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Statistically Recasting the Big Three Anomalies

| | Posted in: Momentum Investing, Size Effect, Value Premium

Do the size effect, value premium and momentum effect derive from common firm/stock characteristics other than size, book-to-market ratio and past return? In the October 2011 version of their paper entitled “Which Firms Are Responsible for Characteristic Anomalies? A Statistical Leverage Analysis”, Kevin Aretz and Marc Aretz statistically isolate and analyze the small minority of firms that drive these three anomalies. Specifically, they exclude firms from the sample experimentally to identify those stocks that contribute the most to each anomaly (exhibit the strongest statistical leverage) and then examine in several ways the characteristics and stock price behaviors of those firms. They define size based on market capitalization, value based on book-to-market ratio and momentum based on three-month past return (which exhibits stronger momentum than 12-month past return during the sample period). They form test portfolios annually on June 30 based on current size and momentum and six-month lagged book-to-market ratio and hold from July 1 to June 30 of the next year. Using monthly stock returns, stock trading data and accounting variables for the firms then included in the S&P 1500, along with contemporaneous benchmark data, during July 1974 through December 2007, they find that:

  • Annualized anomaly magnitudes over the entire sample period are about 1.9% for the size effect, 4.0% for the value premium and 5.5% for the momentum effect.
  • Excluding the 0.1% of stocks with the highest statistical leverage makes the size and the momentum effects disappear and cuts the value premium in half. Excluding the 1% of stocks with the highest statistical leverage reverses the signs of the anomalies. In other words, very small fractions of the sample drive all three anomalies.
  • Stocks that have high statistical leverage for the value premium (size effect) tend to exhibit high idiosyncratic risk (high idiosyncratic risk and high default risk).
  • No alternative variables explain a meaningful fraction of the momentum effect.
  • There is hardly any support for the notion that trading costs explain the anomalies.

In summary, evidence indicates that investors may be able to capture the traditional size effect and value premium more efficiently by focusing on stocks with high idiosyncratic volatility and high default risk.

Cautions regarding findings include:

  • Reported returns are gross, not net. Incorporating reasonable trading frictions would reduce these returns.
  • The study appears not to account for any data snooping bias in testing explanatory values of many variables within the same data set.
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