2 – M4 L1B 02 What Is A Factor Model V4

Okay. So, we’ve talked about factors in the abstract and in your head you’re thinking, “Okay, it’s a vector where the values for each stock are proportional to some aspect of the future performance of that stock.” Yes, you’re right. When I first learned this, in some ways, it wasn’t very satisfying to me. But there’s a sense in which that’s what you need to know. But I want to give you more because there is more to the story but that’s where it gets more complicated. So stay with me and I promise it will pay dividends in your learning for the next several lessons. There is a formalism behind factors, let me tell you a little about it. There’s such a thing in the statistical literature called a factor model. A factor model is a statistical model used to describe variability among observed correlated variables, in terms of potentially smaller number of unobserved variables called factors. This method is actually used in several disciplines including biology, psychology, and business, as well as finance. Whenever practitioners are looking to discover a smaller number of so-called latent variables that explain correlations in a set of variables of interest. We could apply this type of analysis to many situations, but in finance, we’re typically interested in modelling the returns of several assets. We might notice that the returns of some assets seem to vary together. Are these companies similar in some way such that some underlying effect influences both of them in the same way? What if we could model the returns of a large group of stocks with a smaller set of variables which explain their common variability? This is what we attempt to do with factor models. The observed variables, in our case returns, are modeled as linear combinations of the factors returns plus error terms. So a generic linear factor model looks something like this: we model the return on a stock, bond mutual fund or something else as a linear function of returns attributed to several factors. The values of these factor returns are the same for all stocks. The factor exposures tell you how much the return of an individual asset should change per unit change in a factor return. Here, the last term, the error term, is the portion of the return on asset not related to any of the factors. In words, the return of any stock, i, can be decomposed into the returns of factors times the stock’s exposures to those factors, plus an unexplained portion.

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