The Three Types of Factor Models: A Comparison of Their Explanatory Power

Abstract

With some blurring at the boundaries, multifactor models of asset returns can be divided into three types: macroeconomic, statistical, and fundamental. Our empirical findings confirm the conventional wisdom that statistical factor models and fundamental factor models outperform macroeconomic factor models in tenns of explanatory power. The findings also indicate that the fundamental factor model slightly outperforms the statistical factor model. This result is at first surprising, because statistical factor models are estimated by maximizing explanatory power. So, how can an alternative outperform them by this criterion? The explanation lies in the much larger number of external data sources used in fundamental factor models, particularly the large set of industry dummies. Another empirical finding is that the marginal explanatory power of a macroeconomic factor model is zero when it is added to the fundamental factor model. This result may indicate that the fundamental factors {in some unknown combination) capture the same risk characteristics as the macroeconomic factors. TYPES OF FACTOR MODELSMacroeconomic factor models are the simplest and most intuitive type. They use observable economic time series as measures of the pervasive factors in security returns.^ Some of the macroeconomic variables typically used as factors are inflation^ the Gregory Connor is director of research, Europe, for BARRA international. percentage change in industrial production, the excess retum to long-term government bonds, and the realized return premium of low-grade corporate bonds relative to high-grade bonds. The random retum of each security is assumed to respond linearly to the macroeconomic shocks. As in all factor models, each security also has an assetspecific retum unrelated to the factors. A security's linear sensitivities to the factors are called the factor betas of the security. A drawback to macroeconomic factor models is that they require identification and measurement of all the pervasive shocks affecting security returns. A small number of pervasive sources of risk may exist, but without knowing exactly what they are, or lacking data to measure them, they are of little use in explaining returns.Statistical factor models use various maximumlikelihood and principal-components-based factor analysis procedures on cross-sectional/time-series samples of security returns to identify the pervasive factors in returns.Macroeconomic and statistical factor models both estimate a firm's factor beta by time-series regression. Given the nature of security returns data, this limitation is substantial. Time-series regression requires a long and stable history of returns for a security to estimate the factor betas accurately.Fundamental factor models do not require timeseries regression. They rely on the empirical finding that company attributes such as firm size, dividend yield, book-to-market ratio, and industry 42

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