Data-Snooping Biases in Tests of Financial Asset Pricing Models
Andrew W. Lo
A. Craig MacKinlay
We investigate the extent to which tests of financial asset pricing models may be biased
by using properties of the data to construct the test statistics. Specifically, we focus on
tests using returns to portfolios of common stock where portfolios are constructed by
sorting on some empirically motivated characteristic of the securities such as market
value of equity. We present both analytical calculations and Monte Carlo simulations
that show the effects of this type of data-snooping to be substantial. Even when the
sorting characteristic is only marginally correlated with individual security statistics, 5
percent tests based on sorted portfolio returns may reject with probability one under
the null hypothesis. This bias is shown to worsen as the number of securities increases
given a fixed number of portfolios, and as the number of portfolios decreases given
a fixed number of securities. We provide an empirical example that illustrates the
practical relevance of these biases.
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