The "Size Premium" in Equity Markets: Where is the Risk?

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The "Size Premium" in Equity Markets: Where is the Risk?

Stefano Ciliberti
Emmanuel Sérié
Guillaume Simon
Yves Lempérière
Jean-Philippe Bouchaud
Published on 8/2/2017
Equities
Stocks
United States (US)
Factor investing
Small cap
Risk management
Beta factor
Volatility effect
Stock picking

This paper investigates the persistence and nature of the 'Size Premium' in equity markets, challenging conventional risk-based interpretations. By measuring size using dollar-turnover and neutralizing beta and Low-Vol factors, the authors find that the Size Effect remains robust, with the 'Cold-Minus-Hot' (CMH) anomaly exhibiting a t-statistic of 5.1, comparable to well-known factors like Value or Quality. This suggests that size-based strategies are not merely artifacts of other risk exposures.

The study employs methods such as dollar-turnover analysis and statistical neutralization to isolate the pure size effect, revealing that CMH portfolios are less correlated with Low-Vol anomalies than traditional market-cap based SMB portfolios. Key results include the near-zero skewness of size portfolios, with small caps showing positive skewness, which contradicts typical risk premium models that associate small caps with higher risk and negative skewness. The only evidence supporting a risk premium is the higher frequency of extreme drawdowns in small cap/turnover stocks, but this is identified as diversifiable idiosyncratic risk, implying that the size premium may not be fully explained by compensation for systematic risk. This work contributes to factor investing by refining size measurement and questioning risk-based narratives in equity anomalies.

Highlights

  • 1Demonstrates that the Size Effect remains significant when measured by dollar-turnover and after neutralizing beta and Low-Vol factors
  • 2Introduces the 'Cold-Minus-Hot' (CMH) anomaly as a robust alternative to market-cap based SMB, with a high t-statistic comparable to established factors
  • 3Reveals that size-based portfolios exhibit near-zero skewness, with small caps showing positive skewness contrary to risk premium expectations
  • 4Finds that extreme drawdowns are more frequent for small cap/turnover stocks, suggesting idiosyncratic risk that is diversifiable

Methods

  • M
    Dollar-turnover measurement to assess size effects beyond market capitalization
  • M
    Beta and Low-Vol neutralization to isolate the pure size premium from other risk factors
  • M
    Statistical analysis including t-statistics and skewness evaluation of portfolio returns

Results

  • R
    The CMH anomaly has a long-term t-statistic of 5.1, indicating high statistical significance similar to Value or Quality factors
  • R
    CMH portfolios show lower anti-correlation with the Low-Vol anomaly compared to traditional SMB portfolios
  • R
    Size-based portfolios are virtually unskewed, with small caps displaying positive skewness, challenging risk-based explanations
  • R
    Small cap/turnover stocks experience more frequent extreme drawdowns, even after volatility adjustment, pointing to idiosyncratic risk
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