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Optimal Portfolio Sorting

Posted in Equity Premium, Momentum Investing, Size Effect

Are the widely used stock characteristic/factor sorting practices of ranked fifth (quintile) or ranked tenth (decile) portfolios optimal in terms of interpretative power? In their August 2016 paper entitled “Characteristic-Sorted Portfolios: Estimation and Inference”, Matias Cattaneo, Richard Crump, Max Farrell and Ernst Schaumburg formalize the portfolio sorting process. Specifically, they describe how to choose the number of quantile portfolios best suited to source data via a trade-off between variability of outputs and effects of data abnormalities (such as outliers). They illustrate implications of the procedure for the:

  • Size effect – each month sorting stocks by market capitalization and measuring the difference in value-weighted average next-month returns between small stocks and large stocks.
  • Momentum effect – each month sorting stocks by cumulative return from 12 months ago to one month ago and measuring the difference in value-weighted average next-month returns between past winners and past losers.

Using monthly data for a broad sample of U.S. common stocks during January 1927 through December 2015, they find that:

  • Interpretation of the performance profile of sorted portfolios can vary with the number of quantile portfolios chosen.
  • The number of quantile portfolios offering the best interpretative insight/reliability depends on statistical properties of the sample. In general, this number varies over time, increasing with sample size (how many stocks) and sample length (number of observations).
  • The specified universe of U.S. stocks ranges from about 500 in 1927 to about 8,000 in the late 1990s, subsequently falling to about 4,000 in 2015. The optimal number of quantile portfolios for different sorts ranges from about 10 early in the sample period to over 200 in the late 1990s.
  • For the gross size effect among U.S. stocks:
    • For the entire sample period, the optimal number of quantile portfolios ranges from about 50 to 250 as sample size varies over time. For subperiod analyses, ranges are tighter.
    • For the entire sample of stocks, the effect based on extreme optimal quantiles is strong for the entire sample period and all subperiods. The conventional effect based on extreme deciles is weaker, and not evident during the 1980-2015 subperiod.
    • Even based on extreme optimal quantiles, the effect is not robust when excluding the smallest stocks, especially for the 1980-2015 subperiod (during which “larger” small stocks no longer outperform).
  • For the gross momentum effect among U.S. stocks:
    • For the entire sample period, the optimal number of quantile portfolios ranges from about 10 to 55 as sample size varies over time. For subperiod analyses, ranges are tighter.
    • The effect based on extreme optimal quantiles is strong for the entire sample period and all subperiods, with the short side (past losers) contributing substantially more to profitability for the 1980-2015 subperiod than earlier. The conventional effect based on extreme deciles is mostly weaker.

In summary, theory and examples indicate that selecting quantile breakdowns based on sample properties yields more information about stock factor/characteristic anomalies than a conventional decile breakdown.

Cautions regarding findings include:

  • Examples use gross, not net, returns. Accounting for monthly portfolio turnover (especially for momentum) would reduce these returns. Moreover, extreme quantiles may isolate stocks that are exceptionally costly to trade and difficult to short (more so than extreme deciles), such that net findings may differ from gross findings.
  • The methodology described is beyond reach of many investors, who would bear fees for delegating to an expert analyst.
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