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Putting a Price on Popularity

A new model bridges classical and behavioral finance.

Roger Ibbotson and a trio of leading Morningstar researchers recently published Popularity: A Bridge Between Classical and Behavioral Finance. It’s an ambitious effort, checking in at 140 pages and presenting a new view of how assets are priced. The popularity approach incorporates some aspects of William Sharpe’s capital asset pricing model and the various empirical premiums that have been discovered in the literature, but it extends that work in new directions. It also differs from most of its predecessors by offering a single, cohesive explanation for the market’s behavior.

Ibbotson is professor in the practice emeritus of finance at the Yale School of Management. He is also chairman and CIO of Zebra Capital Management and founder of Ibbotson Associates, now a Morningstar company. His co-authors are Thomas Idzorek, CFA, chief investment officer, retirement, with Morningstar Investment Management; Paul D. Kaplan, Ph.D., CFA, director of research with Morningstar Canada; and James X. Xiong, Ph.D., CFA, head of scientific investment management research with Morningstar Investment Management. They recently joined me to discuss their effort and its applications. Our conversation has been edited for length and clarity.

John Rekenthaler: Tell me about the genesis of this work.

Roger Ibbotson: I can take this all the way back to the 1980s when Larry Siegel, Jeff Diermeier, and I wrote an article for the Financial Analysts Journal called “A New Equilibrium Theory.”[1] It was based on the idea that lots of things impact the price of an asset, not just risk—how liquid an asset was, how it was taxed, and so forth. All these sorts of things were involved in an equilibrium. This idea has been around now for 30 years or so.

Thomas Idzorek: We’d all kind of lost sight of the “New Equilibrium Theory” paper. Then, Roger, James, and I noticed the liquidity factor within mutual funds and published a paper[2] that came out in the FAJ before Roger’s more foundational work on liquidity within stocks.[3] After those two papers, we began thinking: Is there a broader encompassing idea or rationale behind what we were seeing? In 2014, we published “Dimensions of Popularity”[4] and coined popularity as the umbrella term.

Ibbotson: The key thing about liquidity is it’s something you like, and less liquidity is something you do not like. The general paradigm in classic finance is risk: Risk is something you don’t like, and less risk is something you like. So, liking or disliking something has to do with how it’s going to be priced. That was the key to the whole perspective here.

Once we’re looking more generally at how things are going to be priced, we don’t have to stick with the idea of liquidity or risk. We can have many other variables, and they don’t even have to be classical. They could be behavioral, as well.

Idzorek: After “Dimensions of Popularity,” I wanted to write more of an academic article rather than something for practitioners. That led me to do a relatively extensive literature review. As I was rereading “A New Equilibrium Theory,” I was astonished to read that many of the ideas that I had written out had been almost identically expressed, only decades earlier.

Rekenthaler: You invented something that others had already invented. I’ve been there and done that myself, Tom.

Idzorek: As I was working on this with James and Roger, struggling to make it an academic-oriented paper, Roger and I were invited to submit a paper to the Journal of Investing for one of their anniversary editions. We ended up using some of the work for that article.[5] Meanwhile, Paul wrote a formal theory for the popularity asset pricing model and called it the PAPM.

Paul Kaplan: I was first exposed to the “New Equilibrium Theory” paper by Larry Siegel himself back when I worked at Ibbotson Associates, the firm that Roger had started back in the 1970s. Larry is the director of research for the CFA Institute Research Foundation, and he is the author of the foreword of our new book. As he relates in the foreword, one of the criticisms of the new equilibrium theory was that it was neither new nor equilibrium nor a theory.

Ibbotson: I disagree with that, by the way! I think it was new, and I think it was clearly all about equilibrium, and from my perspective, it really was a theory. But Paul really made a great contribution by formalizing it; the theory wasn’t formalized enough.

Kaplan: The authors lacked any kind of a formal, academic-style model. Instead, they had some charts.

Ibbotson: A graphical equilibrium, essentially.

Formalizing Popularity
Kaplan: I came up with this idea: Let’s start with the assumptions of the CAPM, and let’s add one additional assumption: that investors don’t care only about risk and return. They care about many other things as well—what Roger and Tom had been calling the dimensions of popularity. I went through the mathematical development of the model, wrote it up as a paper, and circulated it among several people, including Roger. As I recall, Roger, your reaction was that this was the kind of mathematical, rigorous equilibrium theory you had in mind when you wrote the original paper, but that there was no one that had the math skills to put it together at the time.

Ibbotson: Yes. The CAPM is a great framework, because it puts everybody in a risk-averse framework, but the PAPM adds something to that.

We set up an example with three investor types and five securities. One of the investor types is a CAPM investor who doesn’t care about popularity; he or she only cares about risk. That investor tries to take advantage of the way things are priced through popularity. From that investor’s perspective, the most popular securities end up being overpriced, with the lowest expected returns, and the least popular securities end up being underpriced, with the highest expected returns. This CAPM investor effectively takes long positions and levers up in these underpriced securities and then shorts overly popular securities.

The key finding is that prices are formed by the aggregation of the demand of all the investors. So, popularity gets into the prices and ultimately gets into the pricing model. Therefore, that’s what we have—the PAPM.

Kaplan: After having circulated this paper, I was in Chicago one evening having dinner with Larry Siegel. He’s familiar with all three of the papers we’ve been discussing, and he asked us if we would want to put them together into a CFA monograph. Of course, we said yes.[6]

Idzorek: Meanwhile, throughout this time, James was doing a lot of our empirical heavy lifting as we searched for new and different data sets in which to see if we can see the popularity phenomenon at work. We had a wealth of stuff that had been written and studied, all in a hodgepodge. A CFA monograph seemed like a wonderful home, a way to bring it all together.

Rekenthaler: James, as I understand it, your role in this collaboration was to look at some of the specific factors of popularity. Is “factors” the right word?

James Xiong: You can call them factors. Popularity is a kind of umbrella. It can include a bunch of factors or characteristics. The empirical research started back in 2014, before the popularity and asset pricing paper for the Journal of Investing was published. We looked at a bunch of potential popularity-related security factors and characteristics.

The first focus was on brands. Interbrand publishes the Best Global Brands report every year. We got data starting from 2000 of the best 100 brands each year.  Google (GOOGL) was among the lowest on the list in 2000. In 2018, it was second, with  Apple (AAPL) first. Back in 2000, they were not among the top ones. We found a very good empirical result, consistent with the hypothesis of popularity.

The second focus was the Morningstar Economic Moat Rating. Morningstar analysts rate economic moats and sort companies into one of three moat categories: wide, narrow, or none. That’s the second variable that we tested.

The third one was the Harris Poll Reputation Quotient, which rates the reputations of different companies. It’s similar to the brands list and updated annually.

We added two other characteristics related to skewness. Typically, investors prefer lotterylike stocks, stocks with a very positive skewness. And they don’t like the kind of stocks that lose even more than the market when the market is down, stocks that have negative coskewness.

Those are the five characteristics for which we looked at empirical evidence, in chapter six of the book. Chapter seven is based on the work of Roger and [Zebra Capital Management research director] Daniel Kim, and looks at traditional factors, such as size, value, liquidity, and momentum. The results are pretty consistent with the popularity hypothesis.[7]

Ibbotson: In the research that James referred to, Daniel Kim and I were looking at premiums that were already well known and showing that they’re consistent with the idea of popularity. James looked at new tests that are specifically targeted toward measuring popularity, such as brand, which obviously has a clear link to popularity. James was able to confirm the popularity concepts in these new areas of research.

Idzorek: I think “factors” and “characteristics” are appropriate terms. I also like “dimensions” of popularity. These are either company or security characteristics. There are various premiums and anomalies in the marketplace that are well researched. We went on a quest for new proxies or characteristics or attributes that would nearly universally either be liked or disliked by investors. There’s a large number of premiums or anomalies that are not necessarily consistent with the traditional CAPM view of the world, where more systematic risk always should equate to more expected return. Across all these different attributes or dimensions or characteristics, what we see is that the winner is the investor who is willing to hold the less popular attribute or characteristic, and the loser is the person who is overpaying for the liked or loved attribute.

A Unifying Framework
Kaplan: Popularity provides us a conceptual framework to understand all these different premiums—size, value, and so on—that have been studied for decades. Number one, popularity is a unifying framework. Number two, it also predicts that any kind of factor, exposure, or attribute that you can rank on some kind of popularity scale, such as those James talked about, will have a premium associated with buying the unpopular stocks. So, popularity makes a prediction that you can then look at empirically that wasn’t in the literature before.

Ibbotson: Just to be clear, it’s a price premium when we like it, but it’s a return premium when we don’t like it.

Rekenthaler: The PAPM theory is descriptive, in that the model is evaluating how dimensions of popularity affect the prices of stocks. But is it also prescriptive? If somebody doesn’t value those popularity attributes, then securities that have less of them would be sound purchases, right?

Kaplan: That’s right. That’s why I like the term “willing losers,” which Rob Arnott coined.[8] People who buy a stock because of characteristics that are popular, for reasons that have nothing to do with risk and return, they’re the willing losers. They’re willing to give up return in exchange to get the characteristics that they like.

Ibbotson: The simplest example would be liquidity. That’s a classic example in classical economics. Some people really need liquidity and are willing to pay a higher price and get lower returns to get that liquidity. Those who take the other side of this get the higher returns for less liquidity.

Rekenthaler: It sounds as if the pricing for liquidity is pretty rational. People who need liquidity will pay up to get it. The market will settle on the appropriate price. But all factors need not be rational, right? The model is agnostic as to whether the marketplace is making sense when pricing a factor.

Kaplan: Yes. That’s why the subtitle of the book is “A Bridge Between Classical and Behavioral Finance.” The reasons that investors might be drawn to a stock could be completely irrational— just because they like the names of the companies. 

Rekenthaler: Have you run into criticism from the strongly classical side or the behavioral side?

Ibbotson: Some people might say, “Oh, this is so obvious. You’re just telling us what we already knew.” Other people will say, “Well, I don’t see how that could be true.” This is one of those situations where people are either not willing to accept what we’re saying or think it’s so obvious that it shouldn’t have been said. But ultimately it gets back to supply and demand. The PAPM is an equilibrium model, and it equates supply and demand. Demand is related to popularity, and popularity comes from either classical preferences or behavioral preferences. I’m very excited about the PAPM model, because it integrates theories that have been around for many years now, and it enables us to put this all into one perspective.

Idzorek: As for the pure classical perspective that was prevalent in the 1970s and early 1980s, a lot of those guys have softened their position. And a number of behavioralists are seeking some kind of overarching framework that puts the biases and other items that they have noticed into a theory. My hope is that our work appeals to both camps.

Rekenthaler: Is your popularity work a successor to the Fama and French work on factors? They’ve tested different factors to see how that affects market pricing, but to my knowledge, they haven’t tried to pull it together into an overarching explanation.

Idzorek: They’re doing empirical work noticing what is labeled as an anomaly. What we have done is create a theory, a framework, for understanding anomalies. And it explains almost every anomaly that’s been uncovered.

Ibbotson: I really see it as a succession of the capital asset pricing model. Of course, that was developed way back in the 1960s, but it’s the core of our PAPM. It’s the very basis. We’re adding something to the CAPM that integrates all these other preferences that people have.

Kaplan: We have a very interesting quote from Gene Fama in the book. Fama says that “[v]alue stocks tend to be companies that have few investment opportunities and aren’t very profitable. Many people just don’t like that type of company. That, to me, has more appeal than a mispricing story, because mispricing, at least in the standard economic framework, should eventually correct itself, whereas taste can go on forever.”[9]

Ibbotson: That quote comes from a discussion between Fama and Thaler in 2016. He didn’t have a theory for value, so the only sensible thing was to describe it as what people like and don’t like. Of course, that’s what popularity is all about. 

Idzorek: Given that Gene is saying this, that is a softening of a hardcore classical perspective.

Rekenthaler: There is a section in the book that compares the PAPM to the CAPM in terms of accuracy in describing the marketplace.

Idzorek: In Table 7.8, we list a number of either premiums or anomalies and make a statement about whether what’s been observed is consistent with the CAPM view—that more risk equals more return—or whether there is a popularity-based explanation. Out of 10 characteristics, we found that seven were consistent with the popularity framework. Only two were consistent with the CAPM view of the world.

Ibbotson: To be fair, we can make up many different popularity explanations; it’s a flexible theory. There’s only one risk explanation.

Rekenthaler: So, the strength and weakness of the capital asset pricing model is it’s a simple, onefactor model. It seems that the strength and weakness of the PAPM is its flexibility to incorporate just about anything that comes along. We could have 50 models or 1,000 models, depending on what factors are measured and over what time periods.

Kaplan: Empirically, that’s true. There’s what John Cochrane calls the “zoo of factors.”10 Is there really a popularity story you can actually tell about a particular factor? You want to avoid data mining. If you can look at things for the first time that have not been identified as price factors in the past, as James did, and you find that the results are consistent with the popularity framework, then that strengthens the argument.

What’s Your Preference?
Ibbotson: Also, the PAPM is really powerful from a theoretical perspective. The CAPM says that everybody should hold the market portfolio and lever it up or down. The PAPM says everybody should hold a different portfolio, according to their preferences. The CAPM says that the market portfolio is always on the mean-variance efficient portfolio. The PAPM says that the market portfolio is not mean-variance efficient, so even the person who has only CAPM preferences wouldn’t want to hold that portfolio. They’d want to take advantage of the preferences of others.

In the CAPM, diversifiable risk disappears. Essentially, people hold perfectly diversified portfolios. But in the PAPM, you’re going after these preferences here, and you’re not perfectly diversified. Of course, in the CAPM, only beta is priced, whereas in the PAPM, many types of characteristics can be priced. That’s just some sense of some of the differences between the CAPM and the PAPM.

By adding just one extra dimension, and calling it popularity, we’re able to make the theoretical conclusions of the CAPM much more realistic and actually conform with the real world. So, it has some very powerful theoretical content even before you get to the problem that you referred to, John. It’s true that the PAPM is so flexible that there’s no clear menu of how to put it together and use it.

Rekenthaler: What would need to be plugged in to use the PAPM? Would it be a preferences assessment rather than a risk-tolerance assessment? How would the role of the advisor change?

Kaplan: The role for an advisor could be to identify the investor’s preferences, and then, to convince them not to invest based on those preferences. 

Ibbotson: If they’re legitimate preferences, you should. If you need liquidity, you want to have liquid assets.

Rekenthaler: But make sure that they are rational preferences.

Kaplan: Right. Investors do have irrational preferences. If the role of the advisor is to help change behavior, and if an advisor can get clients to hold the unloved, then I think they’ve done a lot.

Idzorek: But in some instances, an advisor could be pointing out a tradeoff that an investor is willing to make due to their preferences. ESG is an example. All else equal, I think people would prefer companies that have better ESG characteristics. But the popularity lens would predict that they would be giving up something in return.

Rekenthaler: And through the work of James, you can attempt to quantify that.

Idzorek: Exactly. And that’ll probably be time-varying as well, as people’s preferences ebb and flow.

Xiong: Practically speaking, I think there are still some challenges in implementing the hypothesis of popularity. For example, how can you determine when a stock is overly popular? How do you quantify that? In the financial world, timing stocks is pretty difficult. You could argue that high-momentum stocks are popular, but they still outperform low-momentum stocks in the next year. Based on the popularity hypothesis, you would say the stock becomes overly popular over time, which will result in a reversal, but the timing could be longer than one year.

Ibbotson: Popularity makes it more complicated. You’d like to buy a security that is getting more popular. It turns out, though, that the less popular stocks are more likely to get more popular than the most popular stocks. But effectively, a change in popularity can impact your returns, as well.

Rekenthaler: So, there’s a tactical element to this as well as the strategic.

Ibbotson: We didn’t stress that in our monograph, but that is a potential part of this whole picture.

Kaplan: The trick there, of course, is to identify the stocks which are becoming more popular, buy them, but then sell them before they lose their popularity. That’s a tricky game to play.

Rekenthaler: If you can do it well, that’s how to make a whole lot of money. But that’s more of a portfolio manager opportunity than a retail investor opportunity. Probably not a game that I would want to play.

1 Ibbotson, R.G., Diermeier, J.J., & Siegel, L. 1984. “The Demand for Capital Market Returns: A New Equilibrium Theory.” Financial Analysts Journal, Vol. 40, No. 1, PP. 22–33.

2 Ibbotson, R.G., Idzorek, T.M., & Xiong, J.X. 2012. “The Liquidity Style of Mutual Funds.” Financial Analysts Journal, Vol. 68, No. 6, PP. 38–53.

3 Ibbotson, R.G., Chen, Z., Kim, D. Y.-J., & Hu, W.Y. 2013. “Liquidity as an Investment Style.” Financial Analysts Journal, Vol. 69, No. 3, PP. 30–44.

4 Ibbotson, R.G. & Idzorek, T.M. 2014. “Dimensions of Popularity.” Journal of Portfolio Management, Vol. 40, No. 5, PP. 68–74.

5 Idzorek, T.M. & Ibbotson, R.G. 2017. “Popularity and Asset Pricing.” The Journal of Investing, Vol. 26, No. 1, PP. 46–56.

6 Ibbotson, R.G., Idzorek, T.M., Kaplan, P.D., & Xiong, J. X. 2018. Popularity: A Bridge Between Classical and Behavioral Finance, CFA Institute Research Foundation.

7 Ibbotson, R.G. & Kim, D. Y.-J. 2017. “Risk and Return Within the Stock Market: What Works Best?” Zebra Capital Management, White Paper.

8 Quoted in Rostad, K.A. 2013. The Man in the Arena: Vanguard Founder John C. Bogle and His Lifelong Battle to Serve Investors First. New York: John Wiley & Sons.

9 Fama, E.F. & Thaler R. H. 2016. “Are Markets Efficient?” Chicago Booth Review, June 30. 10 Cochrane, J. H. 2011. “Presidential Address: Discount Rates.” Journal of Finance, Vol. 66, No. 4, PP. 1047–1108.

This article originally appeared in the Summer 2019 issue of Morningstar magazine. To learn more about Morningstar magazine, please visit our corporate website.

John Rekenthaler does not own (actual or beneficial) shares in any of the securities mentioned above. Find out about Morningstar’s editorial policies.