*By Phillip Brzenk*

This is the third in a series of blog posts relating to the in-depth analysis of performance differential between the S&P SmallCap 600 and the Russell 2000.

As we noted in the previous post, the reconstitution effect seen in the Russell 2000 doesn’t fully explain the differences in returns between the S&P SmallCap 600 and Russell 2000. Our analysis turns to factor testing, first using the Fama-French three-factor model, which includes the Market, Size and Value factors (see table below). All three factors are statistically significant in explaining the index returns, though the S&P SmallCap 600 shows a statistically significant unexplained positive alpha (Intercept). The market factor is similar between the two indices, while the size and value factors differ. The size coefficient is larger in the 2000, leading to the conclusion that the Russell has more exposure to smaller capitalization companies. The 600 has a higher value factor coefficient, thus being tilted more towards value companies versus the 2000.

**Fama and French, 1993**

With a statistically significant unexplained alpha present in the three-factor model for the 600, additional factors are added to the analysis with the introduction of two separate four-factor regressions models.

The first model incorporates the momentum factor (WML) first introduced by Mark Carhart (see table below), to the traditional Fama-French three-factor model. Momentum, the tendency for stocks to exhibit persistence in their relative performance, is a well-known anomaly in investing and gives sufficient reasoning to test its efficacy in explaining small-cap returns. As shown in the exhibit below, the momentum factor fails to add explanatory power to the three-factor model, with both coefficients near zero and both t-statistics insignificant.

**Carhart, 1997**

The second model incorporates the quality factor (QMJ) first introduced in a paper by AQR, defined as companies that are profitable, growing and well managed (see table below). The authors go on to mention that investing in high quality companies earns significant historical risk-adjusted returns. When the quality factor is added to the Fama-French model, interesting effects are seen in the output. In both indices, quality is positive, but the factor is larger for the S&P SmallCap 600 and statistically significant (it is not significant in the Russell 2000). In addition, the unexplained positive alpha of the S&P SmallCap 600 is no longer present - leading to believe that quality is a driving factor in the excess returns. Since profitability is a component of quality, the positive earnings screen implemented in the S&P Dow Jones Indices methodology could be seen as a contributor to the larger factor loading in the 600.

**Asness, Frazzini and Pedersen, 2014**

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