chapter we explain, in detail, the foundations of equity risk factor models. This chapter contributes to the general decision-making process, education, and research on factor models in three important ways: 1.    We provide a taxonomy of the various types of factor models that are the focus of the investment management community. In so doing, we streamline a somewhat fragmented academic and industry literature on factor models and present a consistent terminology to study and understand factor models and their output. 2.    This chapter serves as a blueprint for risk calculations that are based on linear cross-sectional factor models. Such models are widely used among equity investment professionals, and a detailed understanding is critical for practitioners who rely on this information. We provide exact formulas for many factor model-based risk measures. 3.    We present some important empirical issues related to the practical implementation of factor models. A thorough understanding of factor models requires an understanding of factors at both a theoretical and an empirical level. As a concept, factor models are simple and intuitive. They offer the researcher parsimony-the ability to describe a large set of security returns in terms of relatively few factors-and the capacity to identify common sources of correlations among security returns.1 To the portfolio or risk manager, however, factor models are more than a theoretical construct. They offer such managers a way to quantify the risk and attribute return in their !In addition, factor models allow managers to describe the variation of security returns in terms of a relatively small set of systematic components. So, instead of having to analyze potentially massive data sets, the goal of factor models is to allow managers to explain or describe the level of direction, variation, and covariation with other returns in terms of relatively few determinants.