Popularity: A Bridge between Classical and Behavioral Finance

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 behavioral 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, favorable tax treatments, or asset divisibility, making assets more or less valuable to the extent they embody these characteristics.

In behavioral finance, investors may not be completely rational. Thus, investors may have preferences that go beyond rational behavior. We classify behavioral 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. Behavioral 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 behavior. Popularity represents all of our preferences, which can be rational or irrational, providing a bridge between classical and behavioral 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 modeled 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 behavioral 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 behavioral 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 behavioral asset pricing world. In this way, popularity creates a unifying theory—a bridge between classical and behavioral finance.