Popularity

by Roger Ibbotson

  Figure 3.1 presents a complex Venn diagram to illustrate the interaction and subcomponents of the neoclassical and behavioral economics camps in the context of popularity. The left side represents the neoclassical economic view and illustrates the intersection between the CAPM and NET, both of which are nested under the classical view of the world. The CAPM and NET assume that investors are rational, but NET allows for additional characteristics to influence asset prices in a rational manner.

  The right side of Figure 3.1 represents the behavioral finance view, for which we have identified a potpourri of potential behaviors afflicting real-world investors. Representing behavioral finance in this kind of diagram is, arguably, more challenging than representing classical finance because the behavioral area is a bit of a catch-all for a variety of observed behaviors and potential explanations. The largest behavioral theory that can be used to explain a number of the observable so-called irrational investor behaviors is prospect theory . Prospect theory posits diminishing increases in joy for increasingly better outcomes and rising increases in pain for increasingly dire outcomes, particularly related to one’s current endowment. Prospect theory is related to framing, anchoring, and the endowment effect.

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  Figure 3.1. Venn Diagram of Neoclassical Economics, Behavioral Economics, and Popularity

  Source: Based on Exhibit 2 in Idzorek and Ibbotson (2017) .

  Figure 3.2. Major Asset Pricing Theories

  Source: Based on Exhibit 3 in Idzorek and Ibbotson (2017) .

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  Mostly contained within behavioral finance and somewhat intersecting with prospect theory is the affect heuristic. As explained earlier, the notion of affect is similar to popularity and involves emotional decisions that either override or bias rational, cognitive decisions. Affect helps explain irrational popularity premiums but not rational, non-risk-oriented premiums (e.g., liquidity). As illustrated in Figure 3.1 , popularity intersects with the majority of both camps: Risk in a CAPM sense is unpopular; the rationally unpopular premiums of NET are rewarded, and affect-based premiums align with popularity, as do the other premiums explained by prospect theory.

  Through a different lens, Figure 3.2 identifies the contrasting perceptions of the investor (a purely rational person versus an everyday real person) and the spectrum that this creates. Each particular view of the investor leads to one of the various asset pricing theories: CAPM, NET, popularity, affect, and prospect theory. Of these, the CAPM is perfectly suited for a formulaic view of asset prices, whereas prospect theory is the least suited to a formulaic view of asset prices.

  A Popularity-Based Asset Pricing Formula

  We suspect that many of the factors we have discussed are priced factors that can be considered premiums in a pricing equation. 25 We consider these to be dimensions of popularity that are systematically unpopular over an extended period.

  The concept of popularity tells us the direction of the popularity premiums but, thus far, has not provided us with a precise toolkit for estimating their magnitude. In Figure 3.3 , we start to outline a potential linear asset pricing formula based on popularity that simultaneously considers both rational and irrational asset pricing factors.

  At the top of Figure 3.3 , we have somewhat loosely identified traditional and potential popularity-based factors and ordered them from rational to irrational. On the one hand, market risk, size, value, liquidity, and severe downside risk are factors a rational investor would price because they are all characteristics that an investor would seek or want to avoid. On the other hand, competitive sustainable advantage, brand power, and company reputation should already be baked into the price in a rationally efficient market and, therefore, should not be important to a rational investor who only cares about risk and return. For simplicity, tractability, and comparability, we present a linear pricing formula with limited factors.

  Beginning with the CAPM formula, the pricing models are listed down the side. In this way, the connection of the popularity model with the other asset pricing formulas is illustrated—from the CAPM to versions of the Fama–French multifactor model (Fama and French 1996 ), to a linear formula based on NET, and finally to a potentially fully specified popularity-based asset pricing formula that includes momentum (Carhart 1997 ). This final formula starts with the CAPM, and then, factors are added and adjustments made for additional rational and irrational pricing factors based on the various dimensions of popularity.

  We see this build-up as in the spirit of the linear equation of the APT (Ross 1976 ), the Fama–French extension of the CAPM, NET of IDS, and the behavioral asset pricing model of Statman and Glushkov (2011) . 26

  The popularity asset pricing formula depicted in Figure 3.3 is not complete and lacks a rigorous derivation. Chapter 5 presents a formal and rigorously derived PAPM (popularity asset pricing model) that may contain any number of popularity premiums, each multiplied by a security-specific loading. These popularity loadings are based on intrinsic characteristics of securities that investors either like or dislike. Hence, they are not directly linked to the market-based variables used to measure the size, value, risk anomalies, and momentum factor loadings in Figure 3.3 . We regard these market-based variables as proxies for underlying popularity loadings. 27

  Figure 3.3. Toward a Popularity-Based Asset Pricing Formula

  Note: SMB stands for small minus big (the size factor); HML stands for high book/market minus low book/market (the value factor).

  *NET does not specify an asset pricing formula, nor does it identify an exact list of “rational” factors; thus, this formula represents a potential specification of a linear asset pricing formula.

  **The popularity asset pricing formula captures a subset of the characteristics that form the various dimensions of popularity.

  Source: Based on Exhibit 4 in Idzorek and Ibbotson (2017) .

  Statman and Glushkov (2011) argued that in classical finance, the factors in a Fama–French model are interpreted as risk, whereas from a behavioral view, the factors are “interpreted as reflections of the expressive and emotional benefits of positive affect” (p. 6). From a popularity perspective, the factors reflect preferences regarding a collection of characteristics that investors like or dislike, in which some of the preferences are rational and others are irrational. Although these factors are commonly thought of as risk factors, the use of the word “risk” is misleading because exposure to many of the factors (valuation, liquidity, etc.) does not necessarily entail more risk.

  An important question is why the various popularity premiums seem to be permanent, even after they have been discovered and could potentially be exploited and eliminated. Given the recent rapid increase in the popularity of so-called smart-beta and factor-based investment approaches designed to capitalize on what we call popularity premiums, we expect that some of these premiums will eventually diminish. Some may even reverse as the historically popular becomes unpopular and the historically unpopular becomes popular. Candidates for reversal include low-volatility strategies, which appear to be increasing in popularity. The liquidity premium, however, is unlikely to experience an actual reversal because investors will always prefer more liquidity to less. A more likely outcome could be a reduction in the magnitude of the liquidity premium.

  Popularity and Speculative Bubbles

  Similar to our explanation or rationale for how changes in relative popularity can be used to explain price momentum, we believe popularity can help explain bubbles. Let us consider the two most recent examples of so-called irrational exuberance—the technology bubble of the late 1990s and the housing bubble associated with the 2008 financial crisis. 28 Both episodes might be characterized as investing fads that affected large segments of the market rather than a single company. In the 1990s, a point was reached in which it seemed everyone was talking about how much money they were making with internet stocks. Investment clubs were a fad. Similarly, in the years prior to 20
08, people were purchasing multiple homes with little to no money down.

  One might think of these two bubbles as following the classic price momentum pattern. In both cases, some sort of catalyst began to draw increased investor attention to a sector. Because of arbitrage shorting limits, that new-found attention led to an increase in net demand, which simultaneously increased turnover (trading activity). The increase in demand resulted in abnormal price increases, which in turn, resulted in more attention and more demand. A virtuous circle took hold. Eventually, popularity peaked. And as the price exceeded the justifiable price based on fundamentals by ever increasing amounts, attracting enough new fools to maintain the prices became impossible. The tipping point was reached, and the virtuous circle was replaced with a vicious circle as popularity, demand, price, and realized returns all plummeted.

  Others have observed and documented this type of pattern. For example, Hong and Stein (2007) charted the corresponding increase in share turnover and internet stock prices followed by the subsequent decrease in share turnover and internet stock prices associated with the dot-com stock bubble between 1997 and 2002. They noted similar volume-linked patterns associated with the 1720 South Sea Bubble (Bank of England stock) and the US stock market crash in the late 1920s.

  Conclusion

  In this chapter, we continued to develop the popularity framework and laid the groundwork for a popularity-based equilibrium asset pricing theory that would explain almost all of the well-known premiums and anomalies. Many of the cases of mispricing seem also to be consistent with the popularity concept.

  Popularity treats securities as bundles of characteristics, some of which are nearly universally liked or disliked by investors, resulting in priced characteristics that we think of as various dimensions of popularity. Although risk is the most important priced characteristic, investors have preferences for a number of other characteristics that may or may not result in more risk. Popularity applies to all priced characteristics—those that seem rational and those that seem irrational. Popularity builds on NET and is closely related to the affect heuristic of behavioral finance. A number of the behavioral biases associated with behavioral finance contribute to the concept of popularity and popularity premiums.

  A popularity-based asset pricing theory can be advanced either from a classical efficient market view, in which one assumes the market is efficient at pricing the rational dimensions of popularity, or from an irrational view. In both interpretations of popularity, the winners hold the unpopular stocks (or other securities) and those who hold popular stocks are willing or unknowing losers.

  Finally, we put forth a potential popularity-based multifactor linear asset pricing formula in which the expected return of an asset is related to a variety of exposures to the various dimensions of popularity. In the next two chapters, we show how such a formula can be derived in a formal equilibrium model.

  4. New Equilibrium Theory

  In 1984, Ibbotson, Diermeier, and Siegel (hereafter, IDS) published an article in the Financial Analysts Journal that was a precursor to the popularity framework. They dubbed their framework “New Equilibrium Theory” (NET). In this chapter, we review NET, largely by quoting IDS.

  NET was presented in the classical framework but expanded beyond risk preferences to include market frictions. Popularity extends the demand preferences to include both classical and behavioral preferences. The ideas, however, are similar—namely, that preferences, whatever the source, are priced.

  IDS lacked a formal economic model and used charts with informal supply and demand curves. A major advance in this book is that we have developed a formal economic model, which we present fully in the next chapter, that embodies their ideas. Here, we introduce part of that model so that we can present IDS’s central ideas mathematically instead of using their supply and demand graphical analysis.

  The Central Ideas of NET

  IDS summarized their ideas in the abstract of their article:

  Investors demand more of an asset, the more desirable the asset’s characteristics. The most important characteristic is its price, or expected return. By varying price, any and all assets become desirable enough for the capital market to clear.

  Asset characteristics other than price include both risk and non-risk characteristics. The Capital Asset Pricing Model and Arbitrage Pricing Theory [APT] have described the risk characteristics. The non-risk characteristics are not as well understood. They include taxation, marketability and information costs. For many assets, these non-risk characteristics affect price, or expected return, even more than the risk characteristics.

  Investors regard asset characteristics as positive or negative costs, and investors evaluate expected returns net of these costs. The New Equilibrium Theory (NET) framework applies to all assets—including stocks and bonds, real estate, venture capital, durables, and intangibles such as human capital—and incorporates all asset characteristics. (p. 22)

  Note that the costs that IDS explicitly mention—taxation, marketability, and information costs—all fall under the heading of frictional , which is a subset of classical characteristics in the taxonomy of characteristics that we presented in Chapter 1 . In other words, NET is an attempt to expand the classical framework to take into account security characteristics that a rational investor would consider but that are assumed away in such classical models as the CAPM and APT. As we shall do in the next chapter, the main idea of NET can easily be expanded to include the behavioral characteristics included in our taxonomy in Chapter 1 .

  IDS started their article as follows:

  Prices in capital markets are set by the interaction of demand and supply. This relationship is commonly expressed in terms of the “supply of and demand for capital.” But viewing it from the opposite perspective—that is, in terms of the demand for and supply of capital market returns —has the advantage of focusing our attention on returns as the goods being priced in the marketplace. This article provides a framework for analyzing the demand for capital market returns, which we define as the compensation each investor requires for holding assets with various characteristics. (p. 22) [Emphasis in original.]

  The authors continued as follows:

  The basics of the demand for capital market returns can be explained in a few sentences. Investors regard each asset as a bundle of characteristics for which they have various preferences and aversions. Investors translate each characteristic into a cost and require compensation in the form of expected returns for bearing these costs. Thus, although all investors are assumed to perceive the same before-cost expected return for any given asset, each has individually determined costs he must pay to hold that asset. On the basis of perceived expected returns net of these individually determined costs, investors choose to hold differing amounts of each asset. The cost of capital for an asset is the aggregation of all investors’ capital costs on the margin and represents the market expected return on the asset. (p. 22)

  The authors then went on to contrast NET with existing theories:

  Formal demand-side theories such as the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT) have prescribed useful mathematical formulations for deriving assets’ expected returns. Both these theories, however, assume perfect capital markets in which all costs are due specifically to risk. The CAPM specifies the payoff demanded by investors for bearing one cost—beta, or market, risk; APT treats multiple risk factors. Other research has addressed non-risk factors but in isolation. (pp. 22–23)

  They concluded their opening as follows:

  Our framework, which we term New Equilibrium Theory (NET), integrates costs arising from all sources—including various risks, as well as taxability, marketability, and information costs—and affecting all assets in an investor’s opportunity set—stocks, bonds, real estate, human capital, venture capital, tangibles, and intangibles. NET theory does not provide a detailed analysis of each particular cost, nor does it specify a mathematical asset pricing equation.
The NET model is useful, however, in explaining observed investor behavior. (p. 23)

  IDS presented NET in a supply-and-demand graphical analysis, wherein supply is relatively fixed and demand is aggregated across investors. The demand curves reflect investor preferences for more liquidity, less taxation, and so on. Because each investor is risk averse, the marginal demand from each investor is downward sloping for each security or asset class. Consequently, each investor holds a diversified portfolio, not loading up on any one security or asset class.

  In the next chapter, we present a formal model that embodies the main idea of NET, part of which we present here. From this model, we derive the mathematical asset pricing equation that NET lacked.

  A Formal Model for NET

  IDS expressed the main ideas of NET as follows:

  The objective of the NET framework is to determine the equilibrium cost of capital, r j , for each asset j in the market, given the characteristics of asset j and the utility functions of all the investors in the market. Conceptually, the cost of capital is the sum of all capital costs at the margin across all holders of all claims on asset j ; it is typically expressed as a per year percentage of value. This cost of capital can also be interpreted as an expected return to investors or as a discount rate used in valuation. (p. 23) [Emphasis added.]

  They continued to develop the model as follows:

  To focus on the composite market’s cost of capital for asset j , we assume [the first key assumption] that investors have homogeneous expectations concerning r j , the asset’s expected return before investors’ costs, as well as r f , the rate of return on the characteristic-free [i.e., risk-free] asset. Our second key assumption is that investors have heterogeneous, or individually determined, costs associated with the holding of asset j . These differing costs are a natural consequence of the fact that investors differ in regard to wealth, risk aversion, access to information, tax bracket, and numerous other traits. The individual investor may evaluate an asset’s characteristics according to his own classification scheme, and he may measure an asset’s characteristics according to his own judgment. Thus, each investor will have his own particular utility function, according to which he translates all asset characteristics, including all risks, into [marginal] costs. (pp. 23–24)