Modi ed version of short term nancing example in section 3.1 of optimization meth- ods in finance12/27/2022 ![]() While we propose a frequentist approach to overcome this missing data issue, it is unclear how to do this in the Bayesian framework. 3 However, the high dimensionality of the problem combined with the fact that we do not observe all the factors that have been tried poses a big challenge for Bayesian methods. Bayesian approaches to multiple testing and variable selection also exist. We tackle multiple hypothesis testing from the frequentist perspective. Our goal is to use a multiple testing framework to both re-evaluate past research and to provide a new benchmark for current and future research. Our work focuses on evaluating the statistical significance of a factor given the previous tests on other factors. Lewellen, Nagel, and Shanken (2010) critique the usual practice of using cross-sectional R 2s and pricing errors to judge success and show that the explanatory power of many previously documented factors are spurious. Our paper also adds to the recent literature on biases and inefficiencies in cross-sectional regression studies. 2 Their paper tests the statistical biases emphasized in Leamer (1978), Ross (1989), Lo and Mackinlay (1990), Fama (1991), and Schwert (2003). Our research is related to a recent paper by McLean and Pontiff (2015), who argue that certain stock market anomalies are less anomalous after being published. We present a taxonomy of historical factors, as well as definitions. We also project minimum t-statistics through 2032, assuming the rate of “factor production” remains the same as the last ten years. We provide recommended test thresholds from the first empirical tests in 1967 to present day. We begin with 313 papers published in a selection of journals that study cross-sectional return patterns. We present a new framework that allows for multiple tests and derive recommended statistical significance levels for current research in asset pricing. ![]() ![]() Given the known number of factors that have been tried and the reasonable assumption that many more factors have been tried but did not make it to publication, the usual cutoff levels for statistical significance may not be appropriate. However, since that time, hundreds of papers have tried to explain the cross-section of expected returns. The reported t-statistic of 2.57 in Fama and MacBeth (1973, Table III) comfortably exceeded the usual cutoff of 2.0. Over forty years ago, one of the first tests of the capital asset pricing model (CAPM) found that the market beta was a significant explanator of the cross-section of expected returns.
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