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Risk & Behavior

Extending the Capital Asset Pricing Model to the Popularity Asset Pricing Model

Building bridges between classical and behavioral finance

Perhaps one of the greatest controversies among financial economists is that between classical and behavioral finance. Clearly, economists on both sides have made significant contributions to our understanding of how investors behave and how financial markets work, as is evident in that leading thinkers from both schools have received the Nobel Memorial Prize in Economic Sciences.

So, if both schools have something to contribute, is it possible to reconcile their theories and find a middle ground? I believe that the answer is yes. In fact, I worked with an academic (Yale’s Roger Ibbotson) and two of my colleagues at Morningstar (Thomas Idzorek and James Xiong) on a new book published by the CFA Institute Research Foundation called Popularity: A Bridge Between Classical and Behavioral Finance. As the title says, we think that our approach, which we call popularity, provides a bridge between the opposing camps.

The popularity bridge

I didn’t give much thought to how the insights of behavioral finance might affect my own work until I read “ Dimensions of Popularity” by Ibbotson and Idzorek published in the Journal of Portfolio Management (2014) and “ Popularity and Asset Pricing” by Idzorek and Ibbotson in the Journal of Investing (2017). “Dimensions of Popularity” starts:

“We believe that most of the best-known market premiums and anomalies can be explained by an intuitive and naturally occurring (social or behavioral) phenomenon observed in countless settings: popularity.”

The idea of popularity is simple. Investors are willing to pay more for securities with popular characteristics and less for securities with unpopular characteristics. This causes popular stocks to have lower returns and unpopular stocks higher returns. Thus, investors who are willing to hold unpopular stocks will, over the long run, earn higher returns than other investors. Because stocks of smaller companies are less popular than stocks of larger companies, there is a size premium. Similarly, stocks trading at low price/earnings ratios are less popular than stocks trading at high price/earnings ratios, often because they are out of favor, less well-known, or operate in less glamorous industries. Hence, there is a value premium.

The beauty of the idea of popularity is that it applies to all security characteristics, whether concern for them is rational or irrational. Thus, popularity encompasses both rational and behavioral explanations of market phenomena, and serves as a bridge between the rational and behavioral schools of finance.

From the capital asset pricing model to popularity asset pricing model

In “Popularity and Asset Pricing” Idzorek and Ibbotson seek to express the insights of popularity in an equation for the expected return of a security as a linear function of its risk and nonrisk characteristics. What they lacked was a formal theory as to why this would be true. This is where I came in. Making use of my training in microeconomics, I extended the utility function of the capital asset pricing model (CAPM) to include preferences for security characteristics other than risk and expected return. I interpret this extension to be the dimensions of popularity discussed by Idzorek and Ibbotson (2014). I dubbed the resulting model the popularity asset pricing model (PAPM).

3 striking differences between the PAPM and the CAPM

  1. In the PAPM, the expected excess return of each security is a linear function of not only its beta, but also of what I call popularity loadings, which measure the popularity of the security based on its characteristics relative to those of the beta-adjusted market portfolio. The popularity loadings are multiplied by market-wide popularity premiums, which are aggregations of the preferences of the investors regarding the nonrisk characteristics. In this way, the market aggregates investor preferences in determining the influence of security characteristics on the expected returns and prices of the securities.
  2. In the CAPM, the market portfolio is optimal for the average investor, so indexing is an optimal strategy. In the PAPM, the market portfolio may not be optimal for any investor, so the case for indexing is diminished.
  3. In the CAPM, each investor holds the market portfolio in combination with the risk-free asset (long or short), based on the investor’s risk aversion. In the PAPM, each investor forms a customized portfolio of the risky assets that reflects his or her attitudes toward security characteristics, and combines that with the risk-free asset (long or short). Hence, each investor’s portfolio of risky assets is not available in any index fund.

The new book Popularity: A Bridge Between Classical and Behavioral Finance includes everything from the previous work of Roger Ibbotson, Thomas Idzorek, and myself on popularity and the PAPM, and new material including empirical work (thanks to James Xiong). We hope that this work will help tear down walls and build bridges between the classical and behavioral camps.

This blog post is adapted from an article that originally appeared in the April/May 2018 issue of Morningstar magazine. Read the full article.

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