فرضیه ساموئلسون در بازارهای آتی : تجزیه و تحلیل با استفاده از داده های روزانه

This paper considers the Samuelson hypothesis, which argues that the futures price volatility increases as the futures contract approaches its expiration. Utilizing intraday data from 20 futures markets in six futures exchanges, we find strong support for the Samuelson hypothesis in agricultural futures. However, the Samuelson hypothesis does not hold for other futures contracts. We also provide supporting evidence that the ‘negative covariance’ hypothesis is the key factor for the empirical support of the Samuelson hypothesis. In addition, our findings remain largely unaltered even after we control for seasonality and liquidity effects.

This study investigates the futures price volatility as a function of the futures contract’s time to maturity. Specifically, we examine the Samuelson hypothesis (Samuelson, 1965), which proposes that the futures price volatility increases as the futures contract approaches its expiration. Drawing on the concept of realized volatility, introduced by Andersen and Bollerslev (1998), we test the Samuelson hypothesis using intraday data, rather than using daily data as the current literature does. In the past four decades, many researchers have investigated the time pattern of the futures price volatility.1 Much of this interest arises from the importance of the relation between time to maturity and the futures price volatility. First, as Board and Sutcliffe (1990) argue, this relation is important to margin setting. The desired margin is positively related to the futures contract price volatility. Therefore, if the futures price volatility increases as the futures contract approaches maturity, as suggested by the Samuelson hypothesis, the cash balances held by traders to cover for margin calls should also be increased as the maturity date approaches. Second, the relation between volatility and time to maturity also has implications for hedging strategies. Depending on whether this relation is positive or negative, hedgers should choose futures contracts with either a short or long time to maturity, such that the price volatility is minimized. When the Samuelson hypothesis holds, traders might consider switching to contracts further away from expiration day; otherwise, they will face higher volatility and require a higher risk premium. Finally, since the volatility of the underlying asset is an important input for pricing options, the relation between maturity and volatility should be considered when pricing options on futures. Higher volatility of the underlying asset provides greater potential gains for option buyers. As a result, evidence supporting the Samuelson hypothesis will suggest a rise in the price of options on futures such that option sellers are compensated for the risks they face. The current study contributes to the current literature in the following ways. First, we test the Samuelson hypothesis using intraday data for 20 markets in six futures exchanges during the period of 1996–2003. While previous studies measure the futures price volatility using daily futures closing prices, we examine the Samuelson hypothesis using daily realized volatility calculated as the sum of squared intraday returns (Andersen and Bollerslev, 1998). According to Andersen and Bollerslev (1998), although the daily squared return is an unbiased measure of daily volatility, it is also a noisy estimator. Daily squared returns are unable to capture intraday price fluctuations, which can be substantial. In contrast, realized volatility, which is calculated using intraday returns, provides a better, more robust estimate of the actual price volatility.2 Second, for testing the Samuelson hypothesis, we utilize a non-parametric test – the Jonckheere–Terpstra test (JT test) as well as regression-based tests. The non-parametric JT test was developed by Jonckheere, 1954 and Terpstra, 1952 for the purpose of testing ordered differences among classes. Given that testing the Samuelson hypothesis involves testing the order of volatility among different futures with different times to maturity, the JT test is well suited for this purpose. In addition, we also investigate the Samuelson hypothesis based on linear regression with realized volatility and the conditional volatility, as provided by the GARCH (1, 1) model. Consistent with the existing literature, we find support for the Samuelson hypothesis in agricultural futures. Evidence supporting the Samuelson hypothesis in all agricultural futures is robust, even after we control for the effects of seasonality and liquidity. In contrast, support for the Samuelson hypothesis is not documented in any of the financial, metals and energy futures. Our findings support the argument of Bessembinder et al. (1996) that the Samuelson hypothesis is more likely to hold in markets that exhibit a negative covariance between changes in spot prices and changes in net carry costs. We also provide supportive evidence for the role of the information flow in explaining the futures price volatility, as suggested by the ‘state variable’ hypothesis of Anderson and Danthine (1983). However, similar to Bessembinder et al. (1996), we do not find the information flow to be the key condition for the empirical support of the Samuelson hypothesis. Evidence in support of the Samuelson hypothesis remains largely unaltered even after allowing for the information flow in our regressions. Finally, we highlight the economic significance of our empirical findings on the Samuelson hypothesis. The rest of the paper is organized as follows. Section 2 reviews the literature. Section 3 outlines the data used in this study. Section 4 presents the results and discussion while Section 5 concludes the paper.

We test the Samuelson hypothesis in futures contracts using intraday data from a sample of 20 agricultural, energy, metals and financial futures markets in six futures exchanges. Utilizing the Jonckheere–Terpstra test and the OLS regressions with realized volatility and the GARCH (1,1) model, we find evidence supporting the Samuelson hypothesis for agricultural futures. In contrast, we find no support for the Samuelson hypothesis in any of the metals, energy or financial futures. These results are robust even after controlling for the seasonal effects and the liquidity effect. The ‘negative covariance’ hypothesis of Bessembinder et al. (1996) is supported empirically in our study and this explains the differential support for the Samuelson hypothesis in different futures markets. Furthermore, the information flow does not appear to be the key condition for the empirical support for the Samuelson hypothesis. The empirical evidence regarding the Samuelson Hypothesis remains almost identical, regardless of the inclusion or omission of spot price volatility (the proxy for the information flow) in the regression. Overall, our results regarding the Samuelson hypothesis highlight the importance of considering the relation between time to maturity and the futures price volatility when setting margins, developing hedging strategies and pricing options on futures, in agricultural futures markets.