New Testing Procedures to Assess Market Efficiency with Trading Rules

This paper presents two computational techniques and shows that these techniques can improve tests for market efficiency based on profit of trading rules. The two techniques focus on interval estimates for expected profit per trade, in contrast to the standard approach that emphasizes point estimates for profit per trade (Daskalakis, 2013; Marshall, Cahan, & Cahan, 2008). The first technique uses confidence intervals to determine if the expected profit is significantly different from zero. The second technique uses moving-window resampling, a procedure of drawing sub-samples that overlap and move incrementally along a time series, to determine if the expected profit is sensitive to sample selection. The paper develops formal testing criteria based on each technique and uses simulation to establish existence results about the tests for efficiency: the standard approach can give false negative results and the new tests can give correct negative or correct positive results. Using a random walk, I show situations where the standard approach incorrectly determines that a market is inefficient whereas the new techniques do not make this error; the standard approach can be fooled by randomness of profit. Using a mean reverting process and a trading rule designed to exploit mean reversion, based on Bollinger bands, I show that the new techniques can correctly recognize an inefficient market. Since the new testing procedures can correctly identify an efficient or inefficient market, with an error rate discussed in the paper. These results support Fama’s (1970) position that trading rules can form the basis for the theory of efficient markets. This definition of an efficient market in terms of trading profit is timely given the current dominance of algorithmic trading in secondary markets.