WHAT DOES βSMB > 0 REALLY MEAN?

• Author: Gilbert Bassett,Hsiu‐lang Chen
• DOI: http://doi.org/10.1111/jfir.12047
• Published date: 01 December 2014
• Date: 01 December 2014

WHAT DOES b

SMB

>0 REALLY MEAN?

Hsiu-lang Chen and Gilbert Bassett

University of Illinois at Chicago

Abstract

A positive SMB coefficientinaFama–French regression is often interpret ed as

signaling a portfolio weigh ted toward small-cap stocks. W e present a very large

portfolio, which has a positiv e SMB coefficient for all periods . We emphasize that

this is associated with the coexiste nce of both “M”—the market—and “SMB”—the

mimicking portfolio for si ze—in the Fama–French three-fa ctor model. We explain

why the model can attribute small size to large-cap st ocks and portfolios. The results

highlight how coefficients sho uld be interpreted when a self-financin g portfolio is

used for portfolio attributi on.

JEL Classification: G10, G11

I. Introduction

The Fama–French three-factor model has become the standard academic tool for

assessing portfolios as well as individual stocks. The three factors are: (1) a market factor

—RMRF, (2) a size factor—SMB, and (3) a value factor—HML. The model is often used

to identify exposure to the factors—the portfolio’s“style.”

1

Factor investing has recently

gained attention from the financial press and has been finding favor among institutional

investors and high-end financial advisers.

2

As such, it is essential to understand the

meaning of such attribution and particularly the way the inclusion of mimicking

portfolios might affect the interpretation of regression loadings.

The coefficients in the Fama–French regression are often interpreted in absolute

terms, so that, for example, a positive SMB coefficient would indicate a portfolio that

favors small-cap stocks. A recent analysis of a universe of mutual funds, for example,

concluded that there was a general tendency for the funds to hold small stocks because

We are grateful to the referee and Harry Turtle (the associate editor) for their comments. We also thank

seminar participants at University of Illinois at Chicago and the annual meeting of the Global Finance Conference,

Chicago,May 23–25, 2012. This article supersedes our working paper previously circulated as “Returns-Based

Attribution with Fama–French Factors.”

1

Returns-based attribution uses time-series returns of a portfolio with unknown constituents to derive

estimates of the portfolio’s“factor”exposures. The regression coefficients on the returns of factor-based portfolios

provide estimates of the portfolio’s factor exposure. The constant term shows the portfolio’s expected return after

controlling for a passive portfolio invested in the regression-weighted factors.

2

J. Light and B. Levisohn, “Here’s What’s Really Driving Your Returns,”Wall Street Journal (December 24,

2011), B5.

The Journal of Financial Research Vol. XXXVII, No. 4 Pages 543–551 Winter 2014

543

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