0: An Introduction to Factor Models

Introduction:

Factor models attempt to decompose an asset’s risk/return characteristics into separate sources.  The reason for doing so is so that investors can fully understand where an asset’s risk and return is coming from.  In doing so, an investor might be able to diversify away the bits of the risk profile of the asset, and capture the important parts of its return.  For a great analogy, Andrew Ang (Columbia) says:

Just like ‘eating right’ requires you to look through food labels to understand the nutrient content, ‘investing right’ means looking through asset class labels for the underlying factor risks. It’s the nutrients in the food that matter. And similarly, the factors matter, not the asset labels.

For example, investors used to think they could achieve the benefits of diversification by investing in stocks and bonds.  The idea was that the two asset classes generally moved in opposite directions.  However, we saw during the recent financial crisis that having a diversified portfolio in different asset classes didn’t protect the investor from huge losses.  If instead, the investor looked at the underlying factors that make up the risk/return profiles of each asset (not the specific asset itself), perhaps diversification efforts could prove to be more successful.

The basic idea behind a factor model is that there is an underlying, linear relationship between the factors of the universe and the asset.  In general:

r_{i} = \alpha_{i} + \beta_{i,j} f_{j} + ... + \beta_{i,K} f_{K} + \epsilon_{i}

  • \alpha_{i}   represents alpha of the security.  This represents abnormal return generated at a specific cross section of our data.  If we consider a portfolio of all securities in the market, this trends towards zero.
  • \beta_{i,j}   represents beta of the security.  This reflects a measure of significance that a certain factor   f_{j}   has on the risk/return profile of the security.
  • f_{j}   represents some sort of factor that will help explain the risk/return profile of the asset.  For example, we will look into a single factor model, which uses only the excess return on the market as its only factor.
  • \epsilon_{i}   represents the asset specific factor, often attributed to noise, news, or other behavior not captured strongly by the factors.
This blog is meant to help educate both myself and others interested in factor models, factor rotation, statistics, and investing.  I hope you will find this useful!  Please write in comments for suggestions, improvements, or questions.

Leave a comment