1. Performance for Pay? The Relation Between CEO Incentive Compensation and Future Stock Price Performance by Michael J. Cooper (University of Utah – David Eccles School of Business) and Huseyin Gulen (Purdue University – Krannert School of Management) and P. Raghavendra Rau (University of Cambridge)
3. Market Risk Premium Used in 88 Countries in 2014: A Survey with 8,228 Answers by Pablo Fernandez (University of Navarra – IESE Business School) and Pablo Linares (University of Navarra, IESE Business School) and Isabel Fernández Acín (University of Navarra)
3. Learning by Thinking: How Reflection Aids Performance by Giada Di Stefano (HEC Paris – Strategy & Business Policy) and Francesca Gino (Harvard University – Harvard Business School) and Gary Pisano (Harvard Business School) and Bradley Staats (University of North Carolina Kenan-Flagler Business School)
4. …and the Cross-Section of Expected Returns by Campbell R. Harvey (Duke University – Fuqua School of Business) and Yan Liu (Duke University) and Heqing Zhu (Duke University – Fuqua School of Business)
Often we make a basic mistake in finance and economics. We do data analysis and look for significance levels of 5% – which translates into ‘getting it right’ 95% of the time. However, the usual tests apply to independent tests. In practice, these tests are not independent.
To illustrate, suppose we are trying to predict variable Y with variable X. This is an independent test. We estimate the correlation a look for a t-statistic that exceeds 2.0 (significance level of 5%). Now suppose we do the same exercise in predicting Y but now we have 20 different X variables. We try them one by one. In one of the estimations, we achieve the t-statistic of 2.0. Is this significant? The answer is no.
Because we have tried 20 different variables, we need a higher threshold. Indeed, even if the variables were randomly generated, by chance one of them would have a t-statistic greater than 2.0.
Our paper develops a way to adjust the t-statistics for these multiple tests. We document that 315 factors have been published to try to explain the cross-section of equity returns. Indeed, the title of the paper is a play on the number of research papers that propose a new variable and have “… and the cross-section of expected returns” in the title of their paper. We provide recommended statistics through time – from the first tests in 1967 through today and we extrapolate through 2032. Our paper has an analytical contribution over and above what is known in the statistics literature.
We propose a method that allows for correlation among the factors. Our method also deals with the large number of factors that never get published due to publication bias (a bias that results from only “significant” results being published).
Two final remarks. First, this paper is not just about asset pricing. The multiple testing problem occurs in many different fields. For example, in corporate finance, it applies to researchers trying to explain variation in capital structure across firms. Second, the conclusion of our analysis is provocative: “most claimed research findings in financial economics are false”. This echoes the recent research in the medical literature about their published research findings. Importantly, “research” is not just academic research. Our results also imply that the claims of outperformance for the financial products that are sold to investors are also false over 50% of the time.