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When and Why of the Size Effect

Posted in Economic Indicators, Size Effect

Does the size effect vary in an usefully predictable way? In the October 2011 revision of his paper entitled “Predicting the Small Stock Premium Over Different Horizons: What Do We Learn About Its Source?”, Valeriy Zakamulin examines whether eight U.S. market/economic variables exploitably predict the small stock premium at monthly, quarterly, semiannual and annual horizons. The eight variables are: (1) stock market return; (2) stock market dividend yield; (3) equity value premium; (4) stock return momentum; (5) default spread (Moody’s BAA-AAA corporate bond yield spread); (6)one-month Treasury bill yield; (7) U.S. Treasuries term premium (30-year bond yield minus one-month bill yield); and, (8) inflation rate. Using monthly data for the potentially predictive variables and for a broad sample of U.S. stocks/firms during January 1927 through December 2010 (1008 months, 252 quarters and 84 years), he finds that:

  • The size premium exhibits in-sample predictability over horizons of one month, one quarter and one year. However, the set of predictive variables changes with horizon, as follows:
    • Monthly: higher lagged stock market return and increase in lagged default spread indicate a stronger future size effect.
    • Quarterly: increase in lagged default spread and perhaps increase in lagged stock return momentum indicate a stronger future size effect.
    • Semiannual: no predictive variables.
    • Annual: lower lagged stock market return and higher lagged size effect indicate higher future size effect.
  • Out-of-sample testing based on recursive, inception-to-date recalibration of these in-sample models indicates predictability of both the magnitude and sign (either small stocks or large stocks will outperform) of the size effect at a monthly horizon and the sign of the size effect at quarterly and annual horizons.
  • A strategy that invests in either small (one of the bottom five size deciles) or large stocks (top decile) depending on the forecasted sign of the size premium based on at least 20 years of historical data (available starting January 1947) significantly outperforms the stock market at a gross level for monthly, quarterly and annual portfolio formation. However, trading frictions (assumed to be 0.5% round trip) offset most of the outperformance for monthly and quarterly implementations, with an annual implementation still beating the market by 0.2%-0.3% per month.
  • The size effect derives mainly from a strong, delayed reaction of small stocks to good news after prolonged periods of bad times.

In summary, evidence indicates that investors may be able to exploit predictability of the size effect based on a combination of lagged stock market return, lagged default spread and the lagged size effect itself. 

Cautions regarding findings include:

  • As noted by the author, combinations of potentially predictive variables and forecast horizons introduce data snooping bias for in-sample results.
  • The assumed level of trading frictions may be substantially optimistic, even for institutions, over much of the sample period (see “Trading Frictions Over the Long Run”).
  • The sample is not long when defined in terms of number of “prolonged periods of bad times.”

See also “Predicting Variation in the Size Effect” on similar research by the same author.

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