Treasury Practice

CAPM and the three-factor model

Published: Nov 2003

In last month’s issue, we identified a number of problems with the Capital Asset Pricing Model (CAPM) and saw how the Arbitrage Pricing Model sought to overcome them. There is another alternative to the CAPM which recognises its problems without overcomplicating matters.

Research into the CAPM identified two problems:

  • The stocks of small firms outperformed the market’s average returns.
  • The stocks of companies with high book-to-market ratios also outperformed the market.

The researchers, Fama and French, argued that these problems represented factors which were missing from the CAPM.

They argue that three factors need to be considered when assessing asset prices. These are:

  • The market as a whole

    This is defined as the return on assets in the market as a whole less the return on a risk-free investment (such as government bonds or cash).

  • The size of the company issuing the security

    This factor is defined as the return on small company securities less the return on large company securities. Fama and French found that shares in small companies outperformed the market by 0.2% per month in the period 1926-1997.

  • The book-to-market factor

    This factor is defined as the return on securities issued by companies with high bookto-market ratios less the return on securities issued by companies with low book-to-market ratios. Fama and French found that cheap stocks (those with high book-to-market ratios, referred to as ‘value’ stocks) outperformed by 0.43% per month in the period 1926-1997. This was not related to the volatility of these stocks. They argued that the ‘value’ stocks are higher risk because of the perceived risk of failure, preserving the link between risk and return.

As with the Arbitrage Pricing Theory (explained in Treasury Today October 2003), having identified these factors, the risk premium of each factor and the risk sensitivity of each investment to these factors needs to be calculated.

These could then be used to calculate the expected return on an investment, thus:

r = b market  R market factor + b size R size factor + b book-to-market R book-to-market factor


  • r is the expected return on the investment
  • b market etc. are the investment’s sensitivities to each factor


  • R market factor1 etc. are the risk premiums for each factor.

This should provide the expected return on an investment. However, this is not as commonly used as the CAPM, mainly because the findings of French and Fama have been subject to criticisms themselves.

CAPM revisited

As the two criticisms (explained above and in October’s newsletter) illustrate, there is still some debate over the usefulness of the CAPM. However, it remains an important tool for treasurers as it is still used by investors when assessing the relative risk of alternative potential investments.

The key factor to recall when using the CAPM is that it is a predictive model. Many of the criticisms of the model are based on empirical evidence calculated after the event. Most investors (apart from the luckiest) would change their original investments with the benefit of hindsight. As a predictive model, the CAPM does not have that benefit either and its results will never be totally accurate after the event. However, because it is used by investors, it gives treasurers an insight into likely investor behaviour.

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