At CFA Society Toronto’s “Popularity: A Bridge Between Classical and Behavioural Finance” event on Oct. 3, 2019, presented by Paul D. Kaplan, director of research for Morningstar Canada, I had a chance to hear the concept of popularity for the first time, how it offers an alternative to the capital asset pricing model, and its implications in the real world. The presentation was based on the CFA Research Foundation monograph of the same name by Yale professor Roger Ibbotson with Kaplan and his Morningstar colleagues Thomas M. Idzorek and James X. Xiong. In the presentation, Kaplan discussed how this concept offers a bridge between classical and behavioural finance by embracing all investor preferences, whether they’re rational or irrational. As Laurence B. Siegel, director of research of CFA Institute Research Foundation, explains in the foreword to the monograph:

“As long as aggregate preferences are relatively stable over time, they will play a role in setting asset prices. The preferences can be rational (classical), irrational (behavioural), or a combination of the two. The investors with weaker aversion to generally disliked characteristics will load up on the less popular stocks, which will have higher expected returns. Those with stronger aversion to those characteristics will willingly accept lower expected returns. Because the equilibrium includes all preferences, the popularity framework provides a “bridge” between classical and behavioural finance.”

The following is a modified version of Kaplan’s article “Build Bridges, Not Walls,” which originally appeared in the April/May 2018 issue of Morningstar magazine and summarizes some of the content from the popularity monograph. It is used here with permission and is followed by the Overview of the popularity monograph that appears on the CFA Institute Research Foundation website.

From “Build Bridges, Not Walls” by Paul D. Kaplan, Morningstar Magazine, April/May 2018.

Why is it worth it?

Perhaps one of the greatest controversies among financial economists is that between classical and behavioural 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 the answer is yes. In “Popularity and Asset Pricing,” Roger G. Ibbotson and Thomas M. Idzorek 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 non-risk 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. The result is the popularity asset pricing model (PAPM), which is the focus of a new book published by the CFA Institute Research Foundation called Popularity: A Bridge Between Classical and Behavioral Finance.

The CAPM violations and how popularity explains them

The CAPM is the main theoretical basis for index investing and the idea that expected return depends on systematic risk (beta). Behavioural economists have pointed out that by assuming investors are purely rational, they don’t reflect the irrational behaviours and preferences of investors we observe in the real world. The concept of popularity provides a bridge between classical and behavioural finance; it encompasses all preferences: rational or irrational.

It’s the basis for the PAPM that extends the CAPM by adding rational and irrational preferences to the model. One consequence of this is, each investor holds a custom portfolio based on individual preferences rather than holding the market portfolio. Another consequence is, the expected return on a security is a function not only of beta, but also of various security characteristics, which have different degrees of popularity.

Three 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 (what I call) its 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 investor’s preferences regarding the non-risk 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 isn’t available in any index fund.

From the Overview of Popularity: A Bridge between Classical and Behavioral Finance by Roger G. Ibbotson, PhD; Thomas M. Idzorek, CFA; Paul D. Kaplan, CFA; and James X. Xiong, CFA. Copyright 2018, CFA Institute Research Foundation. Reproduced with permission from CFA Institute Research Foundation. All rights reserved.

Popularity is a word that embraces how much anything is liked, recognized, or desired. Popularity drives demand. In this book, we apply this concept to assets and securities to explain the premiums and so-called anomalies in security markets, especially the stock market.

Most assets and securities have a relatively fixed supply over the short or intermediate term. Popularity represents the demand for a security—or perhaps the set of reasons why a security is demanded to the extent that it is—and thus is an important determinant of prices for a given set of expected cash flows.

A common belief in the finance literature is that premiums in the market are payoffs for the risk of securities—that is, they are “risk” premiums. In classical finance, investors are risk averse, and market frictions are usually assumed away. In the broadest context, risk is unpopular. The largest risk premium is the equity risk premium (i.e., the extra expected return for investing in equities rather than bonds or risk-free assets). Other risk premiums include, for example, the interest rate term premium (because of the greater risk of longer-term bonds) and the default risk premium in bond markets.

There are many premiums in the market that may or may not be related to risk, but all are related to investing in something that is unpopular in some way. We consider premiums to be the result of characteristics that are systematically unpopular—that is, popularity makes the price of a security higher and the expected return lower, all other things being equal. Preferences that influence relative popularity can and do change over time. These premiums include the size premium, the value premium, the liquidity premium, the severe downside premium, low volatility and low beta premiums, ESG premiums and discounts, competitive advantage, brand, and reputation. In general, any type of security with characteristics that tend to be overlooked or unwanted can have a premium. The title of this book refers to a bridge between classical and behavioural finance. Both approaches to finance rest on investor preferences, which we cast as popularity.

In classical finance, risk (and in particular, systematic risk) is the primary asset characteristic to which investors are averse. The CAPM says that all assets are priced according to a single, systematic factor—namely, “market risk” or covariance with the capitalization-weighted market portfolio. In contrast, we believe that risks can also be multi-dimensional, including various types of stock or bond risks. The specific structure of risk and different types of risk can also be priced, such as catastrophic risk. Although classical finance usually assumes away market frictions, rational investors may have preferences for market liquidity, favourable tax treatments, or asset divisibility, making assets more or less valuable to the extent they embody these characteristics.

In behavioural finance, investors may not be completely rational. Thus, investors may have preferences that go beyond rational behaviour. We classify behavioural biases into two distinct types, psychological and cognitive. Psychological desires cause some assets to be more popular than others, relative to their expected cash flow and relative to other rational characteristics, such as liquidity. Investors’ rationality is also limited because they make cognitive errors.

Neoclassical economics provides the rationality framework for efficient capital markets. Behavioural economics assumes limited or “bounded” rationality and thus provides the framework for prospect theory, loss aversion, framing, mental accounting, overconfidence, and other inconsistencies with rational behaviour. Popularity represents all of our preferences, which can be rational or irrational, providing a bridge between classical and behavioural finance.

The CAPM is an elegant and easy-to-use theory for describing investor expected returns in an equilibrium setting. It assumes that investors are rational and risk averse. Because they can diversify away from all non-market risk, only systematic market risk in securities is priced. Securities with higher systematic risk have lower relative prices and thus higher expected returns. We introduce a new formal asset pricing model, the popularity asset pricing model (PAPM), that extends the CAPM to include all types of preferences.

The PAPM is an outgrowth of New Equilibrium Theory (NET), a framework proposed by Ibbotson, Diermeier, and Siegel (Financial Analysts Journal 1984) in which investors are rational but have preferences for or aversions to various security characteristics beyond the single market risk of the CAPM. Additionally, NET goes beyond the multiple dimensions of risk that might be modelled in the arbitrage pricing theory (APT). In NET, in addition to systematic risk aversion, investors have a rational aversion to assets that are difficult to diversify, are less liquid, are highly taxed, or are not easily divisible. All of these preferences impact the prices and expected returns of assets that embody these characteristics.

The PAPM goes even further, providing a theory in an equilibrium framework by including both risk aversion and popularity preferences on the part of the investors. These preferences can be rational, as in NET, or irrational, as in behavioural economics. In the PAPM, securities have a variety of characteristics or dimensions of popularity: different systematic or unsystematic risks and a variety of additional attributes that some or all investors care about. All of these characteristics are priced according to the aggregate demand for each of the characteristics. The expected return of each security is determined by its risk and other popularity characteristics.

The concept of a negative return to popularity (which we shorten to just “popularity”) has been shown to be consistent with the empirical premiums found in the stock market. But it is an explanation after the fact. More direct tests involve identifying in advance what characteristics are likely to be popular and then comparing the performance of stocks that should be unpopular with that of stocks that should be popular based on those characteristics.

We did this for five characteristics. First, we argue that companies with high brand values are popular. These companies end up having significantly lower returns than those with the lowest brand value over our period of study. Second, we argue that companies with wide economic moats, having a sustainable competitive advantage, are more popular. We found that companies with no moat outperform the wide moat companies. Third, we found that companies with a better reputation tend to underperform companies with a worse one. Fourth, we argue that stocks that have had historical negative tail risk events (low or negative coskewness) are unpopular. We found that these stocks significantly outperformed those with high coskewness over the period of study. Finally, we argue that stocks with positive historical skewness are popular because they provide the apparent opportunity for outsized gains. We found that these stocks have the lowest risk-adjusted returns over our period of study.

When we did our five direct tests of the popularity hypothesis, we looked at both equally-weighted composites and market capitalization-weighted composites of the stocks, giving us 10 tests. While all results, to a moderate or high degree, were consistent with the popularity hypothesis, only 5 out of 10 were consistent with the “more risk equals more return” paradigm.

We also tested most of the well-known premiums and anomalies for consistency with popularity. We found that low-beta, low-volatility, small-cap, value, and less liquid stocks, being less popular, outperformed their more popular counterparts. To do this, we looked at 10 of the factor tests in Ibbotson and Kim (working paper 2017) through the popularity lens. Of the 10 different factors that we looked at, we found that 7 were consistent with the popularity hypothesis while only 2 were consistent with the “more risk equals more return” paradigm. We also found that within the stock market, the portfolios formed based on these characteristics had an inverse relationship between risk and return, counter to classical theory. Either risk is popular under some circumstances, or other non-risk characteristics dominate returns. We believe that popularity reflects the demand that ultimately determines prices and returns.

The numerous empirical flaws of the CAPM, and the notion that more risk should equate to more return, have given rise to a variety of behavioural based explanations for observed asset prices. Popularity in general, and the PAPM in particular, unifies the driving factors that impact price in the classical finance CAPM world with those that drive price in a behavioural asset pricing world. In this way, popularity creates a unifying theory—a bridge between classical and behavioural finance.