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APE-11: The cross-section of expected returns
1Northwestern University, United States of America; 2Georgia Institute of Technology, United States of America; 3University of Notre Dame, United States of America
We propose new methodology to estimate arbitrage portfolios by utilizing information contained in firm characteristics for both abnormal returns and factor loadings. The methodology gives maximal weight to risk-based interpretations of characteristics' predictive power before any attribution to abnormal returns. We apply the methodology in simulated factor economies and on a large panel of U.S. stock returns from 1965–2014. The methodology works well in simulation and when applied to U.S. stocks. Empirically, we find the arbitrage portfolio has (statistically and economically) significant alphas relative to several popular asset pricing models and annualized Sharpe ratios ranging from 0.67 to 1.12. Data-mining-driven alphas imply that performance of the strategy should decline after the discovery of pricing anomalies. However, we find that the abnormal returns on the arbitrage portfolio do not decrease significantly over time.
Estimating The Anomaly Baserate
1UIUC, United States of America; 2University of Notre Dame; 3University of Chicago
The academic literature contains literally hundreds of variables that seem to predict the cross-section of expected returns. This so-called ‘anomaly zoo’ has caused many to question whether researchers are using the right tests for statistical significance. But, here’s the thing: even if a researcher is using the right tests, he will still be drawing the wrong conclusions from his analysis if he is starting out with the wrong priors—i.e., if he is starting out with incorrect beliefs about the ex ante probability of discovering a tradable anomaly prior to seeing any test results. So, what are the right priors to start out with? What is the correct anomaly baserate? We propose a new statistical approach to answer this question. The key insight is that, under certain conditions, there’s a one-to-one mapping between the ex ante probability of discovering a tradable anomaly and the best-fit tuning parameter in a penalized regression. When we apply our new statistical approach to the cross-section of monthly returns, we find that the anomaly baserate has fluctuated substantially since the start of our sample in May 1973. The ex ante probability of discovering a tradable anomaly was much higher in 2003 than in 1990. As a proof of concept, we construct a trading strategy that invests in previously discovered predictors and show that adjusting this strategy to account for the prevailing anomaly baserate boosts its performance.
Thousands of Alpha Tests
1Yale University; 2Rutgers University, United States of America; 3University of Chicago
Data snooping is a major concern in empirical asset pricing. By exploiting the ``blessings of dimensionality'' we develop a new framework to rigorously perform multiple hypothesis testing in linear asset pricing models, while limiting the occurrence of false positive results typically associated with data-snooping. We first develop alpha test statistics that are asymptotically valid, weakly dependent in the cross-section, and robust to the possibility of omitted factors. We then combine them in a multiple-testing procedure that ensures that the rate of false discoveries is ex-ante bounded below a pre-specified 5% level. We also show that this method can detect all positive alphas with reasonable strengths. Our procedure is designed for high-dimensional settings and works even when the number of tests is large relative to the sample size, as in many finance applications. We illustrate the empirical relevance of our methodology in the context of hedge fund performance (alpha) evaluation. We find that our procedure is able to select -- among more than 3,000 available funds -- a subset of funds that displays superior in-sample and out-of-sample performance compared to the funds selected by standard methods.
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Conference: EFA 2019
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