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The supraview of return predictive signals

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Abstract

This study seeks to inform investment academics and practitioners by describing and analyzing the population of return predictive signals (RPS) publicly identified over the 40-year period 1970–2010. Our supraview brings to light new facts about RPS, including that more than 330 signals have been reported; the properties of newly discovered RPS are stable over time; and RPS with higher mean returns have larger standard deviations of returns and also higher Sharpe ratios. Using a sample of 39 readily programmed RPS, we estimate that the average cross-correlation of RPS returns is close to zero and that the average correlation between RPS returns and the market is reliably negative. Abstracting from implementation costs, this implies that portfolios of RPS either on their own or in combination with the market will tend to have quite high Sharpe ratios. For academics who seek to document that they have found a genuinely new RPS, we show that the probability that a randomly chosen RPS has a positive alpha after being orthogonalized against five (25) other randomly chosen RPS is 62 % (32 %), suggesting that the returns of a potentially new RPS need to be orthogonalized against the returns of some but not all pre-existing RPS. Finally, we posit that our findings pose a challenge to investment academics in that they imply that either US stock markets are pervasively inefficient, or there exist a much larger number of rationally priced sources of risk in equity returns than previously thought.

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Notes

  1. There is a vast academic literature on accounting and finance anomalies, well summarized by survey papers such as Lev and Ohlson (1982), Bernard (1989), Kothari (2001), Keim and Ziemba (2000), Barberis and Thaler (2003), Schwert (2003), and Subrahmanyam (2010). However, these surveys do not seek to identify and gather together the full population of RPS, nor statistically describe the return properties of the RPS population.

  2. There are relatively few signals (just five) that explicitly combine an accounting data item and a finance data item into a composite signal. Our results are not sensitive to the reclassification of accounting signals interacted with finance signals as accounting signals instead of finance signals.

  3. We therefore set aside a goodly number of t-statistics that are not based on a time-series of mean RPS returns, because the Sharpe ratio is only properly defined for a time-series of returns.

  4. The two investing approaches are naïve because RPS returns and excess market returns will be less than perfectly positively correlated. Hence a linear combination of the two approaches would dominate either one separately.

  5. In untabulated analysis we find that the mean t-statistic associated with equally weighted returns is 5.0, as compared to the mean t-statistic of 3.7 associated with value-weighted returns.

  6. Using Google Scholar as of Sept. 17, 2012, it is the case that Jegadeesh and Titman’s (1993) momentum signal is the most heavily cited RPS; Banz’s (1981) firm size signal is the third most heavily cited RPS; Sloan’s (1996) accruals signal is the seventh most heavily cited RPS; and Ball and Brown’s (1968) post–earnings announcement drift signal is the ninth most heavily cited RPS.

  7. Jegadeesh and Titman (1993) examine 32 RPS by varying both the number of months in their lagged-return RPS and the number of months in the post-signal holding period. We focus on their 6-month lagged-return RPS as representative of the 32 they study because the returns produced by that signal are not the largest and are not sensitive to the number of months in the holding period (p. 69). We only include the 6-month lagged-return RPS in our supraview database, not all 32 RPS.

  8. We do not seek to identify working papers before the advent of SSRN. For published papers for which we do not have an electronic copy of the working paper, we set the date of the first working paper to be two years prior to the paper’s publication date.

  9. As of the year 2012, Mr. López de Prado was Head of Global Quantitative Research at Tudor Investment Corp., which in August 2011 had a reported $11 billion of assets under management.

  10. An alternative method of combining individual RPS into a portfolio that can accommodate a large number of RPS is the parametric portfolio policies (PPP) approach of Brandt et al. (2009). In the context of a relatively small number of RPS, the PPP approach has been studied by Green and Hand (2011).

  11. Bailey and López de Prado (2012) employ a “naïve” equal-volatility-weighted portfolio approach because such an approach greatly simplifies the algebra without sacrificing much in the way of portfolio optimization. The equal-volatility approach was first used by DeMiguel et al. (2009), who compare 14 models of optimal asset allocation and find that no single model consistently delivers a Sharpe ratio or certainty equivalent return that is higher than the equal-volatility-weighted approach.

  12. An alternative approach would be to estimate the correlation structure of the underlying signals rather than the correlation structure of the RPS returns. We choose to estimate the correlation structure of the returns to be consistent with the focus on investors’ portfolio returns within the equal-volatility-weighted portfolio framework.

  13. We also note that the difference between the mean excess equally weighted and value-weighted annual market returns reported in Table 6 is just 1.7%, as compared to 2.9% in the RPS population (cf. the means reported in Table 5, panel E versus those in Table 4, panel E). This simply reflects the fact that the difference between the mean excess equally weighted and value-weighted annual market returns in the period 1985–2011 is 1.2%, as compared to 4.5% in the period 1970–1984.

  14. In a paper contemporaneous to our present study, McLean and Pontiff (2012) find using a sample of 82 firm-specific characteristics that the average post-publication decay in the return to an RPS, which they attribute to both statistical bias and price pressure from aware investors, is about 35% and statistically different from both 0% and 100%. Consistent with informed trading, they document that after an RPS is published it experiences higher volume, variance, and short interest, as well as higher correlations with other RPS that have already been published. Consistent with costly (limited) arbitrage, McLean and Pontiff show that the post-publication decline is greater for RPS whose stocks are large, are liquid, have high dividend yields, and have low idiosyncratic risk.

  15. In unreported tests we divided the window January 1985–December 2011 into five-year periods and, consistent with the presence of some alpha decay, find some (albeit weak) evidence that the dispersion of Sharpe ratios and of annualized returns for equal-weighted hedge portfolio returns declined until 2010.

  16. The individual cross-correlations are available from the authors upon request. We do not provide correlation tables because it is all but impossible to fit 741 cross-correlations onto a single page without the font size becoming illegible.

  17. Untabulated results show that the five-year average signed cross-correlations among RPS returns have ranged between approximately 0.01 and 0.08 without any clear linear time-trends.

  18. For example, if the correlation between a portfolio of RPS and the equity market is −0.16, then an equal-volatility weighted portfolio of RPS and the equity market will have an expected Sharpe ratio that is more than 20% larger than that of the component portfolio of RPS and 100% larger than that of the overall US equity market.

  19. In untabulated analysis, we find that five-year average absolute cross-correlations range between 0.23 and 0.38, and that they tend to be larger for equally weighted returns than for value-weighted returns.

  20. Alternatively, a researcher may choose simply to include all available factors—a prospect we would consider a daunting task.

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Acknowledgments

We appreciate valuable comments from Peter Algert, Suresh Govindaraj, Gilad Livne, Russell Lundholm, Jim Ohlson, Panos Patatoukas, Peter Pope, an anonymous referee, and workshop participants at City University London, the 2012 Citi Global Quant Conference, and the 2012 Review of Accounting Studies Conference. A full listing of the papers referenced in and used by this study is available from the authors on request.

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Authors and Affiliations

  1. The Pennsylvania State University, University Park, PA, USA

    Jeremiah Green

  2. University of North Carolina–Chapel Hill, Chapel Hill, NC, USA

    John R. M. Hand

  3. Yale University, New Haven, CT, USA

    X. Frank Zhang

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  1. Jeremiah Green
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Correspondence to John R. M. Hand.

Appendix: Attributes recorded in the return predictive signals (RPS) database

Appendix: Attributes recorded in the return predictive signals (RPS) database

  1. A.

    General paper attributes

    • Title

    • For each author:

      • Last name

      • Area (usually based on their title, e.g., Assistant Professor of Finance):

        • Accounting

        • Finance

        • Economics

        • Law

        • Other academic area

        • Practitioner

    • Date published

    • Journal the paper was published in, if it had been published as of Dec. 31, 2010

    • Date of earliest working paper version of the paper, whether or not the paper was published. If no working paper version could be found but the paper had been published, the date of the earliest working paper version was assumed to be 24 months prior to the publication date.

  1. B.

    Data used in the paper

    • Time period used to analyze the signal (e.g., Apr. 1, 1986–Nov. 30, 1994)

    • Last date used in analyzing the RPS in the earliest working paper (e.g., Dec. 31, 1995)

    • Databases employed, a partial list of which includes the following:

      • CRSP

      • Compustat

      • I/B/E/S

      • First Call

      • CDA Spectrum and Thomson Reuters Insider Filings

      • OptionMetrics

      • SDC

      • TAQ

      • ExecuComp

    • Exchanges used (NYSE, AMEX, NASDAQ, other)

    • Dummy variable coding that analysis was restricted to Dec. 1 fiscal year-end firms

    • Dummy variable coding that analysis excluded financial institutions

  1. C.

    Return predictive signals

    • General features

      • Signal name (e.g., cash flow from operations)

      • Signal definition (e.g., the particular Compustat data items and formula)

      • When calculated (e.g., once annually on May 1)

      • We include only the first paper in which a particular signal was reported. Later papers on the same signal are not included in the database.

      • In the infrequent cases in which a given paper reported results for N > 1 new signal, the underlying paper is entered into the database N different times.

    • Return features

      • Returns are coded as positive numbers as long as the long/short sides are intuitively defined. There are a very few papers for which even after intuitively defining the long and short sides, the actual empirical mean return is negative. These usually arise in the context of robustness tests. We leave these as negative in the database.

      • Frequency over which returns are calculated

        • Daily, weekly, monthly, quarterly, yearly

      • Number of years’ returns (e.g., March 1990 through June 1996 = 6.33 years)

      • Approach used to construct returns

        • Deciles, quintiles, specific (e.g., top and bottom ninth of firms ranked on the RPS), other (e.g., not taking a hedge approach but instead going long in all firms that announced a stock repurchase).

      • Weighting of returns

        • Equally weighted, value-weighted, other. We categorize returns that are calculated using criteria such as “only the largest 500 or 1,000 firms,” or “the largest 10 % or 20 % of firms” as being value-weighted.

    • Return performance

      • Mean return as reported in the paper. This can be the mean of a pooled time-series cross-section of returns or the mean of a time-series of (typically average) returns.

      • Sharpe ratio reported in the paper. Since this is very rarely provided by authors, where we are able we calculate it using information in the paper. However, we do this only for time-series returns, not for pooled time-series cross-sections of returns.

      • t-statistic reported in the paper (pooled or time-series)

      • Percentage of returns that are positive

      • Mean annualized return. We calculate this by scaling up the mean return as reported in the paper in a noncompound way. Thus, if the reported mean return reported is 1.34 % per month, we take the annualized mean return to be 1.34 % × 12 = 16.08 %.

      • Sharpe ratio of annualized returns. We define this as the mean annualized return divided by the standard deviation of annualized returns. We usually derive the standard deviation of annualized returns from the t-statistic on the reported mean return. Thus, if the reported mean return reported is 1.35 % per month based on a time-series of 15 years of monthly returns and a time-series t-statistic of 4.52, we take the annualized Sharpe ratio to be 4.52 divided by the square root of 15. This calculation assumes that the (in this case monthly) RPS returns are serially uncorrelated.

      • When available, the performance of both equally weighted and value-weighted returns is recorded.

      • A few papers report a variety of robustness results for the RPS being studied. When present, we report the average of these (e.g., the average return across the various robustness tests) to avoid data-snooping only the “best” performance.

    • Firm characteristics [factor returns] used to risk-adjust returns

      • Beta [RMKT]

      • Firm size [SMB]

      • Book-to-market [HML]

      • Momentum [MOM]

      • Other

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Green, J., Hand, J.R.M. & Zhang, X.F. The supraview of return predictive signals. Rev Account Stud 18, 692–730 (2013). https://doi.org/10.1007/s11142-013-9231-1

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