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January 25, 2008

Working Paper Synopsis: The Search for the Beta of Commodity Futures
by MA-Research.com

This article summarizes the working paper available at SSRN: http://ssrn.com/abstract=1029243

Is Managed Futures an Asset Class?
The Search for the Beta of Commodity Future

Study suggests that financial models have shortcomings when analyzing the commodity futures markets.

Introduction: Alpha and Beta Quandary

In accordance with the principles of modern portfolio theory, sophisticated investors have increasingly sought to diversify their portfolio through the use of alternative investments. An "alternative investment" is generally regarded as supplementary assets or trading strategies other than long-only exposure to "traditional assets" such as stocks, bonds and/or cash. Alternative investments include various assets such as commodities, currencies, emerging markets and private equity, as well as a variety of trading strategies such as convertible arbitrage, distress securities, global macro, long-short equities, managed futures, short selling, etc.

Adherents commonly assert that alternative investments has (i) a low to negative correlation compared to traditional investments, (ii) historical performance which reflects the potential for attractive positive expected returns, and (iii) is capable of acting as a hedge against inflation. In line with this thinking, and as a proxy to describe such characteristics, the term "alpha," something which is intended to measure a manager's skill-based returns, has ostensibly become synonymous with hedge funds and by extension alternative investments. The combination of these factors suggests that, within the diversification tenets of modern portfolio theory, a strong case can be made for the inclusion of alternative investments in traditional portfolios.

Alpha is typically defined as the excess return that results from active portfolio management adjusted for the risk of a comparable risky asset, portfolio or benchmark. However, as Schneeweis (1999) pointed out in his article "Alpha, Alpha, Whose got the Alpha?" it is inappropriate to compare investment returns to a benchmark, unless the investment strategy being analyzed responds to the same return drivers of the cited benchmark. Similarly, it is inappropriate for a manager to make a claim of positive alpha simply because investment returns are greater than the risk free rate, unless the portfolio is risk-free.¹ Accordingly, investors should first be concerned with the appropriateness of the reference benchmark and factors used.

Conventional investment theory states that when an investor constructs a well-diversified portfolio, the unsystematic sources of risk are diversified away leaving the systematic or non-diversifiable source of risk as the relevant risks. The capital asset pricing model (CAPM), developed by Sharpe (1964),² Lintner (1965)³ and Black (1972)⁴ [zero-beta version], asserts that the correct measure of this riskiness is its measure known as the 'beta coefficient' or just "beta." Effectively, beta is a measure of an asset's correlated volatility relative to the volatility of the overall market. Consequently, given the beta of an asset and the risk-free rate, the CAPM should be able to predict the expected return for that asset, and correspondingly the expected risk premium as well. This explanation is textbook.

However, unbeknownst to most investors, there has been a long running argument in academic circles on the CAPM and other pricing models, even within the milieu of traditional investments. Without going into the details of this debate, certain empirical studies have revealed "cross-sectional variations" in the CAPM questioning the "validity" of the model. In direct response to the challenge by Fama and French (1992),⁵ Jagannathan and Wang (1993, 1996) theorized that "...the lack of empirical support for the CAPM may be due to the inappropriateness of some assumptions made to facilitate the empirical analysis of the model. Such an analysis must include a measure of the return on the aggregate wealth portfolio of all agents in the economy."⁶

Taking into consideration the globalization and integration of the world's economies, and for the purpose of our study on the commodity futures markets, we have extended the definition of "true market portfolio" or "true beta" to encompass the "aggregate wealth portfolio of all agents in the global economy," something plausibly related to 'gross global product' (GGP).⁷ The advantage of this adaptation of Jagannathan and Wang's archetype is that it is a closed box system, yet one which theoretically encompasses all economic factors that exist in the real world. As such, it provides a broad context in which to commence a thorough search for the beta of commodity futures, as well as a framework in which to validate this cerebral concept.

Framing the Futures Market Beta Debate

It is generally assumed that organized futures markets provide important economic benefits. This premise, that properly functioning futures markets serve a valuable economic purpose, is validated by government policy.⁸ The primary benefit provided by these markets is that it allows commercial producers, distributors and consumers of an underlying commodity to hedge.⁹ This reduces the risk of adverse price fluctuations that may impact business operations, which in turn theoretically results in increased 'capacity utilization.'¹⁰ Hence, it follows that the reallocation of risk affords a reduction in prices for commodities because businesses need not offset adverse price change risk with increased margins on products or services.

Such economic benefits should be realized by the businesses that utilize futures markets for bona fide hedging purposes. For that reason, we have assumed that factors such as capacity utilization, price discovery and reduced price volatility are reflected in the economy and therefore in business earnings. Since businesses fall into the category of traditional investments, and the beta proxies for stocks and bonds are well represented, this segment of "true beta" is not the focus of our working paper.

Rather, our investigation starts with established precepts that form the basis of academic studies which attempt to model the sources of return in the futures market. That is, the beta of futures emanates from capturing the "risk premia" hedgers supposedly offer speculators for assuming the risk that hedgers (i.e., aforementioned businesses) are trying to offset. Correspondingly, there are a variety of ideas influencing commodity pricing theory, including: the insurance aspect of commodity futures contracts, which emphasizes the role of the speculator; the theory of storage, which emphasizes the behavior of the inventory holder and commercial hedger; and the importance of yields as a long-term driver of commodity returns.¹¹

The insurance-like context was first proposed by Keynes (1930) in his theory of 'normal backwardation.'¹² Essentially, Keynes believed that hedgers have to pay speculators a risk premium to convince them to accept their risk. A key attribute of this theory is the concept of "congenital weakness" on the demand side for commodities. Theoretically, the expected future spot price is driven down because the commodity is held back from the market and kept in storage. Holding back a commodity in storage is referred to as a "convenience yield," and together with congenital weakness forms the basis of the phenomenon known as "backwardation." These concepts are now part of mainstream thinking.

Nevertheless, the legacy of empirical tests using a variety of asset pricing models, including the CAPM, hedging-pressure hypothesis, or arbitrage pricing theory, have produced inconsistent results as to whether there is, in fact, positive expected returns from speculating in the futures market. The paradox is that for every buyer of a futures contract there is a seller -- a zero sum game. Further, as noted by Greer (1997), the inherent problem with reconciling the CAPM to investment in commodities may be that these "real assets" are not capital assets but instead consumable, transformable and often perishable assets with unique attributes.¹³ Hence, speculative trading, by definition any trading done for financial rather than commercial reasons, likely results in "zero systematic risk," an assertion indirectly supported by the CFTC's Chief Economist in a 2005 staff study.¹⁴

Recently, however, there seems to be a rash of industry papers supportive, if not presumptive, of the idea of a "structural risk premium" in the commodity futures markets. One of the major ideas being touted is that of the "roll return" or "roll yield" which is said to occur when traders "roll the futures contract forward." Given the bullish commodity markets over the past several years, the perspective of these studies is not surprising.

Models of Equilibrium or Disequilibrium?

Our working paper investigated various models which deal with the potential sources of return to speculators in the futures market, including one of our own which exemplifies the complexity of these markets. Admittedly, models are only an abstraction from reality. Expecting such models to be exactly right is unreasonable, and it is generally understood that neoclassical economic theory has inherent limitations related to the analysis of markets within the context of "rational equilibrium systems." Such systems are based on perfect competition, and assume markets naturally return to equilibrium after a disturbance. Hence, modern finance seeks to maximize utility and/or profits in a world of constraints based on the choices of "rational" economic agents. By definition then, these models relegate speculators to the role of that very agent which maintains equilibrium.

Yet a survey of real-life speculators reveals that these practitioners do not as a general rule use academic models in their day-to-day trading decisions.¹⁵ Paradoxically, this same group plays a key influence upon the selfsame futures data from which such models are constructed. So if the data series is assumed to represent equilibrium and "the future is merely the statistical reflection of the past,"¹⁶ then one could inversely argue that perfect competition and rational expectations minimize these models' usefulness as a mechanism from which to make speculative decisions. In other words, rational expectations compel such models to simply validate that current price data is equal to equilibrium, unless the opposite is true -- that markets are in fact imperfect and rational expectations is untenable, which in turn undermines the veracity of these models.

Correspondingly, our investigation shows that the legacy of research is inconclusive with respect to modeling the sources of returns in the futures markets, largely because these models have inherent shortcomings in being able to pinpoint a definitive source of structural risk premium within the complexity of such markets. We hypothesize that the classic arbitrage model contains circular logic, and as a consequence, its natural state is disequilibrium, not equilibrium. We extend this hypothesis to suggest that the "term structure of the futures price curve," while indicative of a potential roll return benefit (or detriment), in fact implies a complex and reflexive series of roll yield permutations. Similarly, the hedging response function elicits a behavioral risk management mechanism, and therefore, corroborates social reflexivity.

However, we are not saying that commodity futures pricing models are erroneous. Rather, while conceived and constructed using rational expectations equilibrium and so interpreted within that framework, the models arguably imply disequilibrium and reflexivity. Further, these models do not operate to the exclusion of the other, nor exclusively from each other; rather, such models are inter-related and each reflect certain aspects and dynamics within the overall futures market paradigm. Hence, we posit that the combination of models we investigated support a post-Keynesian view that the world is messy and uncertain.

Conclusion: Beta of Futures is Behavioral

We do not dispute that the futures markets offer vicarious economic benefits, such as price discovery, price liquidity, reduced price volatility and therefore increased capacity utilization. But again, such attributes benefit the businesses that utilize the futures markets, as well as the economy as a whole, not necessarily speculators. If there is a risk premium that speculators capture from the futures markets, it is likely sourced from irrational behavior and market disequilibrium. If that is the case, then what does that say about commodity asset pricing models founded on the premise of perfect markets and rational expectations?

We suggest that commodity asset pricing models, which are conventionally regarded as validation for persistent and replicable sources of return in the commodity futures markets, may be widely misunderstood. Notably, there are various institutional pressures and economic incentives which lead to the usage of benchmarks and passive indices. Modeling provides the justification for creating and bringing to market many innovative but untested "beta replication" investment products. These investment vehicles for the most part make sense and are justifiable since their underlying investments are capital assets. But... caveat emptor -- the product development process is also a reflexive economic activity. We contend that index vehicles based on commodity assets may prove over the long run to not be the reliable and consistent source of positive expected returns as is propositioned.

The hedging response model, for example, supports the idea that if the wisdom of crowds is balanced, then trends will evolve which the speculator can take advantage of (in a leveraged manner, we will add). However, if the madness of crowds goes too far one way or the other, then a speculator will step in with a counter-trend strategy. If correct, such speculator will be rewarded with sufficient positive returns to have made the bet worth the risk -- but the result may be asymmetric! Others will have lost, and on the whole, the summative profit-loss outcome theoretically remains symmetric -- hypothetically a zero sum game.

Models are not exclusive and each reveals underlying qualities within the "aggregate wealth portfolio of all agents in the global economy." However, unto themselves, they do not provide that one universal asset pricing solution which encompasses all cross-sectional variations. What these models convey is an insightful understanding, provided one accepts that in the real world agents are irrational,¹⁷ that markets drift from disequilibrium to equilibrium and back, and inputs/outputs are reflexive.

Applicability to Portfolio Diversification

So how does "managed futures" relate to our working paper and this article? Simply, managed futures is where the theoretical becomes real world. Those agents called 'speculators' in academic models are best represented in the real world by commodity trading advisors (CTAs). And while real-life speculators who do not hold themselves out to the public as such certainly exist, CTAs and to lesser extent commodity pool advisors, provide the best window into the actual trading practices and performance data of speculators.

At the same time, financial institutions have not been left behind by evolving academic theories. Index creation and benchmarking have become standard fare, and since the introduction of exchange traded funds (ETFs), a veritable industry has developed around the "multiple beta" concept. This backdrop is the principal context which gives impetus to the notion of "exotic betas." The term, a recent addition to the investment lexicon, suggests that certain alternative investment strategies, can be replicated employing a predefined "passive" methodology similar to traditional index construction. In fact, it is the very existence of the idea of exotic betas which is fueling the demand for tailored commodity investment products, such as Goldman Sachs "smart indexes" like GS Connect S&P GSCI Enhanced Commodity Total Return Strategy Index Exchange Traded Note (Symbol: GSC), which uses seasonal and other pricing trends.

This leaves open the question as to whether institutions, through sophisticated financial engineering, can truly capture in a passive way all possible sources of return in the global economy, or if some aspect which the industry loosely calls alpha (i.e., skill-based returns) always remain outside the grasp of these institutions' arbitrary models of beta proxies. At minimum, the legacy of academic research is contradictory and has not yet proved or disproved conclusively that a persistent structural risk premium exists within the commodity futures market.

As for managed futures, in our opinion it is an observable materialization of behavioral finance, where risk, return, leverage and skill operate un-tethered from the anchor of an accurate representation of beta. In other words, it defies rational expectations equilibrium, the efficient market hypothesis and allied models -- the CAPM, arbitrage pricing theory or otherwise -- to isolate a persistent source of return without that source eventually slipping away. Harking back to the old school, over the long-term speculative returns in the commodity futures markets are likely to revert to the mean, which is near zero, if not less than zero due to commissions. But that also doesn't mean there cannot be a secular bull market in spot returns.

So let's say futures market speculation is a zero sum game, then are the returns from managed futures other than zero -- alpha?" The answer to that is "no." It is inappropriate for a manager to make a claim of positive alpha simply because investment returns are greater than the risk free rate, unless the portfolio is risk-free. Managed futures is not risk-free. But that doesn't mean that certain speculators don't have an edge -- the adept consistently capture risk premia from the wisdom of crowds and/or the madness of crowds.

[1] Schneeweis, Thomas (1999). "Alpha, Alpha, Whose got the Alpha?" University of Massachusetts, School of Management.

[2] Sharpe, William F (1964). "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk" Journal of Finance 19, September, pp. 425-442.

[3] Lintner, John (1965). "The Valuation of Risk Assets and the Selection of Risk Investments in Stock Portfolios and Capital Budgets" Review of Economics and Statistics 47, February, pp. 13-37.

[4] Black, Fischer (1972). "Capital Market Equilibrium with Restricted Borrowing" Journal of Business 45, July, pp. 444-455.

[5]5 Fama, Eugene F.; French, Kenneth R. (1992). "The Cross-Section of Expected Stock Returns" Journal of Finance 47, June, pp. 427-465.

[6] Jagannathan, Ravi; McGrattan, Ellen R. (1995). "The CAPM Debate" Federal Reserve Bank of Minneapolis Quarterly Review, Vol. 19, No. 4, Fall 1995, pp. 2-17; Jagannathan, Ravi; Wang, Zhenyu (1993). "The CAPM is Alive and Well" Research Department Staff Report 165. Federal Reserve Bank of Minneapolis; Jagannathan, Ravi; Wang, Zhenyu (1996). "The Conditional CAPM and the Cross-Section of Expected Returns" Journal of Finance, Vol. 51, No. 1, March, pp. 3-53.

[7] The World Bank. Global Citizen's Handbook: Facing Our World's Crises and Challenges. Collins. 2007

[8] In testimony on November 2, 2005 before the Committee on Energy and Commerce United States House of Representatives, Reuben Jeffery III, Chairman U.S. Commodity Futures Trading Commission stated that "Futures markets play a critically important role in the U.S. economy."

[9] By using futures or forward contracts to hedge, a producer, distributor or consumer of an underlying asset can establish a temporary substitute for a cash market transaction that will be made at a future date.

[10] Capacity utilization is a metric used to measure the rate at which potential output levels are being met or used. Capacity utilization rates can also be used to determine the level at which unit costs will rise.

[11] Till, Hilary (2007). "Part I of A Long-Term Perspective on Commodity Futures Returns: Review of the Historical Literature" from Intelligent Commodity Investing, (Till, and Eagleeye, Ed.), Published by Risk Books, a Division of Incisive Financial Publishing, Ltd., pp. 39-82.

[12] Keynes, John Maynard (1930). "A Treatise on Money, Volume II: The Applied Theory of Money" London: Macmillan, 1930, pp. 142-147.

[13] Greer, Robert J. (1997). "What is an Asset Class, Anyway?" Journal of Portfolio Management, Winter, 86-91.

[14] Haigh, Michael; Hranaiova, Jana; Overdahl, James (2005). Office of the Chief Economist, Commodity Futures Trading Commission, Price Dynamics, Price Discovery and Large Futures Trader Interactions in the Energy Complex, Working Paper, First Draft: April 28, 2005.

[15]5 An exception to this assertion is the Black-Scholes option pricing model, which is widely used by practitioners.

[16] Davidson, Paul (1982). "Is Probability Theory Relevant for Uncertainty? A Post Keynesian Perspective" The Journal of Economic Perspectives, Vol. 5, No. 1 (Winter, 1991), pp. 129-143

[17] The Sonnenschein-Mantel-Debreu theorem relates the application of rational expectations to aggregate behavior and theorizes that assumptions about individual behavior do not carry over to aggregate behavior. Therefore, within the context of financial modeling, irrationality of real world agents may develop on three levels: (1) agents may act on imperfect information; (2) agents may follow a set of priorities that is rational within the context of personal agenda, but which may be deemed irrational from an economist's perspective; and (3) pure human irrationality.

The Search for the Beta of Managed Futures (Part 1)
by Mack Frankfurter

This draft research article has been submitted for review. Email comments to: comment@cervinocapital.com

Is Managed Futures an Asset Class?
The Search for the Beta of Managed Futures (Part 1)

I. Introduction: Alpha and Beta Concepts

It is difficult to be an investment professional nowadays and avoid the subject of 'alpha,' something which is intended to measure a manager's skill-based returns. The term, which is derived from statistics, is the byproduct of a linear regression that relates an observed variable y to some factor x, resulting in the equation α = y - βx - ε, where α (alpha) represents the intercept, β (beta) represents the slope, and ε (epsilon) represents a random error term. In finance, alpha is defined as the excess return that results from active portfolio management adjusted for the risk of a comparable risky asset or opportunity set. In industry practice, the term has become a marketing devise.

As Schneeweis (1999) pointed out in his article "Alpha, Alpha, Whose got the Alpha?" it is inappropriate to compare investment returns to the S&P 500, or any other benchmark, unless the investment strategy being analyzed responds to the same return drivers of the S&P 500 or the cited benchmark. Similarly, it is inappropriate for a manager to make a claim of positive alpha simply because investment returns are greater than the risk free rate, unless the portfolio is risk-free. Accordingly, investors should first be concerned with the appropriateness of the reference beta.

Conventional investment theory states that when an investor constructs a well-diversified portfolio, the unsystematic sources of risk are diversified away leaving the systematic or non-diversifiable source of risk as the relevant risks. The capital asset pricing model (CAPM), developed by Sharpe (1964) and Lintner (1965) [and Black's (1972) zero-beta version], asserts that the correct measure of this riskiness is its measure known as the 'beta coefficient' or just 'beta.' Effectively, beta is an index of an asset's correlated volatility relative to the volatility of the overall market. Consequently, given the beta of an asset (and the risk-free rate), the CAPM should be able to predict the expected risk premium (i.e., the expected return) for that asset.

The above explanation is textbook. However, unbeknownst to most investors, there has been a long running deliberation in academic circles on the CAPM and other pricing models, even within the milieu of traditional investments. The evolution of this dispute is thoroughly documented by Jagannathan and McGrattan (1995) in their article, "The CAPM Debate" published by the Federal Reserve Bank of Minneapolis Quarterly Review. The following inquiry (paraphrased from this article) describes the crux issue with respect to how accurately the CAPM performs in determining beta when empirically tested:

When the CAPM assumptions are satisfied, the model predicts that the ratio of the risk premium to the beta of every asset is the same. That is, every investment opportunity provides the same amount of compensation for any given level of risk, when beta is used as the measure of risk. Hence, the betas computed with reference to every individual's portfolio will be the same, and one might as well compute betas using the market portfolio of all assets in the economy. Accordingly, if expected returns vary across assets, it is only because the assets' betas are different. Therefore, one way to investigate whether the CAPM adequately captures all the important aspects of reality is to test whether other asset-specific characteristics can explain the cross-sectional differences in average returns that are unrelated to cross-sectional differences in beta. As a result, in empirical evaluations of the CAPM, researchers want to know if beta is the only characteristic that matters.¹

The earliest empirical studies of the CAPM, including that of Black, Jensen and Scholes (1972) and Fama and MacBeth (1973) concluded that the data was consistent with the predictions of the CAPM. Banz (1981), however, challenged the CAPM and found that a significant factor, firm size, explained cross-sectional variation in average returns on a collection of assets better than beta. The reaction to Banz's findings was that, while the data showed some systematic deviations, such anomalies were not economically important enough to reject the CAPM outright. This view was challenged by Fama and French (1992), who concluded that "Banz's findings may be economically so important that it questions the validity of the CAPM," and that explanatory variables such as the book-to-market equity ratio better explained cross-sectional variation in average asset returns. In response, a series of counter-challenges to Fama and French, while supportive of the CAPM, revealed a variety of other potential statistical concerns, including noisy data, sample period effect and survivorship bias.

Nonetheless, Fama and French's (1992) core challenge has remained that the "resuscitation of the [Sharpe 1964, Lintner 1965, Black 1972] model requires that a better proxy for the market portfolio... leaves β (beta) as the only variable relevant for explaining average returns." As a consequence, academic and institutional focus has shifted to alternative asset pricing methods involving the development of 'multi-factor models.' These additional factors have extended beyond the use of broad stock market indices in order to capture intangible assets such as human capital, variables such as business cycles, as well as other attributes.

Meanwhile, in a direct response to Fama and French's (1992) challenge, Jagannathan and Wang (1993) theorized that "...the lack of empirical support for the CAPM may be due to the inappropriateness of some assumptions made to facilitate the empirical analysis of the model. Such an analysis must include a measure of the return on the aggregate wealth portfolio of all agents in the economy." By following Jagannathan and Wang's thought process to its logical conclusion, taking into consideration the globalization and integration of the world's economies, the authors hypothesize that the 'true market portfolio' or 'true beta' should be defined as the 'aggregate wealth portfolio of all the agents in the global economy,' something related to the "gross global product" (GGP).² The beauty of this archetype is that it is a closed box system, yet one which encompasses all possible economic activities that exists in the world, including alternative investments.

Financial institutions have not been left behind by these evolving academic theories. Since the introduction of 'exchange traded funds' (ETFs), a veritable industry has developed around the 'multiple beta' concept. But by no means has the plethora of these instruments captured every aspect of the aggregate wealth portfolio of all agents in the global economy. If one assumes that true beta is equivalent or linked to GGP, it becomes evident that the customary benchmarks for beta, such as the S&P 500, Russell 1000, Lehman Brothers Aggregate Bond Index, and S&P GSCI™ Commodity Index, etc., and even economic indicators such as the Consumer Price Index, Employment Report, etc. represent arbitrary slices or aspects of true beta. Further, the overlapping and inherently reflexive nature of these benchmarks' intrinsic attributes becomes apparent.

The authors suggest that this is the principal context which gives impetus to the notion of 'exotic betas.' The term, a recent addition to the investment lexicon which evolved from within the context of alternative investments, propositions that certain alternative investment assets and/or strategies, representing commonly pursued market paradigms, can be identified, replicated and tracked employing a predefined approach/model similar to traditional index construction. It is from this presupposition -- that the 'true market portfolio' is defined as the aggregate wealth portfolio of all the agents in the global economy -- where we begin our investigation into the problem of how to determine the beta of the futures market.

II. Framing the Futures Market Beta Debate

It is assumed that organized futures markets provide important economic benefits. This premise, that properly functioning futures markets serve a valuable economic purpose, is validated by government policy.³ The secondary benefit provided by the futures market is that it functions as a mechanism for transparent price discovery and liquidity, which therefore mitigates price volatility. However, the primary benefit provided by these markets is that it allows commercial producers, distributors and consumers of an underlying cash commodity or financial instrument to hedge.⁴ This reduces the risk of adverse price fluctuations that may impact business operations, which in turn theoretically results in increased 'capacity utilization.'⁵ Hence, it follows that the reallocation of risk affords a reduction in prices of the underlying commodity because businesses need not offset adverse price change risk with increased margins on products or services.

These economic benefits should be realized by the businesses that utilize futures markets for bona fide hedging purposes. As a consequence, such factors (i.e., capacity utilization, price discovery, liquidity and reduced price volatility) are assumed to be reflected in the economy and therefore in business earnings. Since businesses fall into the category of traditional investments, and beta proxies for stocks and bonds are well represented, this segment of 'true beta' is not the focus of our research. Rather, our investigation starts with established precepts that form the basis of academic studies which attempt to model the sources of return in the futures market. That is, the beta of futures emanates from capturing the 'risk premia' hedgers supposedly offer speculators for assuming the risk that these aforementioned businesses are trying to offset.

This insurance-like context was first proposed by Keynes (1923, 1930) in his theory of 'normal backwardation.' Essentially, Keynes believed that hedgers have to pay speculators a risk premium to convince them to accept their risk. A key attribute of this theory is the concept of 'congenital weakness' on the demand side for commodities. As expounded by Hicks (1939, 1946), "undiversified producers are in a more vulnerable position than consumers, who can choose amongst alternatives as well as time their purchase. Given that producers are more vulnerable to commodity price fluctuations, they will consequently be under more pressure to hedge than consumers."⁶ Another attribute of Keynes theory relates to actual business operations. For example, a producer's current commitment to deliver an underlying commodity in the future may supersede the increased reward that could result from selling the underlying in the future. Therefore, the current expectation of the future spot price (which is actually an unknown) is theoretically driven down because the commodity is held back from the market and kept in storage. As described by Kaldor (1939), holding back a commodity in storage is referred to as a 'convenience yield,' and together with congenital weakness, these factors form the basis of the phenomenon known as 'backwardation.'

That said, the legacy of academic studies using a variety of asset pricing models, including CAPM/C-CAPM, Hedging-Pressure Hypothesis, or General Equilibrium Theory, have produced inconsistent results as to whether there is, in fact, positive expected returns from speculating in the futures market or just zero systematic risk (i.e., futures trading sans transaction costs is a zero sum game). Dusak (1973) was the first to investigate the beta of the futures market using the CAPM and found zero systematic risk. However, Bodie and Rosansky (1980) and Fama and French (1987) found positive expected returns which supported the theory of 'normal backwardation.' The list of academic research in this area is quite extensive and continues to grow.⁷ Even so, as documented by Allen, Cruickshank, Morkel-Kingsbury and Souness (1999), "there is no consistent evidence about the existence of normal backwardation despite a long tradition of research which dates back to Keynes (1930), Hardy (1940), Working (1948, 1949), Houthakker (1957), Telser (1958, 1967), Cootner (1960, 1967), Rockwell (1967) and Dusak (1973)."

Paraphrasing Spurgin (2000), the argument against speculating in futures is based on the premise that if there were excess returns to speculative capital in futures trading, assuming there are participants willing to lose money over time such as risk averse hedgers, then since barriers to entry for trading futures are low, so much capital would flow to this industry that returns would be driven to zero over time, and as a result returns would be spread so thinly that economic profits would not be possible. A recent study by Erb and Harvey (2006) posits the question: "for investors considering a long-only investment in commodity futures: how can a commodity futures portfolio have 'equity-like' returns when the average returns of the portfolio's constituents have been close to zero?" As noted by Ebrahim and Rahman (2004), who "echo" Bray (1992), Sheffrin (1996) as well as Malliaris and Stein (1999), "this discrepancy between theoretical assertions and empirical behavior is a puzzle. Is there something missing in the theory?"

The authors hypothesize that, in concurrence with Jagannathan and Wang's (1993, 1996) premise that the lack of empirical support for the CAPM may be due to inappropriate assumptions, some of the assumptions underlying academic models which analyze sources of return in the futures market may likewise be inappropriate. Further, it is dangerous to extrapolate past performance into multi-factor models as a means to predict future outcomes -- it should be well understood that expanding the number of factors, conditions and variables increases the likelihood of curve-fitting to historical data, also referred to as 'over-optimization.' Admittedly, models are only an abstraction from reality, expecting such models to be exactly right is unreasonable. Nevertheless, from the perspective of most real-life speculators, such theoretical models have little to do with how these practitioners (i.e., traders) actually speculate in the futures markets. That said, the models are not erroneous; rather, while conceived and constructed using rational expectations equilibrium and so interpreted within that framework, the models arguably imply disequilibrium and social reflexivity.

III. Models of Equilibrium or Disequilibrium?

Our research investigates two pivotal models which theoretically explain the sources of return to speculators in the futures market. First, we review the "arbitrage model" which ensures convergence of the futures contract price and the current spot price, and from which the concepts of backwardation and contango market conditions are derived. Second, we look at the "hedging response model" which is based on Spurgin's (2000) draft article "Some Thoughts on the Source of Return to Managed Futures," and from which he theorizes symmetric and asymmetric 'hedging response functions.' As this article is an abridged version, only the arbitrage model is discussed below.

Arbitrage Model

The arbitrage model focuses on the normal relation between the present state and future expectations of three variables: (i) the current spot price of an asset; (ii) the current futures or forward contract price of the underlying asset; and (iii) the expected spot price on delivery of the underlying asset sometime in the future. Let S₀ be the current spot price of the asset; F₀ be the current price for future delivery of the underlying asset, and E(S_t) be the expected spot price of the underlying asset on the delivery date. It is also noted that S₀ is a known variable equal to a price currently obtainable in the spot market for the underlying asset; F₀ is a known variable equal to the current futures or forward contract price quoted on a futures exchange or over-the-counter market; but that E(S_t) is an unknown variable which converts into S₀ at some future point in time.

There are two underlying arbitrage strategies (A) and (B), implying a third strategy (C)⁸ derived from the first two. These strategies are reviewed below:

(A) The first arbitrage strategy exploits the relation between S₀ and E(S_t). This relation is arbitraged by borrowing money and taking physical delivery of the commodity today, and selling the same commodity in the future at the then prevailing spot price. In this scenario, an equilibrium state is achieved when S₀ plus borrowing interest expense is equal to E(S_t). So theoretically, if S₀ < E(S_t), then arbitrageurs could make a profit by taking physical delivery of a greater quantity of the commodity today (driving up the current spot price), with the intention of selling a greater quantity of the commodity in the future (driving down the expected spot price).

(B) The second arbitrage strategy exploits the relation between F₀ and E(S_t). This relation is arbitraged by buying the futures contract today and taking physical delivery of the commodity when the contract expires, and at that time simultaneously selling the same commodity in the spot market. In this scenario, an equilibrium state is achieved when F₀ is equal to E(S_t). So theoretically, if F₀ < E(S_t), then arbitrageurs could make a profit by purchasing the futures contract (driving up the futures contract price), with the intention of taking delivery and selling the commodity at the prevailing spot market price in the future (driving down the expected spot price).

The above scenarios do not take into consideration storage (and transportation) costs, which if dominant, is stated to be responsible for producing the 'contango' phenomenon; nor does it take into consideration 'convenience yield,' which if dominant, is said to be the basis for the phenomenon known as 'backwardation.' In combination, storage costs and convenience yield is expressed as the 'cost-of-carry,' which is equal to borrowing interest expense plus storage costs minus convenience yield. As a result, E(S_t) should theoretically equal S₀ plus the cost-of-carry.

(C) Therefore, as a result of arbitrage strategies (A) and (B), assuming rational expectations equilibrium (that is, market participants are risk neutral, have perfect knowledge of supply-demand fundamentals, and transaction costs are zero) and arbitrage convergence is perfect, then F₀ should equal S₀(r,i,s,y,ε)^t, where r is the risk-free rate of return, i is interest expense associated with borrowing costs, s is the cost of storing and transporting a commodity, y is the 'convenience yield' as defined by Kaldor (1939), ε (epsilon) represents a random error term equal to zero, and t is the time to delivery of the underlying asset. This describes the third implied arbitrage.

Interestingly, the models states that if one assumes arbitrage convergence is imperfect, and there exists the presence of fundamental factors which lead to either (a) backwardation or (b) contango market conditions, the model deems it possible to have the E(S_t) (which is actually an unknown) valued above or below S₀(r,i,s,y,ε)^t, where ε represents a random error term which is either: (a) negative, if convenience yield dominates (backwardation) in which case F₀ < E(S_t); or (b) positive, if storage costs dominates (contango) in which case F₀ > E(S_t). In either scenario, the relationship between S₀ and F₀, while reflexive and material to the model, is not deliberated.

The authors argue that the preceding logic regarding (a) backwardation or (b) contango market conditions is an unworkable statement, which at worst is nonsensical because E(S_t) is by definition (and in reality) an unknown, or which at best infers a circular reference where arbitrage convergence is assumed to be perfect (i.e., market participants have the best available knowledge of fundamentals at any point in time, and if better information comes to light market prices will respond accordingly). Therefore, the question facing arbitrageurs, with respect to either of these scenarios, is how to determine: (1) whether ε is zero and either (y)^t or (s)^t has increased due to a change in fundamentals; or (2) whether ε is negative or positive, and an arbitrage opportunity exists. Since the model's logic is circular, the reflexive relationship between S₀ and F₀ should be under constant deliberation, as well as (y)^t and (s)^t. Therefore, if an arbitrage opportunity does exist, a speculator should be able to take advantage of the situation by either: (i) immediately buying S₀ and simultaneously selling F₀, or vice versa; or (ii) if a bona fide hedger by holding a long or short S₀ or F₀ and then delivering/taking E(S_t) when it converts into S₀.

As mentioned previously in this article, Keynes (1923, 1930) formulated his theory of 'normal backwardation' in the futures market, arguing that F₀ is typically less than E(S_t). This is based on the assumption that market participants are risk averse; therefore E(S_t) > S₀(r,i,c,y,ε)^t, which also implies that F₀ is naturally < E(S_t); accordingly, the futures markets are naturally backwardated. Further, commodity assets, which are used for consumption or production purposes, may not be easily shorted (S₀ borrowed and sold). As a consequence, arbitrage cannot force F₀ = S₀(r,i,c,y,ε)^t; rather, it can only assure that F₀ ≤ S₀(r,i,c,y,ε)^t ≤ E(S_t). Yet Keynes' model allows for the possibility of E(S_t) < S₀(r,i,c,y,ε)^t, which the authors note implies that F₀ can be > E(S_t).⁹ Accordingly, there are situations when Keynes' classic model acknowledges that futures markets can exhibit contango conditions, although the term was never specifically used by Keynes in describing his theory. Nevertheless, Keynes classic model does not detract from the concern that the model exhibits circular logic, rather the theory of congenital weakness just places certain constraints on the model.

At the time Keynes et alia offered little in terms of empirical evidence for the theory of normal backwardation: "Since the expected future spot price is not observable, the signature of normal backwardation will be the tendency of the forward price to rise (more than the opportunity costs of holding the commodity would suggest) as the delivery date approaches."¹⁰ Conventional wisdom remains, however, that for certain types of underlying assets, normal backwardation is the natural result of arbitrage pressures. Such notions persist despite studies such as Allen, Cruickshank, Morkel-Kingsbury and Souness (1999) who concluded that "few of the contracts studied consistently exhibit normal backwardation while many show evidence of contango."

The authors take the argument a step further and offer the following criticism as to why the research continues to produce contradictory results with respect to studies on futures market risk premia: Despite that rational expectations equilibrium is the underlying assumption, modeling the normal relation between the current spot price of an asset, or the current price for future delivery of an asset, versus the expected spot price of that underlying asset on the delivery date, will intrinsically encompass some form of circular logic, and accordingly be subject to reflexivity. Since the arbitrage model is actually a reflexive model, its natural state is disequilibrium, not equilibrium; therefore, the slightest change to any of the variables will result in price movement and trigger price momentum in that direction. This creates feedback within the arbitrage model, as well as reflective feedback within complimentary models such as Spurgin's (2000) hedging response model.

Regardless, the arbitrage model, while an abstraction from reality, provides significant insight into various aspects of how the futures market operates. Further, we do not claim that backwardated or contango market conditions do not exist -- individual hedgers can readily determine such conditions in relation to their specific business and economic situation at a particular point in time. Rather, it is impossible for the broad mass of market participants, specifically a "crowd" of speculators, to know perfectly whether ε is zero and (y)^t or (s)^t has increased due to fundamentals, or ε is negative or positive. Further, analysis of such fundamentals is highly prone to subjectivity and error -- this is well understood by professional traders who rely on money management techniques, and perhaps why the key to Spurgin's (2000) hedging response model is a behavioral risk management mechanism.

[1] Paraphrased from Jagannathan, Ravi; McGrattan, Ellen R. 1995. "The CAPM Debate" Federal Reserve Bank of Minneapolis Quarterly Review Vol. 19, No. 4, Fall 1995, pp. 2-17.

[2] The World Bank. Global Citizen's Handbook: Facing Our World's Crises and Challenges. Collins. 2007

[3] In testimony on November 2, 2005 before the Committee on Energy and Commerce United States House of Representatives, Reuben Jeffery III, Chairman U.S. Commodity Futures Trading Commission stated that "Futures markets play a critically important role in the U.S. economy."

[4] By using futures or forward contracts to hedge, a producer, distributor or consumer of an underlying asset can establish a temporary substitute for a cash market transaction that will be made at a future date.

[5] Capacity utilization is a metric used to measure the rate at which potential output levels are being met or used. Capacity utilization rates can also be used to determine the level at which unit costs will rise.

[6] Quoted passage from: Till, Hilary; Gunzberg, Jodie. 2005. "Absolute Returns in Commodity (Natural Resource) Futures Investments" EDHEC Risk and Asset Management Research Centre.

[7] The following list catalogues post-Dusak (1973) studies identified in this area of research: Dusak (1973): Breeden (1980); Bodie and Rosansky (1980); Rolfo (1980); Newbery and Stiglitz (1981); Anderson and Danthine (1983); Carter, Rausser and Schmitz (1983); Baxter, Conine and Tamarkin (1984); Britto (1984); Marcus (1984); Raynauld and Tessier (1984); Jagannathan (1985); Chang (1985); Park (1985); Fama and French (1987); Erhardt, Jordan and Walking (1987); Hartzmark (1987); Hirshleifer (1988); Young and Boyle (1989); Bessembinder (1992); Bessembinder and Chan (1992); Kolb (1992); Kolb (1996); de Roon, Nijman and Veld (1998); Allen, Cruickshank, Morkel-Kingsbury and Souness (1999); de Roon, Nijman and Veld (2000); Francis (2000); Miffre (2000); Lee (2003); Ebrahim and Rahman (2004); Dietz, Good, Irwin and Shi (2005); de Roon and Szymanowska (2006); Erb and Harvey (2006); Szymanowska, Goorbergh, Nijman and de Roon (2006); Gorton and Rouwenhorst (2006).

[8] It is noted that this third implied arbitrage between the current spot price and futures or forward contract is a trade that can be executed in real time. Because this is an easier concept to describe, this implied arbitrage has become mythologized as the relationship which explains backwardation and contango market conditions.

[9] Synopsis of equations for Keynes theory sourced from Rubenstein, Mark. 2006. "A History of the Theory of Investments" Publisher: Wiley, ISBN-10: 0471770566.

[10] Quoted passages on Keynes theory sourced from Rubenstein, Mark. 2006. "A History of the Theory of Investments" Publisher: Wiley, ISBN-10: 0471770566.

References:

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Allen, Beth; Jordan, James S. (1998). "The Existence of Rational Expectations Equilibrium: A Retrospective" Federal Reserve Bank of Minneapolis, Research Department Staff Report 252.

Banz, Rolf W. (1981). "The relationship between return and market value of common stocks" Journal of Financial Economics 9, March, pp. 3-18.

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Michael "Mack" Frankfurter
Chief Investment Strategist
Managed Account Research, Inc.

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