by E/P. We refer to these assets as group L. 3.   Use the market values and returns on each asset to form group returns. That is, we compute the return on group H and group L, respectively. 4.   The return to the value factor is defined as the difference between the return on group H and the return on group L. The return H minus L represents a return on a zero investment strategy that is long the high E/P assets and short the low E/P assets. The return on this strategy is what is known as the factor return because it reflects movements in the underlying factor. A mimicking portfolio that exhibits large return volatility is consistent with the underlying factor contributing a substantial common component to return movements. A TAXONOMY OF EQUITY FACTOR RISK MODELS_____________ Equity risk factor models take a variety of forms. In this section we provide an overview of the different types of factor models that are used by practitioners. We categorize factor models based on whether the model assumes the factor returns are observed or unobserved. Factor models that rely on observed factor returns include the market model and the macroeconomic factor model. Alternatively, factor models that assume factor returns are unobserved and, therefore, require that we estimate their values include statistical, technical, and fundamental models. Background Understanding a factor model begins with understanding factors. Given the wide application of factor models and the different variables that factors attempt to explain, it should not be surprising that the term "factor" has come to mean almost anything. For example, Chan, Karceski, and Lakonishok (1998) offerthe following categorization of factors: II Macroeconomic 11 Fundamental II Technical II Statistical ill Market Within each of these sets of factors are different variables, each of which attempts to capture a particular feature of individual security returns. Figure 20.1 presents a classification of factors. In order to make this classification a bit less abstract, Table 20.1 presents examples of factors for each factor class. In addition to the different types of factors, factor models are differentiated by the data and model estimation methods that are used to estimate factor returns. For the most part, this estimation process consists of a combination of cross section and time series modeling. Figure 20.2 shows the relationship between the type of factor