An Introduction to Financial Markets

Chapter Nine Factor Models

In Chapter 8, we have investigated the mathematics of mean–variance portfolio optimization. From a computational viewpoint, this leads to rather easy optimization models, but things are far from trivial from a financial perspective. One could question the use of a symmetric risk measure, as well as a model neglecting multiperiod dynamics, transaction costs, etc. Some of these issues may be addressed by introducing more sophisticated optimization models, but an essential question remains: How can we provide the optimization model with suitable inputs? The mean–variance model, in its basic form, does not seem to require much: A vector of expected returns and a covariance matrix. Apparently, all we need is simple inferential statistics to estimate these parameters. Reality, unfortunately, is a tad more complicated. To begin with, we would be better off with forecasts rather than estimates based on past history. Moreover, a huge amount of data would be needed to estimate a covariance matrix reliably, and these data are simply not available. Last but not least, the solution of the optimization problem critically depends on the reliability of the estimates, leaving all of the mean–variance optimization framework to rest on shaky foundations. As we have seen in Section 8.6, the resulting portfolio may be quite sensitive to perturbations in the data. In this chapter, we consider factor models as a possible remedy. As we shall see, factor models have deep ...