Examining the validity of a test of futures market efficiency

Abstract

he efficiency of futures pricing has been investigated using the model: T S,+i = a + bF:+i + e,+i (1) where St+i is the spot price at t + i; F:+i is the price at t for the futures contract maturing at t + i; e,+i is a random disturbance with mean zero and variance a : ; and a and b are fixed parameters. Pricing is considered efficient if a = 0 and b = 1. However, empirical estimates of the a's have generally been positive and the b's less than one, at least for futures contracts several weeks before maturity (e.g., Bigman, Goldfarb and Schechtman (1983) ' Leuthold (1974)). From such results it has been concluded that futures prices provide inefficient (or biased) estimates of the futures (or spot) prices at contract maturity.In an article in this journal, Maberly (1985) disagrees with the conclusion that a^ > 0 and b < 1 (where A denotes an estimate) imply that futures pricing is inefficient. He argues that the empirical findings are the result of applying ordinary least squares (OLS) to censored data. He believes that an inherent restri9ion on the dependent variable in Equation (1) is responsible for a^ > 0 and b < 1. More details of Maberly's argument follow.The objective of this paper is to, show that the censoring argument is incorrect. The reason for a^ > 0 and b < 1 can be attributed to using OLS on a model with a lagged dependent variable. In what follows, Maberly's argument is critiqued and an alternative argument is made as to why the customary test of a = 0 and b = 1 is not valid. This argument is then supported with Monte Carlo evidence.

A cointegration rank test of market linkages with an application to the U.S. natural gas industry

“…I am indebted to an anonymous referee for suggesting this more general way of quantifying the strength of market integration. Elam and Dixon (1988) for futures markets indicate that this incorrect test would be biased towards rejecting the hypothesis that the two prices are from the same market.…”

Searching for fractal structure in agricultural futures markets

“…These apply to asset prices in general, rather than to futures prices, in particular. Studies that deal with the appropriateness of the random walk or the martingale model in futures markets include: the investigation of the treasury bill and treasury bond futures markets by Chance (1985), Klemkosky and Lasser (1985), Cole, Impson, andReichenstein (1991), andMacDonald andHein (1993); the investigation of the agricultural commodities by Bigman, Goldfarb, and Schechtman (1983), Canarella and Pollard (1985), Maberly (1985), Bird (1985), Elam and Dixon (1988); the investigation of the metal futures market by Gross (1988); and the investigation of the foreign currency markets by Glassman (1987), Saunders and Mahajan (1988), Harpaz, Krull, and Yagil (1990).…”

Linear dependence, nonlinear dependence and petroleum futures market efficiency

“…However, evidence that asset prices contain unit roots raises questions about the appropriateness of standard hypothesis tests applied to ordinary least squares (OLS) estimates of (2) [see, for example, Elam and Dixon (1988) and Shen and Wang (1990)]. In addition, nonstationary time series can yield spurious results [see, for example, Granger and Newbold (1974) and Engle and Granger (1987)] because the variables of interest may not be cointegrated, i.e., they may not be tied together in a long-run relationship.…”