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A Matter of Opinion

How the PAPM incorporates investor preferences and allows for unique forecasts.

The Capital Asset Pricing Model, or CAPM, remains the most influential model in finance, largely due to its elegant structure and powerful conclusions. The main conclusions of the CAPM are 1) all investors hold the market portfolio in combination with a risk-free asset (long or short) making optimization unnecessary and 2) the expected return in excess of the risk-free rate of each security is proportional to its systematic risk with respect to the market portfolio (beta). These conclusions, however, depend heavily on the assumptions of the model. Changing the assumptions leads to very different conclusions.

In previous issues of Quant U, I showed what happens when we separately relax or change three of the CAPM’s assumptions:1 

  1. The standard CAPM assumes investors only care about the expected return and risk as measured by the standard deviation of the returns on their portfolios. In “The Popularity Asset Pricing Model” (June/July 2018), I relaxed this assumption to allow for investor preferences regarding characteristics other than expected return and standard deviation, thus forming the Popularity Asset Pricing Model, or PAPM. The conclusions: Each investor holds a portfolio tailored to reflect his or her preferences arrived at via an optimization, and the expected excess return on each security depends not only on beta but also on exposure to the other characteristics that investors care about. 
  2. The standard CAPM assumes investors are free to take short positions in any security. In “What Harry Markowitz Doesn’t Like About the CAPM” (Summer 2019), I presented an example developed by Markowitz (2015) to show what happens if investors cannot short. In this case, portfolios are often investor-specific because it may not be possible to short some securities. Somewhat surprisingly, there is no relationship between expected return and beta. 
  3. The standard CAPM assumes there is a riskless security, which an investor can hold or short. In “Why the CAPM Falls Flat” (Fall 2019), I presented a version of the CAPM called the Black CAPM or the Zero-Beta CAPM, developed by Black (1972). In this version of the CAPM, there is no riskless security. In this model, each investor selects a portfolio on the efficient frontier based on his or her level of risk aversion. Therefore, portfolios are investor specific. Also, while there is a linear relationship between beta and expected return, the line plotting beta versus expected return can be flatter than it is in the standard CAPM. Hence, securities with high betas have lower expected return than predicted by the standard CAPM, and securities with low beta have higher expected returns than predicted by the standard CAPM. 

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