Competing hypotheses on the Samuelson effect in futures markets

ABSTRACT

Using data of 12 commodity futures traded on three major futures exchanges in U.S., we find that about 55% of the agricultural futures contracts exhibit the Samuelson effect, about 30% for energy futures contracts, but only about 20% for metal and financial futures contracts. The proposed approach also enables us to take the unprecedented step of directly comparing explanatory power of the state variable hypothesis and the mean reversion hypothesis over the Samuelson effect. The result overall suggests that the mean reversion hypothesis can better explain the Samuelson effect.

KEYWORDS:

• Futures markets
• the Samuelson effect
• the state variable hypothesis
• the mean reversion hypothesis

JEL CLASSIFICATION:

• G13

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ The assumptions are: (1) the current futures price is an unbiased predictor of the spot price on the delivery date, and (2) the price of the underlying asset is a stationary AR(1) process.

² See for example, Khoury and Yourougou (1993), Anderson (1985), Grammatikos and Saunders (1986), Milonas (1986), Galloway and Kolb (1996), Duong and Kalev (2008), Kalev and Duong (2008), Chen, Duan, and Hung (1999), Gurrola and Herrerias (2011), Liu (2014), Pati (2018), and Barnhill, Jordan, and Seale (1987).

³ The slope of the futures term structure, which is essentially the net cost of carrying the spot, refers to the relation between the logarithmic ratio of the futures price to the spot price and the time to maturity of the futures. This can be easily obtained from the cost of carry model: $F_{t,T}=S_t{e}^{((r-q)(T-t))}$ where $F$ and $S$ are the futures and spot price respectively, $r$ is the financing cost, $q$ is the convenience yield, and $T$ and $t$ refer to the maturity and current date respectively. It then follows that $ln{F}_{t,T}-ln{S}_t=(r-q)(T-t)$ where $(r-q)$ can be regarded as the slope of an equation linking the two variables, $(ln{F}_{t,T}-ln{S}_t)$ and $\left(T-t\right)$.

⁴ They find that prices of agricultural commodities and crude oil show a strong mean reverting tendency, which arises solely from positive covariation between spot prices and convenience yields. The mean reverting tendency of metal prices, however, is relatively small and arises both from interest rate sensitivity and from positive covariation between spot prices and convenience yields. At the other extreme are prices of financial assets, whose mean reverting tendency is weak and wholly results from interest rate sensitivity.

⁵ The state variable and the mean reversion hypotheses are sometimes referred to as the information flow and the negative covariance hypotheses respectively.

⁶ Previous studies such as Bessembinder et al. (1996), Duong and Kalev (2008), and Gurrola and Herrerias (2011) address the issue by including spot volatility as an additional independent variable in the regression model of futures volatility on time to maturity. If the addition of spot volatility has little impact on the point estimate and the significance of the coefficient of the time to maturity variable, it can be taken as evidence against the state variable hypothesis. Such an approach, however, has its limitations since it assumes that spot volatility is the sole determinant of futures volatility.

⁷ We essentially exclude daily price observations of contracts within their delivery month.

⁸ Contracts within a futures market might have different life spans. In this case, some futures contracts could have been labelled from only the K^th nearby contract to the 1^st nearby contract where the integer number K is smaller than N.

⁹ Variables of the model are measured in the same way as those in Bessembinder et al. (1996).

¹⁰ The average percentages for energies and agriculturals are 6.5% and 7.2% respectively. However, the distribution of the percentages within each category varies greatly. Percentages of significantly positive coefficient estimates are 8% and 5% for crude oil and heating oil futures respectively, while percentages of significantly positive coefficient estimates for agriculturals disperse over a large range from 20% of soybean to 1% of pork bellies and sugar.

¹¹ The Lehman Brothers financial crisis, bursting in September of Year 2009 falls into the sample period of the study from Year 1981 to Year 2009. To see if the crisis can have any impact on the result of the study, we perform the same analysis by excluding the data of Years 2008 and 2009. The new result is qualitatively the same as the original result. The authors would like to thank the reviewer for pointing out the concern.