The “Roll Yield” Myth

Abstract

Futures investors are frequently said to periodically pay or receive the difference in futures prices across contracts with different delivery dates. But this “roll yield” is mythical: No such cash flow occurs—at the time of roll trades or on any other date. However, although the term is a misnomer, the roll yield does contain useful information. It explains when futures gains exceed or fall short of spot-price changes, and for storable assets, it provides information regarding benefits to the marginal holder of a spot position. This article clarifies the actual role of the roll yield.

Disclosure: The author reports no conflicts of interest.

Editor’s Note

This article was externally reviewed using our double-blind peer-review process. When the article was accepted for publication, the author thanked the reviewers in the acknowledgments. Hilary Till was one of the reviewers for this article.

Submitted 21 September 2017

Accepted 6 February 2018 by Stephen J. Brown

Acknowledgment

This article draws on my keynote speeches at the 2017 Commodity and Energy Markets Conference, hosted by the Oxford University Mathematical Institute, and at the 2017 International Conference on Energy Finance in Hangzhou, China. I thank Allen Carrion, CFA, Bjorn Eraker, Avi Kamara, Craig Pirrong, Hilary Till, Laura Tuttle, Kumar Venkataraman, and an anonymous reviewer for helpful comments.

Notes

¹ For examples of academic papers, see Mou (2011); Guedj, Li, and McCann (2011). For additional examples from the financial press, see Blas (2009); Denning (2013); Nussbaum and Javier (2016); Sider (2017); Terazono (2015); Yang and Sider (2017).

² If the futures price is not a sufficiently good proxy for the spot price, then Equation 1 should be expanded to include the change in the “basis” (defined as the nearest-to-expiration futures price minus the spot price) from the initial date to the final date. Some authors and training materials present a version of Equation 1 that refers to “spot return” instead of “change in spot price,” in which case, the expression is not typically correct.

³ This observation also relies on the assumption that the spot price does not change over time. If so, the difference between the nearby futures price and the spot price as of an earlier date will (assuming perfect convergence), indeed, be equal to the gain or loss on the nearby futures from the earlier date to the expiration date.

⁴ See, for example, Main, Irwin, Sanders, and Smith (2016); Bhardwaj, Gorton, and Rouwenhorst (2015); Bessembinder, Carrion, Tuttle, and Venkataraman (2016).

⁵ To draw another analogy, the roll yield is similar to the identification of depreciation as a positive cash flow on certain accounting statements. Book depreciation (distinct from tax depreciation) is an accounting accrual with no cash flow consequences. It is deducted from revenues on the company’s income statement, however, in the course of computing net income. To reconcile the company’s net income with its actual cash flow requires that depreciation be added back, even though it involves no cash, simply because it was previously deducted.

⁶ The existence and magnitude of convenience yields are typically inferred from a futures term slope that is less than would be implied by observable storage costs and cash flows.

⁷ The astute reader will note that the difference between the futures gain and the roll yield is, for every year, equal to the change in the spot price when focusing on rolls at expiration or rolls 5 days before expiration but not when focusing on rolls 15 days before expiration. The reason is that the trading date that is 15 days ahead of contract expiration often falls in the calendar month preceding the expiration date, and for January expirations, it often falls in the preceding calendar year.

⁸ The Goldman Roll refers to the fact that the S&P Goldman Sachs Commodity Index shifts from tracking futures prices for nearest-to-expiration contracts to tracking prices for more distant contracts. Traders who wish to achieve futures gains that closely track the index roll their futures positions simultaneously with changes in the index composition.

⁹ A more precise statement is that changes in roll yields are relevant except when they result from a change in the pair of contracts used to compute the yield (e.g., the roll yield is computed from the February and March prices instead of the January and February prices). That is, somewhat ironically, changes in roll yields are relevant in that they reveal actual gains and losses except when they occur because of a roll trade.

¹⁰ In the Eraker and Wu (2017) model, the term structure of VIX futures can be either upward or downward sloping, depending partly on whether current volatility is above or below the long-term mean. In contrast, the expected risk premium to a long futures position is always negative. Hence, the Eraker–Wu model does not imply a strong link between roll yields and gains to long futures positions if initial volatility is above or below the long-term mean.