From the CAPM to the Fama—French five-factor model

Risk factors have been a key ingredient to quantitative models since the Capital Asset Pricing Model (CAPM) explained the expected returns of all N assets  using their respective exposure  to a single factor, the expected excess return of the overall market over the risk-free rate . The model takes the following linear form:

This differs from classic fundamental analysis a la Dodd and Graham where returns depend on firm characteristics. The rationale is that, in the aggregate, investors cannot eliminate this so-called systematic risk through diversification. Hence, in equilibrium, they require compensation for holding an asset commensurate with its systematic risk. The model implies that, given efficient markets where prices immediately reflect all public information, there should be no superior risk-adjusted returns, that is, the value of should be zero. 

Empirical tests of the model use linear regression and have consistently failed, prompting a debate whether the efficient markets or the single factor aspect of the joint hypothesis is to blame. It turns out that both premises are probably wrong:

  •  Joseph Stiglitz earned the 2001 Nobel Prize in economics in part for showing that markets are generally not perfectly efficient: if markets are efficient, there is no value in collecting data because this information is already reflected in prices. However, if there is no incentive to gather information, it is hard to see how it should be already reflected in prices.
  • On the other hand, theoretical and empirical improvements on the CAPM suggest that additional factors help explain some of the anomalies that consisted in superior risk-adjusted returns that do not depend on overall market exposure, such as higher returns for smaller firms.

Stephen Ross proposed the Arbitrage Pricing Theory (APT) in 1976 as an alternative that allows for several risk factors while eschewing market efficiency. In contrast to the CAPM, it assumes that opportunities for superior returns due to mispricing may exist but will quickly be arbitraged away. The theory does not specify the factors, but research by the author suggests that the most important are changes in inflation and industrial production, as well as changes in risk premia or the term structure of interest rates.

Kenneth French and Eugene Fama (who won the 2013 Nobel Prize) identified additional risk factors that depend on firm characteristics and are widely used today. In 1993, the Fama—French three-factor model added the relative size and value of firms to the single CAPM source of risk. In 2015, the five-factor model further expanded the set to include firm profitability and level of investment that had been shown to be significant in the intervening years. In addition, many factor models include a price momentum factor.

The Fama—French risk factors are computed as the return difference on diversified portfolios with high or low values according to metrics that reflect a given risk factor. These returns are obtained by sorting stocks according to these metrics and then going long stocks above a certain percentile while shorting stocks below a certain percentile. The metrics associated with the risk factors are defined as follows:

  • Size: Market Equity (ME
  • Value: Book Value of Equity (BE) divided by ME
  • Operating Profitability (OP): Revenue minus cost of goods sold/assets
  • Investment: Investment/assets

There are also unsupervised learning techniques for a data-driven discovery of risk factors using factors and principal component analysis that we will explore in Chapter 12, Unsupervised Learning.

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