A Note on the Variability of Futures Prices - Rutledge, D. J. S. (The Review of Economics and Statistics, 1976)
Statistical analysis of commodity futures prices and, indeed, of speculative prices in general has largely been carried out on the assumption that prices or first differences of prices are covariance stationary. Examples of this abound in the literature, the best known probably being parametric tests of the random walk hypothesis (see, for example, Stevenson and Bear, 1970) and studies of individual behaviour in futures markets (see, for example, Telser, 1967). This assumption of stationarity implies, of course, that the possibility of non-constant variance of the process generating prices is not admitted. On the surface this may not appear to be a severe constraint, but Samuelson (1965) has proposed a model of futures price formation in which prices become increasingly volatile as the expiry date of the contract draws nearer. On the other hand, little empirical evidence is available to enable judgment to be made on the plausibility of the assumption of constant variance. The purpose of this note is to suggest that, in Samuelson's model, a law of increasing price volatility may not generally hold. This proposition is examined in section II. In section III some of the difficulties associated with the testing of hypotheses about price variability are discussed and in section IV evidence is presented from several futures markets.