spot market. Because the future
spot price is unknown today, a futures contract is a way to lock in
the terms of trade for future transactions. In determining the fair
futures price, market participants will compare the current futures
price to the spot price that can be expected to prevail at the maturity
of the futures contract. In other words, futures markets are forward
looking and the futures price will embed expectations about the future
spot price. If spot prices are expected to be much higher at the maturity
of the futures contract than they are today, the current futures price
will be set at a high level relative to the current spot price. Lower
expected spot prices in the future will be reflected in a low current
futures price. (See Black (1976).)
Because foreseeable trends in spot markets are taken into
account when the futures prices is set, expected movements in the spot
price are not a source of return to an investor in futures. Futures
investors will benefit when the spot price at maturity turns out to
be higher than expected when they entered into the contract, and lose
when the spot price is lower than anticipated. A futures contract is
therefore a bet on the future spot price, and by entering into a futures
contract an investor assumes the risk of unexpected movements in the
future spot price. Unexpected deviations from the expected future spot
price are by definition unpredictable, and should average out to zero
over time for an investor in futures, unless the investor has an ability
to correctly time the market.
What then is the return that an investor in futures can
expect to earn if he does not benefit from expected spot price movements,
and is unable to outsmart the market? The answer is the risk premium:
the difference between the current futures price and the expected future
spot price. If today's futures price is set below the expected future
spot price, a purchaser of futures will on average earn money. If the
futures price is set above the expected future spot price, a seller
of futures will earn a risk premium.
is also true at the end of each day when the value of a futures
contract is reset to be zero. Gains and losses during the day are
settled by the two parties to the contract via transfers from their
Are there any theoretical reasons for the risk premium
to accrue to either buyers or sellers of futures contracts? Keynes'
(1930) theory of normal backwardation postulated that the risk premium
would accrue to the buyers of futures. He envisioned a world in which
producers of commodities would seek to hedge the price risk of their
output. For example, a producer of grain would sell grain futures to
lock in the future price of his crops and obtain insurance against the
price risk of grain at harvest time. Speculators would provide this
insurance and buy futures, but demand a futures price which is below
the spot price that could be expected to prevail at the maturity of
the futures contract. By "backwardating" the futures price relative
to the expected future spot price, speculators would receive a risk
premium from producers for assuming the risk of future price fluctuations.6
How is the risk premium earned? Do speculators have to
hold the futures contract until expiration? The answer is no. Over time,
as the maturity date of the futures contract draws close, the futures
price will start to approach the spot price of a commodity. At maturity,
the futures contract will become equivalent to a spot contract, and
the futures price will equal the spot price. If futures prices were
initially set below the expected future spot price, the futures price
will gradually increase over time, rewarding the long position.
Whether Keynes' theory of normal backwardation is an accurate
theory of the determination of the futures price is an empirical matter,
and much of this paper will be devoted to examining the existence of
a risk premium in commodity futures.7 The above discussion
of the mechanics of futures markets, however, serves to make the following
important points about an investment in futures:
The expected payoff to a futures position is the risk
premium. The realized payoff is the risk premium plus any unexpected
deviation of the future spot price from the expected future spot price.
A long position in futures is expected to earn positive
(excess) returns as long as the futures price is set below the expected
future spot price.
If the futures price is set below the expected future
spot price, the futures prices will tend to rise over time, providing
a return to investors in futures.
Expected trends in spot prices are not a source of
return to an investor in futures.
(1930, p. 144) put it this way: "In other words, the quoted forward
price, though above the present spot price, must fall below the
anticipated future spot price by at least the amount of normal backwardation."
7Attempts to empirically measure the risk premium
have yielded mixed results (for example, see Gray (1961), Dusak
(1973), Jagannathan (1985), and Bessembinder (1992)). Part of the
reason for the lack of success is no doubt the volatility of futures
prices. This makes it difficult to accurately measure the risk premium
using data covering short time intervals - a problem that is not
unique to commodities; it is equally applicable to equities.
To further illustrate these points, consider a
stylized example, adapted from Weiser (2003). The example is displayed
in Figure 1 below. Assume that the spot price of oil is $30 a barrel
and that market participants expect the price of oil to be $27 in three
months. In order to entice investors into the market, the futures price
is set at $25, which is a discount to the expected future spot price.
The difference between the futures price and the expected future spot
price, or $2, is the risk premium that the investor expects to earn
for assuming short-term price risk.
Now suppose that at the time the contract expires, oil
is trading at the expected price of $27. An investor in physical commodities,
who cares about the direction of spot prices, has just lost $3 (i.e.,
$30 - $27). An investor in the futures contract, however, would have
gained the difference between the final spot price of $27 and the initial
futures price of $25, or $2.
The example above, and the figure, examine the case where
the expected future spot price of $27 is, in fact, realized. But suppose
the expectation of a price of $27 is not realized and instead the final
spot price turns out to be $26. Then the realized return to the investor
would be $1. This realized return can be broken down into the risk premium
($27 - $25 = $2), less the difference between the final spot price and
the expected price ($26 - $25 = $1).
The remainder of the paper will be devoted to empirical
evidence on the historical performance of commodity futures as an asset
class. One final remark needs to be made regarding the calculation of
futures returns. At the beginning of this section, we explained that
the value of a futures contract is zero at origination, and does not
require any cash outlay for either the long or the short position. In
practice, both the long and short position will have to post collateral
that can be used to settle gains and losses on the futures position
over time. The collateral is typically only a fraction of the notional
value of the futures position, which implies that a futures position
can involve substantial leverage.
In order to draw a meaningful comparison between the
performance of futures and other asset classes, we need to control for
leverage when calculating futures returns. We make the assumption that
futures positions will be fully collateralized. When an investor buys
a contract with a futures price of $25, we will assume that the investor
simultaneously invests $25 in T-bills. The total return earned by the
investor over a given time period, will therefore be the change in the
futures price and the interest on the $25 (calculated daily), scaled
by the $25 initial investment.
3. An Equally-Weighted Index of Commodity
To investigate the long-term return to commodity futures
we constructed an equallyweighted performance index of commodity futures.
The source of our data is a database maintained by the Commodities Research
Bureau, which has daily prices for individual futures contracts since
1959. We append these data with data from the London Metals Exchange.
A detailed description of the data is given in Appendix 1, but a few
general comments are in place.
Our index potentially suffers from a variety of selection
and survivorship biases. First, the CRB database mostly contains data
for futures contracts that have survived until today, or were in existence
for extended periods during the 1959-2004 period. Many contracts that
were introduced during this period, but failed to survive, are not included
in the database. It is not clear how survivorship bias affects the computed
returns to a futures investment. Futures contracts fail for lack of
interest by market participants, i.e. lack of trading volume. See Black
(1986) and Carlton (1984). While this may be correlated with the presence
of a risk premium, the direction of the bias is not as clear cut as
would be the case of the calculation of an equity index. Among other
reasons, stocks do not survive because of bankruptcy, and excluding
bankrupt firms would create a strong upward bias in the computed returns.
Second, in order to avoid double counting of commodities, we selected
contracts from a single exchange for inclusion in our index, even though
a commodity might be traded on multiple exchanges. We based our selection
on the liquidity of the contract, and it is therefore subject to a selection
bias that may or may not be correlated with the computed returns. Finally,
for each commodity, there are multiple contracts listed that differ
by maturity. On each day, we selected the contract with the nearest
expiration date (the shortest contract) for our index, unless the contract
expired in that month, in which case we would roll into the next contract.
In each month, we therefore hold the shortest futures contract that
will not expire in that month.8
The performance index is computed as follows: at the beginning
of each month we hold one dollar in each commodity futures contract.
(If the futures price is $25, we hold 1/25th of a contract). At the
same time we purchase $1 in T-bills for every contract that the index
invests in. The index is therefore "fully collateralized" by a position
of T-bills. The contracts are held until the end of the month, at which
time we rebalance the index to equal weights. More detail is contained
in Appendix 1.
There are many different ways in which we could have weighted
individual commodity futures in our index.9 By analyzing
the returns of an equally-weighted index of commodity futures we can
make statements about "how the average commodity future behaves during
the average time period."
4. The Historical Returns on Commodities:
Spot Prices, Collateralized Futures, and Inflation
We now turn to the empirical evidence on spot and future
returns. What is the average return to commodity futures? Does the collateralized
futures position outperform the spot return for the "average commodity
future"? Figure 2a compares the equally-weighted total return index
of commodity futures to an equally-weighted portfolio of spot commodities
between 1959 and 2004. Both indices have been adjusted for inflation
by deflating each series by the consumer price index (CPI). The index
of commodity spot prices simply tracks the evolution of the spot prices,
and ignores all costs associated with the holding of physical commodities
(storage, insurance, etc). It is therefore an upper bound on the return
that an investor in spot commodities would have earned. The main conclusions
from examination of the figure are that:
1. There are large differences between the historical
performance of spot commodity prices and collateralized commodity futures
returns. The historical return to an investment in commodity futures has
far exceeded the return to a holder of spot commodities. 2. Both commodity spot prices and commodity futures
returns have outpaced inflation.
rolling itself is not a source of return. Because the futures price
adjusts continuously, and gains and losses are settled daily, a
futures contract has zero value at the end of each day. Even though
a distant futures contract may have a different futures price than
a near contract, the exchange of one for another has no cash flow
implications. 9The popular traded indices of collateralized
commodity futures sometimes use (a combination of) production and
liquidity data as the basis for calculating weights (e.g., the Dow
Jones AIG Commodity Index and the Goldman Sachs Commodity Index).
The Reuters-CRB index uses equal weights, but does not rebalance
like our index.
What is perhaps not directly apparent from Figure
2a is that the return on the futures position is highly correlated with
movements in the spot. As explained in Section 2, an investment in commodity
futures benefits from unexpected increases in spot prices. Especially
in times of high spot market volatility, the returns to spot and futures
will be highly correlated. This is illustrated in Figure 2b. It presents
the same data as Figure 2a of the graph, but the scale is in logs, which
facilitates identification of proportional changes in series that differ
in levels. What is clear from Figure 2b is that the two series are highly
correlated, but diverge because of differing trends. The spot index includes
trends in the spot price, which are excluded from the futures index. In
turn the futures index rises with the risk free rate plus any risk premium
earned by the futures position. Figure 2a also gives a clue about the risk premium
of commodity futures. Part of the return to collateralized futures is
the return on collateral (T-bills). Because the historical inflation adjusted
return to T-bills is about the rate of inflation, the (inflation adjusted)
real return to collateralized commodity futures is an indication of the
risk premium earned by investors. We will return to a discussion of the
risk premium in the next sections. 5. The Risk and Return of Commodity Futures Compared
with Other Asset Classes Figure 3 compares the cumulative performance of the
Ibbotson corporate bond index ("Bonds"), the SP500 index (Stocks), and
the equally- weighted commodity futures index total return ("Commodity
Futures") for the period July 1959 to the end of March of 2004. All series
have been deflated by the CPI index, and therefore measure the inflation
adjusted performance of the three asset classes. Figure 3 shows:10 1. Over the last 43 years, the average annualized
return to a collateralized investment in commodity futures has been comparable
to the return on the SP500. Both outperformed corporate bonds. 2. Stock and Commodity Futures have experienced higher
volatility than Bonds. 3. Commodity Futures outperformed Stocks during the
1970s, but this performance was reversed during the 1990s. Figure 4 gives the historical risk premiums (not adjusted
for inflation) for the three asset classes. Next to each bar depicting
the average risk premium is the t-statistic, which measures our confidence
that the risk premium is different from zero.
10 Summary statistics, including standard errors, are
contained in Appendix 2.
Two observations stand out: 1. The historical risk premium on Commodity Futures
has been positive at about 5% during the 1959-2004 period, and significant
in a statistical sense (t-statistic = 2.84). 2. The historical risk premium on Commodity Futures
is about the same as the risk premium on Stocks (SP500), and more than
double the risk premium of Bonds. As pointed out in Section 2, there has been much debate
among economists about the existence of a risk premium in commodity futures.
Keynes (1930) and Hicks (1939) assumed that hedgers outnumber speculators
in the futures markets, which was the basis for the theory of normal backwardation.
The estimated risk premium in Figure 4 is not only consistent with the
theory of normal backwardation, but - more importantly - it also shows
that the risk premium has been economically large and statistically significant.
Our commodities total return index covers a period
of more than 40 years, and is diversified across many commodities. As
such it provides a unique opportunity to examine the risk premium across
a variety of commodities and time periods. Figure 5 compares the performance (unadjusted for
inflation) of stocks, bonds and commodities in the familiar average return
- standard deviation diagram. The volatility of the equally-weighted Commodity Futures
total return is slightly below volatility of the SP500. So, the Sharpe
Ratio has been slightly higher for Commodity Futures than for Stocks (also
indicated by the higher t-statistics in Figure 4). Financial returns are not completely characterized
by the mean return and the standard deviation of returns. This is because,
as is well known, the returns on financial securities are not normally
distributed, but rather have "fat tails" compared to the Normal Distribution.
This is also true of commodity futures. Commodity futures returns are
positively skewed; stock returns are negatively skewed. Bodie and Rosansky
(1980), and others, also note that commodity futures returns are considerably
positively skewed compared to stock returns. This is further illustrated in Figure 6, which compares
the empirical distribution of monthly returns for the SP500 and our equally-weighted
commodity futures index between 1959 and 2004. Three observations stand out: 1. Commodity Futures and Stocks have about the same
average return, but the standard deviation of stock returns is slightly
higher. 2. The return distribution of equities has negative
skewness, while the distribution of commodity returns has positive skewness.
This means that, proportionally, equities have more weight in the left
tail of the return distribution while commodities have more weight in
the right tail. 3. Both the return distributions have positive excess
kurtosis, that is, they are "peaked" relative to the normal distribution.
The slightly higher variance of equities, and the
opposite skewness, together imply that equities have more downside risk
relative to commodities. For example, the 5% tail of the empirical distribution
of equities occurs at -6.56% compared to -4.05% for commodities. From
the perspective of risk management, an important question is whether these
tail events occur simultaneously for both assets, or in isolation. We
will turn to the question of correlation next. 6. The Correlation of Commodities with Other
Asset Classes We examine the correlation of Commodity Futures returns
with Stocks and Bonds over various investment horizons. In addition to
monthly returns, we report correlations computed using overlapping returns
over quarterly, annual and 5-year intervals. Because asset returns are
volatile, examining correlation over longer holding periods may reveal
patterns in the data that are obscured by short-term price fluctuations.
Figure 7 illustrates the correlations of Commodity Futures returns with
Stocks, Bonds, and Inflation over the period between 1959 and 2004:
1. Over all horizons - except monthly - the equally-weighted
Commodity Futures total return is negatively correlated with the return
on the SP500 and long-term bonds. This suggests that Commodity Futures
are effective in diversifying equity and bond portfolios.
2. The negative correlation between Stocks and Bonds
tends to increase with the holding period. This suggests that the diversification
benefits of Commodity Futures tend to be larger at longer horizons.
3. Commodity Futures returns are positively correlated
with inflation, and the correlation is larger at longer horizons. Because
Commodity Future returns are volatile relative to inflation, longer-term
correlations better capture the inflation-properties of a commodity
In Figure 5 we showed that equities contain more downside
risk than Commodity Futures. So it is important to ask whether the negative
correlation between equities and Commodity Futures holds up when equity
returns are low - a time when diversification is especially valuable.
We examined the returns to Commodity Futures during the months of lowest
equity returns. The results are given in Figure 8a and 8b. Figure 8a
shows the equity returns during the 5% of worth months of lowest performance.
Figure 8b concentrates on the lowest 1% of realized equity returns.
The figures show the following:
1. During the 5% of the months
of worst performance of equity markets, when stocks fell on average
by 9.18%, Commodity Futures experienced a positive return of 1.43%,
which is slightly more than the full sample average return of 0.88%
2. During the 1% of months of lowest performance of equity
markets, when equities fell on average by 13.87%, Commodity Futures
returned an average of 2.32%.
It seems that the diversification benefits of Commodity
Futures work well when they are needed most. Consistent with a negative
correlation, Commodity Futures earn above average returns when
stocks earn below average returns.
7. Commodity Futures Returns and Inflation
Investors ultimately care about the real purchasing
power of their returns, which means that the threat of inflation is a
concern for investors. Many traditional asset classes are a poor hedge
against inflation - at least over short and medium-term horizons. Bonds are nominally denominated assets, and their
yields are set to compensate investors for expected inflation over the
life of the bond. When inflation is unexpectedly higher than the level
investors contracted for, the real purchasing power of the cash flows
will fall short of expectations. To the extent that unexpected inflation
leads to revisions of future expected inflation, this loss of real purchasing
power can be significant. There are reasons to expect equities to provide a
better hedge than bonds against inflation - at least in theory. After
all, stocks represent claims against real assets, such as factories, equipment,
and inventories, whose value can be expected to hold pace with the general
price level. However, firms also have contracts with suppliers of inputs,
labor and capital, that are fixed in nominal terms and hence act very
much like nominal bonds. In addition, (unexpected) inflation is often
not neutral for the real economy. Unexpected inflation is associated with
negative shocks to aggregate output, which is generally bad news for equities.
(See Fama (1981).) In sum, the extent to which stocks provide a hedge
against inflation is an empirical matter. Figure 7 suggested that commodity futures might be
a much better inflation hedge than stocks or bonds. First, because commodity
futures represent a bet on commodity prices, they are directly linked
to the components of inflation. Second, because futures prices include
information about foreseeable trends in commodity prices, they rise and
fall with unexpected deviations from components of inflation. This is
exactly why futures do well when stocks and bonds perform poorly. Figure 9 compares the correlations of stocks, bonds,
and commodities with inflation. As before, correlations are computed over
various investment horizons. Several observations stand out from Figure 9: 1. Commodity Futures have an opposite exposure to
inflation compared to Stocks and Bonds. Stocks and Bonds are negatively
correlated with inflation, while the correlation of Commodity Futures
with inflation is positive at all horizons. 2. In absolute magnitude, inflation correlations tend
to increase with the holding period. The negative inflation correlation
of Stocks and Bonds and the positive inflation correlation of Commodity
Futures are larger at return intervals of 1 and 5 years than at the monthly
or quarterly frequency. Our previous discussion suggested that stocks, and
especially bonds, can be sensitive to unexpected inflation. In order to
measure unexpected inflation, a model of expected inflation is needed.
For this purpose we choose a very simple method that has been used by
others in the past (e.g., see Fama and Schwert (1977) and Schwert (1981)).
The shortterm T-bill rate is a proxy for the market's expectation of inflation,
if the expected real rate of interest is constant over time. Consequently,
unexpected inflation can be measured as the actual inflation rate minus
the nominal interest rate (which was known ex ante). Because inflation is persistent over time, unexpected
inflation often causes market participants to revise their estimates of
future expected inflation. The change in expected inflation can be measured
by the change in the nominal interest rate. This is not necessarily perfectly
correlated with the unexpected inflation rate since investors may use
more information than just the current rate of inflation to revise their
expectations of future inflation.11 11 Following the large
literature on inflationary expectations, we choose the 30-day and 90-day
T-bill yield as our measure of expected inflation for the next month,
and quarter. See Fama and Schwert (1977) and Schwert (1981) for a discussion.
11Following the large literature on inflationary expectations,
we choose the 30-day and 90-day T-bill yield as our measure of expected
inflation for the next month, and quarter. See Fama and Schwert
(1977) and Schwert (1981) for a discussion.
Figure 10 illustrates the correlations of Stocks,
Bonds, and Commodity Futures returns with the components of inflation.
These observations stand out: 1. The negative sensitivities of Stocks and Bonds
to inflation stem mainly from sensitivities to unexpected inflation. The
correlations with unexpected inflation exceed the raw inflation correlations.
2. Commodity Futures are also more sensitive to unexpected
inflation, but (again) in the opposite direction. 3. Stock returns and (especially) Bond returns are
negatively influenced by revisions about future expected inflation. Revisions
about future inflationary expectations are a positive influence on Commodity
Futures returns. 4. Unreported results show that these patterns in
the exposures to unexpected inflation are stronger at the quarterly horizon
than at the monthly horizon. Commodity Futures returns are negatively correlated
with stock returns. Commodity Futures have opposite exposures to unexpected
inflation from Stocks and Bonds. It is tempting to put both together and
ask: does the opposite exposure to unexpected inflation account for the
negative correlation between Commodity Futures and Stocks and Bonds? Preliminary
findings suggest that this only part of the story behind the negative
correlations. If we isolate the portion of the returns of commodity futures,
stocks and bonds that is unrelated to unexpected inflation and examine
the correlations again, we find that the residual variation of commodity
futures and stocks or bonds continue to be negatively correlated.12
At the quarterly horizon, the correlation between futures and stocks increases
from -0.13 to -0.09, while for bonds the correlation increases from -
0.22 to -0.18. In other words there are additional factors that drive
the negative correlation between futures returns and stocks and bonds.
The next section describes one of these sources: business cycle variation.
8. Commodity Returns over the Business Cycle.Modern finance theory identifies two components to
asset returns: a systematic component and a nonsystematic, or idiosyncratic,
component. Holding a portfolio of many different securities can diversify
idiosyncratic components. But, the systematic component corresponds to
movements in the market as a whole, and so is viewed as nondiversifiable.
The nondiversifiable component, associated with beta in the Capital Asset
Pricing Model, also corresponds to the business cycle since business cycle
risk is nondiversifiable. Stock and bond returns are negative in (the
early phase of) recessions, in particular.
12In other words, we examine the correlation of regression
residuals from regressions of each asset class' returns on unexpected
Commodity future returns and equity returns are negatively
correlated at quarterly, annual, and five-year horizons. This means that
commodity futures are useful in creating diversified portfolios, with
respect to the idiosyncratic component of returns. But, importantly, there
is also evidence of another "diversification effect." Commodity futures
have a feature quite unique to this asset class, namely, commodity futures
have some power at diversifying the systematic component of risk - the
part that is not supposed to be diversifiable! Weiser (2003) reports that
commodity futures returns vary with the stage of the business cycle.13
In particular commodity futures perform well in the early stages of a
recession, a time when stock returns generally disappoint. In later stages
of recessions, commodity returns fall off, but this is generally a very
good time for equities. Figure 11 displays a business cycle, where the National
Bureau of Economic Research (NBER) peak and trough are identified.14
The NBER identifies peaks and troughs, but the figure further divides
the cycle into phases. Phases are identified by dividing the number of
months from peak to trough (trough to peak) into equal halves to indicate
Early Recession and Late Recession (Early Expansion and Late Expansion).
Clearly, the Early and Late Expansion phases correspond to an economic
expansion, while the Early and Late Recession phases correspond to a recession.
13Weiser (2003) looks at the period 1970-2003, and determines
business cycle dating in terms of the rate of change of the quarterly
GDP growth rate. Vrugt (2003) also analyzes the period 1970-2003.
He uses National Bureau of Economic Research (NBER) business cycle
dating, and divides the business cycle into phases. We have used
Vrugt's (2003) figure to show the phases. 14The NBER is a private, nonprofit, economic research
consortium, which dates business cycles in the U.S. by identifying
business cycle peaks and troughs. See http://www.nber.org/cycles.html
In order to analyze the behavior of commodity futures
over the business cycle, we would like to include as many business cycles
as possible. The equally weighted commodity futures index that we constructed,
detailed in Appendix 1, is useful for this. Starting in 1959 allows us to analyze seven full business
cycles, more than Weiser (2003) and Vrugt (2003). (The relevant NBER business
cycle chronology for this period is shown in Appendix 3.) Average annualized (monthly) returns for the major
asset classes are given below in Figures 12 and 13. We examine the returns
during expansions and recessions, and for the four phases of the cycle.
Looking at Figure 12, note the following: 1. Over the period July 1959 through March 2004, average
monthly annualized returns on the S&P and the equally-weighted commodity
futures total return are remarkably similar, 10.8% and 10.5%, respectively.
2. They are also remarkably similar over expansions,
12.8% on the S&P and 12.9% on the equally weighted commodity futures.
Over recessions, the average monthly annualized returns for the S&P and
the equally weighted commodity futures are 1.7% and 0.5%. Based on these two observations, stocks and the commodity
futures index appear to be very similar. But, these similarities obscure
an important difference when the business cycle is examined in more detail
in Figure 13. 3. During the Early Recession phase the returns on
both stocks and bonds are negative, - 15.5% and -2.9% respectively. But,
the return on commodity futures is a positive 3.5%. During the Late Recession
phase the signs of the returns reverse, stocks and bonds are positive,
while commodity futures are negative. 4. The diversification effect is not limited to the
early stages of recessions. Whenever stock and bond returns are below
their overall average, in the Late Expansion and Early Recession phases,
commodity returns are positive and commodities outperform both stocks
and bonds. The last two conclusions are not evident if the sample
is confined to the period 1990- 2004, a period which does not cover enough
business cycles. To explore this business cycle diversification effect
just a bit further we ask whether there are certain individual commodity
futures that are responsible for the result. A further breakdown by stage
of the business cycle for individual commodity futures is shown below.
* Period after the last trough in November
2001 was included in overall average and expansion average, but was not
included in Phase 4 or Phase 1 because the border between these two phases
depends on the next peak, the timing of which is not known at this time.
There are many intriguing patterns in the table, too
many to pursue in this study.15 To highlight just a few, we
note the following: 1. There are a number of commodity futures that perform
well in the Early Recession, but not well in the Late Recession. In particular,
crude oil futures, unleaded gas future, and heating oil futures display
this pattern. Thus, an equally weighted energy futures index shows a positive
return of 5.4% in the Early Recession, and a negative return of 7.8% in
the Late Recession. 16 2. But, this pattern of strong performance over the
Early Recession phase, followed by weaker performance over the Late Recession
phase, is not confined to energy futures. For example, Industrial Metals
also appears to have strong cyclical features. This subgroup returns 15.7%
on average over the Early Recession phase and -29.8% over the late Recession
phase. Similarly, the index of Other Food Futures displays this pattern
quite strongly. 3. Without energy, the equally-weighted nonenergy
commodity futures return is still positive over the Early Recession phase
(1.8%), and it is also positive over the Late Recession (0.5%).
15To conserve space the standard errors are not included
in the table. 16Note that it starts in 1979 because this is when heating
oil futures contracts started trading.
That energy is important for the commodity futures
business cycle result is not surprising because the oil crises of the
1970s and 1980s are associated with major recessions. Notable examples
are the Arab OPEC oil embargo associated with the Yom Kippur War of 1973,
the oil price increase shocks of 1979-1980 and 1990-1991, and a major
oil price collapse in 1986. See Hamilton (1985). Many researchers argue
that oil shocks disrupt economic activity. That is, unexpected increases
in oil prices are associated with declines in the macroeconomy, as measured
by output or employment. For example, see Hamilton (2003, 1983). Essentially
what happens during the Early Recession phase, generally speaking, is
that oil and energy-related prices unexpectedly increase, causing a windfall
gain to long futures investors. However, as noted, the results do not
depend solely on energy futures. Also, keep in mind that energy futures
are somewhat recent contracts, e.g., crude oil only started trading in
1983. The fact that industrial metals and other foods are
very cyclical is also interesting. In fact, the cross section behavior
of different commodity futures over the business cyclical is an interesting
subject for further research. 9. Commodity Future Returns, Backwardation, and
Contango The empirical evidence presented in this paper is
consistent with Keynes' theory of normal backwardation. He envisioned
a world in which commodity producers use futures markets to transfer the
price risk to speculators who are risk averse. To compensate speculators,
hedgers agree to set the futures price below the expected spot price.
As a consequence, the futures price is expected to appreciate over time,
because the futures price has to equal the spot price at expiration of
the contract. The notion of normal backwardation involves a comparison
of the futures price to the expected spot price in the future, which is
unobservable when the futures price is set. In the practice of commodity
trading backwardation is commonly used to describe the position of futures
prices in relation to current spot prices (or to characterize the prices
of futures contracts for the same commodity but with different maturities).
A commodity is said to be "backwardated" if the prices for future delivery
are below the price in the spot market. While "normal backwardation" in
the sense of Keynes is equivalent to the existence of a positive risk
premium, backwardation in the latter sense is not. For example, assume
as in the example in Figure 1, that the current spot price of oil is $30.
But now let's change the example and assume that market participants expect
the future spot price to be $34, and that speculators and hedgers agree
to set the futures price at $32, offering a $2 risk premium to speculators
for assuming price risk. The market is in "normal backwardation" (futures
below expected spot), but not backwardated in the second sense because
the futures is above the current spot (contango). The two definitions of backwardation are often used
interchangeably - as if they were equivalent. But only backwardation in
the sense of Keynes refers to the notion of a positive risk premium to
investors in commodity futures. Where the futures contract trades relative
to the current spot does not directly speak to the presence of a risk
premium. In an efficient market, it is unlikely that trading on publicly
available information will lead to abnormal profits. In Section 5, above, we showed that on average the
equally weighted commodity futures index displays a large risk premium.
This is consistent with Keynes' idea. But, the second notion of backwardation
should not have anything to do with a positive risk premium. To verify
this we conducted two experiments. First, we computed for each commodity
the average historical return and the average percentage of months that
commodity was in backwardation. Figure 14 illustrates that there does
not seem to be any systematic relationship between the two. A simple cross-sectional
regression of average returns on average % backwardation has an R-squared
of 3%. The slope coefficient is positive, but it is insignificantly different
from zero. The conclusion from this figure is that commodities that have
been more backwardated (by the second definition) have not earned larger
historical returns. In the second experiment we examined whether a strategy
that invests in the most backwardated commodities (by the second definition)
outperforms a strategy that invests in the least backwardated commodities.
We implement this as follows. At the end of each month since July 1959,
we sort the available commodities based on their degree of backwardation,
and divide them into two portfolios (highest and lowest backwardation).
After each ranking, we hold our position for a month. At the end of the
month we re-rank the commodities based on backwardation, and rebalance
our portfolios for the next month. Figure 15 shows the cumulative performance of these
two portfolios. Consistent with market efficiency, there is no noticeable
difference between the performance of the two indices. Backwardation -
defined as the difference between the current futures price and the current
spot price - carries no information about the relative attractiveness
of investment in commodity futures. If instead of comparing the spot price to the nearest
maturity futures price, two futures prices corresponding to different
maturities are compared to determine backwardation, in the second sense,
the above results do not change. To reiterate, none of this is surprising
if futures markets are efficient, as it should not be possible to profitably
trade on the basis of public information. 10. Commodity Futures in an International Setting
The majority of commodities in our index are traded
on US exchanges - with the exception of some metals that are traded in
London. Physical delivery takes place at a location within the contiguous
48 states, and settlement is in US dollars. The US markets for some commodities
(gold, crude oil) are probably integrated with global markets, but prices
of others are likely to be influenced by local conditions (natural gas,
live hogs). It is conceivable that a common country-specific US factor
has positively influenced both stock and commodity futures returns in
the US. If that were the case, commodity futures might look quite different
from the perspective of a foreign investor. Therefore, it is interesting
to ask whether a Japanese or UK investor would draw the same conclusion
as a US investor about the relative performance of these asset classes.
Figures 16 and 17 illustrate the performance of commodities
from the perspective of UK and Japanese investors. The equity benchmarks
we use are the total return indices from Morgan Stanley Capital International
(MSCI) for the UK and Japan, and the cumulative performance of long-term
government bonds in both countries published by the International Monetary
Fund. All indices are computed in local currency (GBP and YEN), and deflated
by the local CPI-index. Similarly, for commodity futures we compute the
performance of the index measured in GBP and Yen, before deflating it
by the local CPI.1717 The collateral for the futures position
is US T-bills. It is possible to collateralize the futures position by
Three observations stand out from Figures 16 and 17:
1. Between 1970 and March of 2004 the historical performance of commodities
has been similar to equities in both the UK and Japan. Commodity Futures
have outperformed long-term government bonds 2. Commodity Futures have outpaced local CPI inflation
in the UK and Japan. 3. The relative rankings of inflation-adjusted performance
Stocks, Bonds, and Commodity Futures are the same in the Japan, the UK,
and the US. Our earlier conclusions about the relative performance
of commodity futures have not been specific to the US experience. Foreign
investors - evaluating performance in local currency, and relative to
local inflation - would have drawn the same conclusions.18
18 We are in the process of validating the hedging and
diversification properties of commodity futures from the perspective
of foreign investors.
11. Commodity Futures vs. Stocks of Commodity
Producing CompaniesIt is sometimes argued that the equities of companies
involved in producing commodities are a good way to gain exposure to commodities.
In fact, some argue that the stocks of such "pure plays" are a substitute
for commodity futures. We can examine this argument by constructing an
index of the stock returns on such companies and then comparing the performance
of this index to an equally weighted commodity futures index. In order
to make this comparison we need to identify companies that can be most
closely matched with the commodities of interest. There is no obvious
way to match companies with commodities since companies are almost never
"pure plays," but rather are involved in a number of businesses. We chose
to match based on a simple rule, namely, with each commodity that can
be associated with a four-digit SIC code, we take all the companies with
that same four-digit SIC code. On this basis we can match 17 commodities
with companies having publicly-traded stock. The details are in Appendix
4. Figure 18a shows a significant difference between
the average return of commodity futures and investment in commodity company
stocks. Over the 41-year period between 1962 and 2003 the cumulative performance
of futures has been triple the cumulative performance of "matching" equities.
A plot of the same indices on a logarithmic scale
indicates that the two investments have limited correlation as well -
the full-sample average monthly correlation is 0.38. The conclusion of
Figure 18 is that an investment in commodity company stocks has not been
a close substitute for an investment in commodity futures. 12. Summary This paper provides evidence on the long-term properties
of an investment in collateralized commodity futures contracts. We construct
an equally-weighted index of commodity futures covering the period between
July 1959 and March 2004. We show empirically that there is a large difference
between the historical performance of commodity futures and the return
an investor of spot commodities would have earned. An investor in our
index of collateralized commodity futures would have earned an excess
return over T-bills of about 5% per annum. During our sample period, this
commodity futures risk premium has been equal in size to the historical
risk premium of stocks (the equity premium), and has exceeded the risk
premium of bonds. This evidence of a positive risk premium to a long position
in commodity futures is consistent with Keynes' theory of "normal backwardation".
In addition to offering high returns, the historical
risk of an investment in commodity futures has been relatively low - especially
if evaluated in terms of its contribution to a portfolio of stocks and
bonds. A diversified investment in commodity futures has slightly lower
risk than stocks - as measured by standard deviation. And because the
distribution of commodity returns is positively skewed relative to equity
returns, commodities have less downside risk. Commodity futures returns have been especially effective
in providing diversification of both stock and bond portfolios. The correlation
with stocks and bonds is negative over most horizons, and the negative
correlation is stronger over longer holding periods. We provide two explanations
for the negative correlation of commodities with traditional asset classes.
First, commodities perform better in periods of unexpected inflation,
when stock and bond returns generally disappoint. Second, commodity futures
diversify the cyclical variation in stock and bond returns. On the basis of the stylized facts we have produced,
two conclusions are suggested. First, from the point of view of investors,
the historical performance of collateralized investments in commodities
suggests that commodities are an attractive asset class to diversify traditional
portfolios of stocks and bonds. Second, from the point of view of researchers,
there are clearly challenges for asset pricing theory, which to date has
primarily focused on equities. Appendix 1: Construction of the Equally-Weighted
Commodity Futures Index The equally-weighted index is constructed using Commodity
Research Bureau (CRB) data (http://www.crbtrader.com/crbindex/ndefault.asp)
and data from the London Metals Exchange.19 The CRB data set
covers all commodity futures that are in existence today from the date
of inception. Commodity futures contracts that were introduced, but later
discontinued - due to lack of liquidity - are not covered by the CRB,
and are not included in the equally-weighted index. As discussed in the
main text, this omission is a type of survivor bias, but is fundamentally
different from survivor bias in other asset classes, like mutual funds
and stocks. In other asset classes, assets disappear because they had
low returns or failed. Consequently, calculating returns that omit these
assets biases the returns upwards. In the case of commodity futures, contract
types do not disappear because of failure in the same sense. Rather, there
is a lack of liquidity, not low returns. (See Black (1986) and Carlton
(1984).) Therefore, this type of survivor bias is less of an issue here.
We construct the equally-weighted commodity futures
index in steps. First, we construct monthly returns on each commodity
future using the nearest contract, which on the last business day of the
month before expiration is rolled into the next nearest contract. The
return is computed assuming that the futures position is fully collateralized
and marked-to-market on a daily basis and earns interest on the daily
basis (based on the current 91-day Treasury Bill auction rate). Second, using monthly returns for each commodity,
we construct the index by adding the monthly returns together each month
and dividing by the number of commodities in the index that month. A commodity
enters the index on the last business day of the month following its introduction
date except the first seven commodities entered the index on 07/01/59,
not 07/31/59. This corresponds to monthly rebalancing. The table below
shows the introduction dates of the commodities. For Lean Hogs the contract
specification changed in 1996 from Live Hogs to Lean Hogs. We used the
CRB backfill of Lean Hogs to the introduction date of Live Hogs.
19 We used only the contracts listed in the table below.
Before October 1993, we interpolate between cash and three month
forward prices to get the futures price for the third Wednesday
expiration for January, March, May, July, September, and November.
After October 1993 we used data from the third Wednesday of January,
March, May, July, September, and November.
Source: NBER, http://www.nber.org/cycles.html
Appendix 4: Matching Commodity-Producing Firms
to CommoditiesAs mentioned in the main text, we chose to match companies
with commodities based on associating with each commodity a four-digit
SIC code. We then search the University of Chicago Center for Research
in Security Prices monthly stock database for all the companies with that
same four-digit SIC code. On this basis we can match 17 commodities with
companies having publicly-traded stock. For all companies with same SIC
code we form the equally weighted monthly stock return series, and then
using these series we form the equally weighted commodity-producing firms
stock index. There were several exceptions to the general rule.
In the case of Palladium, we looked at SIC codes 1099 and 1090, i.e.,
Misc. Metal Ores. This category includes companies mining palladium, but
it also includes companies mining uranium and other metals. From the list
of all these companies we found two palladium mining companies, namely,
North American Palladium (PAL) and Stillwater Mining (SWC); the remaining
companies were ruled out. Silver does not occur in a pure form. It is usually
found as a byproduct of either gold and copper ores or lead and zinc ores.
SIC code 1044 "Silver Ores" contains very few stocks, especially in the
recent period. There is, however, an SIC code 1040 - "Gold and Silver
Ores". There are about 200 stocks with this SIC code. Among these stocks
we were able to identify several companies specifically focusing on silver
- Pan Amer Silver (PAAS), Silver Standard Resources (SSRI), Apex Silver
Mines Ord (SIL), Helca Mining (HL), and Coeur d'Alene Mines (CDE). These
stocks were added to silver stocks. The rest of the stocks in the 1040
SIC code "Gold and Silver Ores" were added to gold stocks. In the case of Milk, we looked at SIC code 2020. From
the SIC code 2020 "Dairy Products" we excluded all stocks that we could
identify as ice cream producers - these are consumers of milk, not producers
of milk. The remainder were taken as Milk stocks. The table below provides
the detail on the number of stocks for each commodity and the period covered.
If there are zero stocks, then that commodity was not included because
not matching company could be found.
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