Book-to-market and size effects: Risk compensations or market inefficiencies?

By Hossein Asgharian and Björn Hansso: 

Department of Economics, Lund University, Box 7082 S-22007 Lund, Sweden.

자료: FMA, http://www.fma.org/Siena/Papers/310355.pdf

※ abstract: 

Are the size and book-to-market effects in US data related to risk factors besides the

market risk? Are the portfolios, HML and SMB, proper representations of latent factors? We

apply the orthogonal portfolio approach to model the risk premium when not all factors are

known.

The results show that the size effect is a compensation for a latent risk factor related to

relative distress, but the book-to-market effect is mostly non-risk-based. Our results validate

SMB as a proper factor-mimicking portfolio, while HML is successful in asset pricing tests

since it shares the same non-risk-based components as the test portfolios.

Keywords: Optimal orthogonal portfolio, asset pricing, anomaly, mimicking portfolios

※ 메모:

There is a long research history, starting with Banz (1981), showing the existence of a

size effect in stock returns in the sense that small firms have a higher average return than big

firms and this phenomenon cannot be explained by their market beta. Analogous to this

finding, the early studies of Basu (1983) and Rosenberg et al. (1985) show the importance of

the so-called book-to-market effect, according to which firms with high ratios of the book

equity to the market equity have higher average returns than firms with low ratios. Fama and

French (1992, 1993) pull the two strands together and show the importance of the book-tomarket

ratio and firm size in explaining cross-sectional differences in expected stock returns.

Fama and French (1993) construct two factor-mimicking portfolios based on size and bookto-

market characteristics, SMB and HML respectively. The average returns of these portfolios

are supposed to capture the premium for a latent state variable related to relative distress.

These mimicking portfolios are now extensively employed in empirical research.

There are a large number of studies that attempt to interpret and explain the observed

size and book-to-market effects. According to Chan and Chen (1991), small firms (firms with

low market value of equity) are usually the firms that lost market value because of poor

performance. These firms are typically highly leveraged and are less likely to survive

economic downturns. Accordingly, the cross-sectional differences in average return between

small and large firms may be interpreted as a compensation for the risk connected to the

relative distress of the small firms. Analogous to this idea, Fama and French (1995, 1996) and

Davis et al. (2000) consider the variables book-to-market and size as proxies for relative

distress. From this viewpoint, the asset pricing is rational and the observed higher returns for

small firms or high book-to-market firms should be considered a compensation for additional

undiversifiable sources of risk besides the market risk. This explanation has been rejected by several other studies. Lakonishok et al. (1994) and Haugen (1995) consider the observed

book-to-market effect as an irrational asset pricing resulting from systematic errors in

investors’ expectations about future returns. Naive investors may be more willing to invest in

low book-to-market firms, which are usually firms with strong fundamentals, because these

firms performed well in the past. This behavior pushes up the prices and lowers the expected

returns for stocks of strong firms. Similarly, investors’ lower attention toward the stocks of

the historically weak firms undervalues these firms and results in higher ex post average

returns for their stocks. Daniel and Titman (1997) follow the idea of investors’ behavioral

irrationality and argue that the relatively higher average return of the high book-to-market

firms is due to growth and distress characteristics rather than a compensation for firms’ risk

loading. Finally, MacKinlay (1995) puts forward data-snooping bias and Kothari et al. (1995)

use the survivorship bias as explanations for the observed CAPM anomaly in the US data.

This debate continues (e.g., Petkova and Zhang, 2003; Ang and Chen, 2004).

Our purpose is to investigate whether the observed size and book-to-market effects in

US data are related to some risk factors beside the market risk or if these effects are due to

non-risk-based components. We also examine the validity of HML and SMB as factormimicking

portfolios in an asset pricing context, i.e. whether the mean returns of these

portfolios are able to capture the risk premium associated with latent state variables. These

issues are tackled by employing a latent factor model that can identify the pricing impact of

unknown factors. This approach enables us to estimate the maximum amount of the expected

returns that can be derived from a linear asset pricing model for a given set of test portfolios.

MacKinlay and Pastor (2000) construct a new framework for modeling asset prices by

combining information in the covariance matrix with average returns to define an exact factor

model that excludes all non-risk-based elements from the expected returns. The model

includes some known and observed factors plus an unspecified factor that represents all potential risk factors that are missing from the model. This unspecified factor is constructed

with the help of the “optimal orthogonal portfolio”, which by construction is orthogonal to the

observed factor/factors and is also optimal since it eliminates mispricing when added to the

initial factor model. 1 Ideally, the estimated expected return from using this approach is

supposed to include the risk premium due to all the risk factors and exclude all the

components of the mean return that are non-risk-based.