When modeling portfolio risk, one can think about the distribution of financial returns at a particular point in time. This is the approach we took in Chapter 3—we reviewed probability distributions that can be used to represent observed characteristics of financial returns. A complementary approach is to use statistical models for asset return dynamics. Such models do not look at returns at a particular point in time in isolation—they identify factors that drive returns, or model the asset price process over time.
In this chapter, we review the most widely used statistical estimation models in portfolio management and explain how they are estimated and applied. We begin with a general discussion about return estimation models in finance followed by a review of linear regression analysis, factor analysis, and principal components analysis. We then discuss ARCH and GARCH models. The level of the chapter is intended to be introductory, and the emphasis is specifically on concepts that are useful in portfolio construction.1
4.1 Commonly Used Return Estimation Models
By far the most widely used return models in finance are models of the form
|is the rate of return on security i,|
|is the sensitivity of asset i to factor ...|