Market   Macro                           Security Specific                                         Technical   Sector   Fundamental   Statistical FIGURE 20.1 Hierarchy of Factors and the data required to estimate the risk parameters of a factor model (i.e., factor return covariance matrix and specific variances). In the next few sections, we explain the different methods shown in Figure 20.2. We introduce the reader to different types of factors so that the term "factor" becomes more precise. We begin by considering observed factors and then move on to factor models where the factor returns are unobserved. It is important to note that in the factor models presented, factors are used to model the conditional mean of stock returns in equation (20.3). There are other types of factor models such as the one studied by King, Sentana, and Whadwani (1994) where factors are part of the conditional covariance matrix specification. We do not consider such factor models in this chapter. Observed Factor Returns The first class of factors that we consider is one that has observed factor returns. Two examples of factors that have observed returns are market factors and macro-economic factors. The Market The market model is probably the most common and simplest representation of a factor model. Suppose we want to model the relation between the ex- TABLE 20.1 Examples of Factors Factor Class Examples Market S&P 500, Wilshire 5000, MSCI World indexes Macroeconomic Industrial production, unemployment rate, interest rates Technical Excess stock return on previous month, trading volumes Sector Energy, transportation, technology Fundamental Value, growth, return on equity Statistical Principal components