@techreport{NBERw3001,
title = "Data-Snooping Biases in Tests of Financial Asset Pricing Models",
author = "Andrew W. Lo and A. Craig MacKinlay",
institution = "National Bureau of Economic Research",
type = "Working Paper",
series = "Working Paper Series",
number = "3001",
year = "1989",
month = "June",
doi = {10.3386/w3001},
URL = "http://www.nber.org/papers/w3001",
abstract = {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.},
}