Testing Lead-Lag Effects under Game-Theoretic Efficient Market Hypotheses

A game-theoretic efficient market hypothesis says that a trading strategy will not multiply the capital it risks substantially relative to a specified market index. This implies that the autocorrelation of returns with respect to the index will be small and that a signal x will have approximately the same lead-lag effect on all traded securities. These predictions do not depend on assumptions about probabilities and preferences. Instead they rely on the game-theoretic framework introduced by Shafer and Vovk in 2001, which unifies statistical testing with the notion of a trading strategy that risks only a fixed capital. In this framework, we reject market efficiency at significance level α when the capital risked is multiplied by 1/α or more. This approach identifies the same anomalies as the conventional approach: statistical significance for the autocorrelations of small-cap portfolios and equal-weighted indices, as well as for the ability of other portfolios to lead them. Because it bases statistical significance directly on trading strategies, the approach allows us to measure the degree of market friction needed to account for this statistical significance. We find that market frictions provide adequate explanation.