Term Structure and Roll Yield: Not Your Father’s Backwardation
Michael Mack Frankfurter
IQ3 Solutions Group
Pepperdine University - Graziadio School of Business
June 1, 2010
This paper investigates potential sources of return to speculators in the commodity futures market. Initially, we focus on “classic commodity theory” based on the ideas of Keynes (1930), Hicks (1939, 1946), Kaldor (1939), Working (1948, 1949) and Brennan (1958). Next our study examines backwardation and contango in line with current convention which references the term structure of the futures price curve. This “simplified commodity theory” provides rationale for a structural risk premium commonly referred to as the ‘roll yield’ (or ‘roll return’). We then introduce our theory of “roll yield permutations” which is derived from integrating the term structure of the futures price curve with the expected future spot price variable. Discussion includes implication of rational expectations, equilibrium theory, reflexivity, the Sonnenschein-Mantel-Debreu theorem and microfoundations theory upon commodity pricing models.
Our research indicates that these models have inherent shortcomings in being able to pinpoint a definitive source of structural risk premium within the complexity of the commodity futures markets. We surmise that the roll yield is a flawed concept derived from an accounting fiction which mixes past and present prices, and skews performance attributions either on a levered or delevered basis. We conclude that classic commodity theory encompasses reflexivity, and as a consequence, reflects the potential for disequilibrium as well as equilibrium. We extend this disequilibrium/equilibrium hypothesis and argue that the term structure of the futures price curve, while suggestive of a potential roll yield benefit or detriment, in fact implies a complex series of roll yield permutations. We are not saying, however, that commodity pricing theory is erroneous. Models as reflections of reality do not operate to the exclusion of the other; rather, these models are inter-related and each reflect certain aspects and dynamics within the futures market paradigm. Consequently, we assume market dynamics reverberate between models, as well as feedback within models resulting in a constant disequilibrium/equilibrium tension.
Number of Pages in PDF File: 39
Keywords: Arbitrage, Backwardation, Contango, Convenience Yield, Equilibrium, Futures Price Curve, Hedging Pressure, Rational Expectations, Roll Yield, Reflexivity, Term Structure, Theory of Storage
JEL Classification: B23, C53, C68, D41, D84, E12, G13, Q11
Date posted: May 17, 2010 ; Last revised: June 15, 2010