Efficiency of Price Movements in Futures Markets

Abstract

We study behaviour in the E-mini S&P (ES) commodity futures data market to test for violation of the efficient market hypothesis (EMH), and test for market inefficiency. We demonstrate that, on long timescales, a single scaling determines dynamics. ES returns behave in a more general manner than random walks. We find that deviations from the EMH, and the associated heavy-tailed distributions, are more common than expected, and price returns can be fitted with an alpha-stable Lévy distribution. Our results indicate that while the ES futures market operates close to the state predicted by the EMH, the observed transient deviations from this state fail to have a statistical origin consistent with a purely random geometric Brownian motion, and are better described by the fractal market hypothesis.