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Getting defensive about the small cap premium

  • The small cap premium has long been a staple of equity investing, but recently some practitioners have called its very existence into question.
  • New research suggests that the mix of quality, volatility and size factors is important. This is confirmed with an analysis of the Russell 2000® Defensive Index, which combines these three factors and exhibits a strong small cap premium.
  • The performance of the Russell 2000® Defensive Index points the way to exploring further multifactor combinations in the small cap asset class.

Academic researchers have been studying the small cap premium for more than 30 years. The first breakthrough, reported in a 1981 paper by Rolf Banz, was the finding that “smaller firms have had higher risk-adjusted returns, on average, than larger firms.”[i] This performance difference has come to be known as the “size effect” or the “small cap premium.” The notion of both a small cap premium and a value premium in equity returns was solidly established with the publication of papers by Nobel Prize winner Eugene F. Fama and co-author Kenneth R. French.[ii] The Fama-French three-factor model of market, value and small cap factors has become a bedrock of academic and practitioner research.

Around the same time Banz was publishing his research, the just-formed Russell Indexes was conducting research into the behavior of investment managers who focused on smaller companies. The immediate need was for a benchmark that could be used by Russell Investment’s consulting clients to gauge the success of those managers. This led to the development, in 1984, of the Russell 2000® Index, the first index to comprehensively measure the small cap segment of the U.S. equity market.[iii]

It is natural to ask whether the comprehensive Russell 2000 Index captures the small cap premium. One possible answer can be provided by the Fama-French three-factor model mentioned above. The equation below makes use of the Fama-French model and applies it to the Russell 2000 Index:

R2000 - rf = a + b ∙ (Market - rf) + c SmallCap + d Value + error

Market is the broad market factor return.[i] The coefficient b is the “market beta” from the capital asset pricing model (CAPM) developed by William Sharpe.[ii] A market beta of 1.0 indicates that, all else equal, the index or portfolio on the left side tends to move up and down in percentage-wise lockstep with the broad market. Rf is the “risk-free rate” of financial theory, which is proxied by the one-month T-Bill return. SmallCap is the “small-minus-big” (SMB) portfolio return, which is calculated as the difference between the returns to the sub-portfolio of smallest cap stocks and the returns to the sub-portfolio of largest cap stocks. The coefficient c measures the exposure of the Russell 2000 Index to the small cap factor. Value is the “high-minus-low” (HML) portfolio return, which is the difference between the returns to the sub-portfolio of highest book-to-price stocks and the returns to the sub-portfolio of lowest book-to-price stocks. Book-to-price (or book-to-market) is widely considered to be one of the most powerful indicators of how cheap a stock is – i.e., whether it is a value stock. The coefficient d measures the Russell 2000 Index’s exposure to the value factor.

Regression estimates of the Russell 2000 Index against the Fama-French model for June 1996 through August 2015 are given in Table 1. The market beta was very close to 1.0, suggesting that the Russell 2000 has tended to move in lockstep with the broad market, if one did not consider other factors. The two other factors considered were the small cap and value factors, which were both statistically significant. The estimated small cap exposure was especially large and statistically significant. The value exposure coefficient d was also statistically significant, indicating that the Russell 2000 had a slight value tilt. The value tilt was a natural result of the Russell 2000 Index’s inclusiveness, whereby some stocks with relatively large book values, which were likely “beaten down” in price enough to be classified as small cap, would then also have high book-to-price ratios.

Sources: FTSE Russell and Kenneth French website. Data as at August 2015. Past performance is no guarantee of future results. Returns shown may reflect hypothetical historical performance. Please see the end for important legal disclosures.

Table 1 establishes that the Russell 2000 Index has had a statistically significant exposure to the Fama-French measure of the small cap premium. But how did that contribute to performance? To get a sense of that, we calculated the performance of the Russell 2000 Index by factors. This was accomplished by running three-year rolling regressions of the Russell 2000 Index against the Fama-French model from June 1996 through August 2015 to capture time-varying exposures, then multiplying the exposures by the time-varying returns to the Fama-French portfolios, and summing them. This produced smoothed contributions to total index return not accounted for by the market factor or the constant. Figure 1 displays the results.[i]

Measured this way, the annualized index return attributed to the small cap factor within the Russell 2000 Index was 3.5%, while the return to the much smaller value tilt was 1.1% per annum. The compounded annual total return for the Russell 2000 Index was 7.6%, which suggested that a substantial portion of the total return was attributable to the small cap premium. This would seem to be compelling evidence in favor of efforts to capture the small cap premium through the Russell 2000 Index. Despite this evidence, doubts about the very existence of a small cap premium have been voiced, and that is the subject of the next section.

Figure 1. Performance by factor within the Russell 2000 Index

Source: FTSE Russell and Kenneth French website. Data as at August 2015. Past performance is no guarantee of future results. Returns shown may reflect hypothetical historical performance. Please see the end for important legal disclosures.

 


[i] The series must begin at May 1999, because this is calculated from three-year rolling regressions.


[i] Fama and French use the CRSP broad market index as their market proxy, which we use here to maintain consistency with their methodology.

[ii] Sharpe, W., “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk,” Journal of Finance, 1964.


[i] Banz, R., “The Relationship between Market Value and Return of Common Stocks,” Journal of Financial Economics, 1981.

[ii] Fama, E., and K. French, “The Cross-Section of Expected Stock Returns,” Journal of Finance, 1992; Fama, E., and K. French, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics, 1993.

[iii] Koenig, D. “The Russell 2000 Index: 30 Years of Small Cap,” Russell Index Insights, 2014.

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