Barra's Risk Models
categories: Factor and Risk Modeling, PMA, Equities, Research Paper, SHEIKH Aamir
Investment decisions boil down to picking a risk-return combination with which one is comfortable. At one end of the spectrum lie nominally riskless savings accounts, whereas at the other end lie exotic derivative securities whose structures, let alone their risks, are difficult to understand. It is natural to think that greater risks are rewarded with greater average returns. This, however, is an oversimplification. Greater risk is rewarded only to the extent that the economy as a whole is concerned about the source of greater risk. Proper investment decisions, therefore, should begin by considering the set of investment opportunities that provide a given level of return for the smallest level of risk. This set is referred to as the efficient set.Within the efficient set, greater return may be obtained only by bearing greater risk. Key to defining the efficient set is a definition and measurement of risk. A commonly used and eminently justifiable definition of risk is the dispersion of actual returns around the expected or average return. This dispersion is measured via the standard deviation of returns. Although this dispersion is readily quantified for individual securities, the dispersion of portfolio returns is crucially dependent on the degree of comovement in security returns. For example, consider two securities whose returns move in lock step. When one security returns 15 percent, the other returns 15 percent, and so on. Both securities are risky, but by selling one and buying the other, we can obtain a guaranteed return! Thus, in defining the efficient set, we need measures of security dispersion and co-movement. These are contained in the covariance matrix of security returns. There are a number of ways of estimating the covariance matrix of security returns. Substantial gains are made by recognizing that covariances are driven by common sources of returns across securities. These common sources of returns are called common factors. Estimating the covariance matrix of security returns thus depends on estimating a factor model for security returns. In this article, we will discuss the benefits and costs of the different approaches to estimating factor models of security returns. We will begin by discussing how portfolio standard deviations are computed from the covariance matrix of security returns. Next, we will discuss how we might estimate the covariance matrix and the role that factor models play in this estimation. This leads us into the different types of factor models, and the strengths and weaknesses of each. We will focus on Barra's approach to estimating factor models, and contrast it with other approaches. Empirical evidence regarding the accuracy of Barra's risk forecasts will be presented, and the performance of Barra's model relative to other approaches will be discussed. As we shall see, Barra's risk model provides accurate, robust, and intuitively appealing risk forecasts.