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Selection bias and pseudo discoveries on the constancy of stock return anomalies

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Abstract

There are now a large and rapidly growing number of studies that test the constancy of stock return anomalies. In this study, we produce new and convincing evidence that the standard constancy test is heavily influenced by selection bias. Backed by a carefully designed Monte Carlo simulation, we show that selection bias predisposes the standard constancy test to reject the null by a factor of five to 12 times more than normally expected. Failure to recognize this bias can result in publication of the type of pseudo discoveries that Harvey (J Finance 72(4):1399–1440, 2017) warns about in his Presidential Address to the American Finance Association. We then describe the Quandt/Andrews test, a correct and unbiased test for anomalies and changes in anomalies, and apply it to test the constancy of 15 well-known stock return anomalies.

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Notes

  1. See also Harvey et al. (2016) and Harvey’s Keynote Address at the 2019 Annual Meeting of the Financial Management Association entitled “Fake Research” for more on statistical bias in financial research.

  2. See, for example, Jaffe et al. (1989), Jegadeesh and Titman (2001), Schwert (2003), Darrat et al. (2013), Chordia et al. (2014), McLean and Pontiff (2016), Bhattacharya et al. (2017), and Linnainmaa and Roberts (2018).

  3. See, for example, the momentum anomaly of Jegadeesh and Titman (1993), the accruals anomaly of Sloan (1996), and the investment anomaly of Cooper et al. (2008).

  4. Greenstone and Oyer (2000) also raise this fundamental and important concern in the context of testing for industry-specific calendar anomalies.

  5. Ten of the 15 anomalies we will later test for constancy are significant at the one percent level.

  6. It is not possible to test all subperiods only all possible subperiods. As a difference in means test, the Chow F-test requires two subperiods in which to calculate and then compare the means. We follow the standard approach, which is to start by testing a subperiod containing the first 15 percent of total observations against a subperiod containing the last 85 percent of total observations. Then continue by moving forward one month and re-doing the test. The final test is between the first 85 percent of total observations against the last 15 percent of total observations. The sequence of Chow F-statistics is thus only calculated between the first 15 percent and the last 15 percent of total monthly return observations. The value of 15 percent is known as the trimming parameter.

  7. The current Web address is http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

  8. We analyze the data with computer software by the R Project for Statistical Computing in conjunction with the strucchange package of Zeileis et al. (2002) and Zeileis et al. (2003).

  9. Robins and Smith (2016) bootstrap the five percent critical value of the supF-statistic and find that their bootstrapped critical value is equivalent to the five percent critical value in Andrews (1993, 2003).

  10. The supF-statistics in Figs. 2 and 3 and in Table 2 are corrected for heteroskedasticity and autocorrelation whereas the subperiods in Table 3 correspond to the month of the uncorrected supF-statistics. This is exactly the correct approach though because the exogenous subperiods are defined by minimum total RSS and this is not affected by heteroskedasticity and autocorrelation.

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Acknowledgements

We thank P. Richard Hahn, Cheng-Few Lee (Editor), Ivo Welch, an anonymous referee, and the participants at the 2018 Annual Meeting of the Southern Finance Association for their helpful comments and suggestions.

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  1. AB Freeman School of Business, Tulane University, New Orleans, LA, 70118, USA

    Russell P. Robins

  2. WP Carey School of Business, Arizona State University, Tempe, AZ, 85287, USA

    Geoffrey Peter Smith

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Robins, R.P., Smith, G.P. Selection bias and pseudo discoveries on the constancy of stock return anomalies. Rev Quant Finan Acc 55, 1407–1426 (2020). https://doi.org/10.1007/s11156-020-00878-w

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