Roger Ibbotson Popularity: A Bridge Between Classical and Behavioral Asset Pricing Models

Overview
This article follows a previous article on factor investing: https://clck.ru/E6C9t​.  

​In a recently published book, Popularity: A Bridge Between Classical and Behavioral Finance (Roger Ibbotson, et.al.) the authors present an asset pricing model -- Popularity Asset Pricing Model (PAPM) -- that expands the widely used Capital Asset Pricing Model (CAPM) by adding non-risk, behavioral and non-pecuniary factor characteristics to CAPM’s sole factor, risk. 
 
The PAPM model introduces the concept of popularity -- a measure of investors’ demand for or aversion to factors such as size, value, volatility, and momentum. The popularity model is taken for a test drive and applied to all the commonly used factors. The results are then compared to those of CAPM. It turns out that PAPM can explain several asset premiums that have eluded explanation by CAPM, including small stocks, low volatility and value premiums.
 
Finally, the authors construct a framework that organizes the “Factor Zoo” into two broad categories, classical and behavioral, with sub-categories in each. The result is both comprehensive and useful for asset pricing.
 
The book covers many topics in asset pricing and is well worth reading for its comprehensive look at the issues in this area.

Factor Premiums 
A key component of asset pricing is the factor premium; the expected excess return of an investment relative to an appropriate benchmark or risk-free rate that meets the following criteria: the premium can be explained by economic analysis, is relatively stable over time, and can be implemented.  The best-known premium is the equity market risk premium, which is the amount that an asset, stocks for example, is expected to exceed the risk-free rate. Because stocks have volatility risks investors in stocks expect be rewarded with a risk premium above Treasuries, the risk-free rate. Indeed, the stock market has consistently outperformed government bonds (risk-free assets), as predicted by the model. 

CAPM and Factor Premiums 
CAPM is the most-often used model for asset pricing. The model only recognizes one factor and thus one factor premium, risk. The riskier the security, as measured by its volatility. For example, stock volatility is measured by beta, which is the stock’s volatility compared to that of the entire market. Stocks with higher betas have a higher risk compared to the market and should provide investors with a premium to compensate them for taking on the additional risk. Later models revised CAPM.  However, they limited premiums to risk. At the end of the day, CAPM (and its many variants) hold that a stock’s expected return and premium is proportional to the amount of risk incurred by investors.

Popularity Model 
Classical finance holds that investors make decisions based entirely on an asset’s expected return and level of risk (the risk/return) model. This assumption is key for the development of asset pricing models and portfolio optimization.
 
The popularity model agrees that risk aversion is a powerful motivation for investors, and typically causes risky assets to entice investors with a premium.  However, it also finds that risk is only one characteristic considered by investors when making investment decisions, and, in some cases, may not be the most important one. This is a limitation that PAPM addresses.
 
PAPM states that investors have a positive or negative feeling for many factors other than risk.  Any factor that investors find to be intrinsically unattractive -- for example, low liquidity, high taxability, difficulty of diversifying, high search costs, bad management, distress, and so on – must provide a payoff or premium to reward investors who are willing to take on the exposure to factors that other investors want to avoid or underweight. In a marked departure from classic finance, the authors hold that “An asset can be liked or disliked by investors for any reason, rational or irrational.”  
 
The classical model assumes that investors base their decisions solely on risk and return. It also assumes that investor preferences are homogeneous so, that overall portfolios can be built by aggregating the preferences of individual investors.
 
The authors of Popularity claim that “We believe that popularity reflects demand that ultimately determines price and returns.” As with all economic models, the more popular an asset (i.e., the higher its demand), the higher its price and lower its yield. A portfolio is constructed by aggregating by aggregating investors’ preferences for a list of factors.
 
A Framework for the Factor Zoo 
The research on factor investing has focused on the quantitative analyses of individual factors with little attention paid to developing a framework for organizing the “factor zoo.”  Popularity provides this framework by capturing every known factor that earns investors’ attraction and aversion. The authors present a classification model of factor characteristics in two broad categories with two subcategories each, as follows.
 
Classical Characteristics

• Risks – characteristics to which any rational investor would be adverse
• Frictional – taxes, trading costs, etc. that are often overlooked by investors

 
Behavioral Characteristics

• Psychological – characteristics that make investors feel good/bad (i.e., performance during market turmoil)
• Cognitive – systematic cognitive errors (i.e., use of brand rather than economic performance in selecting investments)

 
This framework, by including both classical and behavioral characteristics, justify the book’s subtitle: A Bridge between Classical and Behavioral Finance.
 
PAPM EXTENDS CAPM
The CAPM model is modified by popularity by adding behavioral, non-pecuniary factors to the classical model’s risk factors. The modified CAPM is called a Popularity Asset Pricing Model (PAPM).  In addition, popularity presents a multidimensional investor with a unique demand or aversion to any factor, rational or irrational. As shown below, these modifications (and others) improve the results of CAPM in asset pricing and portfolio allocation, as shown below. (See Popularity, Chapter 5).
 
In more recent work, the authors challenge the classic assumption of investors’ homogeneous preferences, and replace it with heterogeneous assumption that every investor’s preference is based on their individual attitude towards various factor characteristics, resulting in important changes in asset allocation and portfolio construction.

Taking Popularity for a Test Drive
 The authors state that “popularity helps explain most, if not all, the well-known premiums and anomalies including the equity premium puzzle, the under-diversification puzzle, momentum, bubbles and crashes, high beta/high volatility, and high liquidity.”
 
Popularity analyzes the premiums of ten factors to test the relative explanatory power of classical finance and the popularity model. They find that “10 out of 10 of the analyses to be at least somewhat consistent with the popularity framework, while 5 out of 10 are consistent with the more-risk/more-return paradigm.” (pg. 107) The following are examples of the application of the popularity model to various factors.
 
Low Beta and Low Volatility:  This well-known anomaly presents an enigma for classical pricing models. CAPM assumes that higher risk should be compensated by higher returns (i.e., a risk premium). Thus, high beta/high volatility stocks, which have a greater risk, should provide higher returns than a low beta/low volatility stock. Instead, higher risk factors have lower factor premium and returns.
 
The popularity model presents a cogent explanation for this “anomaly.”  The popularity of high volatility/high beta factors result from behavioral motives of three groups of investors:  investors who are hesitant or unable to use leverage and instead use high volatility/high beta as substitutes; investment managers looking to distinguish themselves from the pack by taking on greater risk in the hopes of greater returns; and investors who find the lottery-like return profile of these factors attractive. These groups increase the popularity (i.e. create demand) for high beta/high volatility, thereby bidding up their prices, reducing return and reducing their factor premium.
 
Value vs. Growth Anomaly
 
The value effect is one of the best-known violations of the CAPM. Value stocks outperform growth stocks over long periods of time even though growth stocks possess higher volatility.  Therefore, according to CAPM, growth stocks should provide a premium because of their higher volatility. Instead, it turns out that value stocks, which have the lower volatility, have the premium. What causes the popularity of growth stocks?  Investors have an affinity for growth stocks based on non-risk factors such as company brand.  For example, investors favor companies with familiar brand names, assuming these companies will provide greater returns. They also mistakenly assume that stocks that are often in the news and considered “hot,” will outperform value stocks. These non-risk popularity factors drive up the price of growth stocks, reducing their premiums.
 
Momentum Mispricing
 
Momentum is a special case and its premium appears to be caused by market inefficiency. However, momentum contains an inner contradiction that leads to the reversal of its own stock.  Initially, investors gravitate to high-momentum stocks, which are increasing in popularity and price.  After a while, the fundamentals work against high momentum stocks which should cause a decline in price. However, the reversal does not happen immediately. A behavioral explanation of this phenomena is that these stocks’ popularity causes the demand to remain high for a period despite the deterioration fundamental. There is a lag between the worsening fundamentals and the decline in the popularity of high momentum stocks, which postpones the stocks’ price reversal.   
 
Company and Stock Specific Factors:  Popularity has an innovative model to explain why stocks of high-quality companies command a higher premium than low-quality company stocks, which is unexplained by CAPM. Popularity identifies and measures five non-risk characteristics that “should” increase the popularity (demand) for a company and its common stock: high brand values, sustainable competitive advantages, better reputations, lottery-like payoff and companies without significant negative tail-risk. In fact, companies that score high on these characteristics underperform companies that lack them, indicating that the shares of companies that underperform are more popular than those that overperform, causing a premium for the latter, contrary to CAPM’s prediction. The authors conclude that the high demand for stocks possessing these popular characteristics – despite their lower returns -- leads to higher prices and lowered premium, as predicted by the popularity model.
 
Conclusion
 
Popularity is rich in theory, evidence and models for asset pricing, asset allocation, and portfolio construction. The authors make a convincing case that popularity can explain and predict factors that the CAPM risk-reward model cannot. The authors summarize their argument by citing one of the first principals of economics. I anticipate the incorporation of the key concepts of the model by traditional asset pricing models.