Working Paper Synopsis: The Search for the Beta of Commodity Futures
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.
 Schneeweis, Thomas (1999). "Alpha, Alpha, Whose got the Alpha?" University of Massachusetts, School of Management.
 Sharpe, William F (1964). "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk" Journal of Finance 19, September, pp. 425-442.
 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.
 Black, Fischer (1972). "Capital Market Equilibrium with Restricted Borrowing" Journal of Business 45, July, pp. 444-455.
5 Fama, Eugene F.; French, Kenneth R. (1992). "The Cross-Section of Expected Stock Returns" Journal of Finance 47, June, pp. 427-465.
 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.
 The World Bank. Global Citizen's Handbook: Facing Our World's Crises and Challenges. Collins. 2007
 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."
 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.
 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.
 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.
 Keynes, John Maynard (1930). "A Treatise on Money, Volume II: The Applied Theory of Money" London: Macmillan, 1930, pp. 142-147.
 Greer, Robert J. (1997). "What is an Asset Class, Anyway?" Journal of Portfolio Management, Winter, 86-91.
 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.
5 An exception to this assertion is the Black-Scholes option pricing model, which is widely used by practitioners.
 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
 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.