The Relation Between Volatility and Maturity in Futures Contracts

Some students of futures markets believe that the volatility of futures prices increases as the futures contract nears maturity (see Telser, 1956; Segall, 1956; and Samuelson, 1965). Samuelson offers an explanation for the existence of the variability effect as reviewed in Section 1 of the paper. His hypothesis about the behavior of futures prices requires that the stochastic process characterizing spot prices must be of a particular kind; other processes will yield different relations between the variability and maturity of futures contracts. Section 2 of the paper examines the behavior of a sample of futures returns for existence of a systematic volatility effect. Evidence, in this particular case, supports the view that such an effect exists. Section 3 examines the underlying spot-return series to see if its properties are consistent with the empirical results for the sample of futures returns examined in Section 2. Although the process generating the spot returns is consistent with the implications of Samuelson's hypothesis, there is a discrepancy between the observed pattern of futures return volatility and the pattern implied by the Samuelson relationship. Whether or not sampling variability could account for the discrepancy is discussed briefly at the end of the paper.