In some time periods, popular stocks become even more popular and temporarily outperform less popular stocks, such as the five-year period preceding the dot-com crash. In all the cases that we discuss, however, over reasonably long periods of time, the less popular stocks have earned premiums. This result may be counterintuitive, but we demonstrate it empirically in Chapters 6 and 7 .
Premiums vs. Mispricing
The notion of mispricing requires the existence of a “true price” from which the price has diverged. Such a true price can never be known, so to declare any particular security to be “mispriced” is daring. If a true price were known and the price had, in fact, diverged from this price, the market would be in a state of disequilibrium with numerous investors trying to either buy or short the mispriced security (i.e., not every market participant would be able to hold the desired shares).
Practitioners frequently use the term “mispriced” to describe a security that they believe (but do not know with certainty) has diverged from what they believe to be something akin to the true price. This usage simply reflects different opinions about expected returns and other preferences; it does not represent true mispricing and is consistent with market equilibrium (i.e., every market participant is able to hold the desired shares). For example, like all models, the CAPM is a crude model of reality. It produces an expected return, and hence an estimate of price, that in most cases is wrong. So, one might say a security is mispriced relative to the price given by the CAPM. To repeat, the CAPM may be wrong and the market may be in equilibrium.
Because most of the premiums we discuss are relatively permanent, we do not consider that the differential returns various clienteles can expect to earn are market inefficiencies. Rather, they are the premium payoffs for the willingness to invest in stocks that other investors want to avoid or underweight in an equilibrium setting. The investors with strong preferences might be called “the willing losers” or, in some cases, “unknowing losers.” 11 They allow other investors to earn excess returns by taking on more risk, tolerating less liquidity, having longer time horizons, or investing in companies that are shunned by others. The investors with weaker preferences (even if the preferences are in the same direction) should expect to earn higher returns, even in equilibrium.
Various investor portfolios will have different returns from one another, even over the long run. There are three possible explanations:
Long-term premiums—portfolios have risk premiums and other types of premiums.
Luck—investors were lucky or unlucky.
Skill—investors skillfully bought and sold the mispriced securities at the appropriate times (or had perverse skill and did the opposite).
The first and second explanations are consistent with efficient markets. The third explanation involves mispricing and inefficient markets. Mispricing, by its very nature, must be relatively short term because the skilled investor can benefit from the distortions only if prices tend to correct themselves.
To sum up, popularity can be viewed from both a classical and a behavioral perspective and can include both long-term premiums and mispricing.
Popularity and Adaptive Markets
Andrew Lo (2017) has written a book about how ideas and markets evolve under changing economic, behavioral, and technological circumstances. Although Lo does not use the term “popularity,” his approach is consistent with ours. His focus is on the dynamics of financial thought over time.
Investors, markets, and products adapt, but the economic environment is also continually changing. As imperfect beings, we never fully reach the classical ideal, and although we learn, we cannot fully dissociate ourselves from our evolutionary selves in purely rational ways. Some assets will always be more popular than others, for both rational and irrational reasons. In adaptive markets, premiums may shift over time, prices may be corrected, but new pricing discrepancies may be introduced.
Although our book is broad, it is more limited in scope than Lo’s (2017) Adaptive Markets . We focus on investor demand to show how investor preferences can be characterized by the popularity of various assets and premiums. The returns we measure are long term and span decades, but they do not span the centuries and millennia that Lo addresses. Our premiums adapt over time, but that change is not our main emphasis. Rather, we are trying to characterize why the premiums exist. We set out to understand how prices are formed in a market environment made up of investors with both rational and irrational preferences. Both Lo’s and our approaches help bridge the gap between classical and behavioral finance.
2. Premiums, Anomalies, and Popularity
Popularity provides an explanation for the relative performance of different asset classes and different securities. 12 Asset pricing theories have long recognized that expected returns should not be the same for instruments in the marketplace that have different characteristics. The primary explanation for these differences has been differences in risk. Of course, risk is unpopular: Investors do not like risk and want to be compensated for it. But other characteristics matter too.
For a given security or asset class, the capital asset pricing model (CAPM), which is an equilibrium model, splits risk into two parts: the beta (or systematic or market risk) and the residual (or diversifiable risk). According to the CAPM, only the beta part of the risk should be compensated with higher expected returns because the residual risk can easily be eliminated by diversification but systematic risk cannot be diversified away. Other theories, such as the arbitrage pricing theory (an arbitrage model) developed by Ross (1976) , posit multiple risk factors that bear premiums.
Following the publication of Fama and French (1992) , although even before that time, size and value became generally accepted as additional risk factors for the stock. 13 Fama and French originally characterized size and value as “risk” premiums, even though little evidence exists that value is associated with risk, as measured by volatility. If one were forced to attempt to explain the value premium as a risk premium, one might focus on the expectation of an increased risk of bankruptcy or having financial distress that manifests itself when investors are most vulnerable, in which the higher risk of bankruptcy at the macro level has yet to be realized in the data series most often studied.
Other characteristics were also recognized as affecting returns. For some time, we have known that liquidity affects bond yields and that investors demand the expectation of a premium to lock up their capital in real estate or private equity, which are illiquid. Amihud and Mendelson (1986) , among others, showed that liquidity also affects stocks. Ibbotson, Chen, Kim, and Hu (2013) demonstrated that liquidity could be considered a style factor because liquidity premiums appear to be at least comparable to size or value premiums. Building on stock-level liquidity premiums, Idzorek, Xiong, and Ibbotson (2012) found that after controlling for other characteristics, mutual funds that, on average, held the less liquid stocks outperformed—even net of fees. Liquidity can be cast as the risk of not being able to turn your investment into cash extremely quickly without a price concession.
Another factor that might affect stock returns is momentum. Jegadeesh and Titman (1993) suggested that momentum affects stocks because they found that stocks that have performed well in the previous 12 months appear to do better than those that performed relatively poorly. The momentum anomaly has been more erratic over more recent periods; much of the research since 1993 has attempted to understand how and why momentum seems to have worked. Xiong and Ibbotson (2015) showed that stocks that have accelerating prices are more likely to have poor returns and crash.
Asset Class Risks
Across the asset classes, Ibbotson and Sinquefield (1976a) measured various types of risk premiums, including the equity risk premium and small-cap premium for stocks and the horizon risk (maturity) premium and default premium for bonds. When added to the base of expected inflation and real (inflation-adjusted) interest rates, Ibbotson and Sinquefield (1976b) formed forecasts of returns for the stock and bond
asset classes. The expectation of higher returns for stocks than bonds was explained by the fact that stocks are much riskier than bonds. Furthermore, small-cap stocks are riskier than large-cap stocks and longer-term bonds. Those with default risk are riskier than shorter-term bonds and those with less default risk. Table 2.1 shows the results of the Ibbotson and Sinquefield approach updated for the period 1926–2017.
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Table 2.1. Stocks, Bonds, Bills, and Inflation: Summary Statistics of Annual Total Returns, 1926–2017
Asset Class
Geometric
Mean
(%)
Arithmetic
Mean
(%)
Standard
Deviation
(%)
Large-cap stocks
10.2
12.1
19.8
Small-cap stocks
12.1
16.5
31.7
Long-term US government bonds
5.5
6.0
9.9
Intermediate US government bonds
5.1
5.2
5.6
US Treasury bills
3.4
3.4
3.1
Inflation
2.9
3.0
4.0
Source: Ibbotson (2018) .
Figure 2.1 provides a plot of the annual geometric local currency real returns and standard deviations associated with stocks, bonds, and Treasury bills for 19 countries from 1901 through 2017 based on data from Dimson, Marsh, and Staunton (2002) and updated through 2017. The Dimson et al. data set includes 21 countries, but we omitted Germany and Austria because of their incomplete or extreme returns associated with World Wars I and II.
For the three asset classes (stocks, bonds, and bills), the risk–return paradigm appears to work reasonably well—that is, a regression line passed through all of the data points results in the expected positive slope. In contrast, if one passes a regression line separately through each of the asset classes, for all the countries, the relationship within all three asset classes is somewhat negative, suggesting that risk is the dominant factor among different asset classes but not within an asset class.
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Figure 2.1. Risk and Return of Stocks, Bonds, and Government Bills of 19 Countries: 1901–2017
Source: Dimson et al. (2002) updated through 2017 with data from Morningstar Direct.
The Equity Premium
First and foremost of the risk premiums is the equity risk premium. The additional risk of equities relative to safer investments represents an unpopular characteristic, so the positive equity premium is consistent with the idea of popularity. The notion of an equity or market risk premium was explicitly defined and modeled by Williams (1938) and robustly measured on an ongoing basis starting with Ibbotson and Sinquefield (1976a) . That equities are riskier than bonds makes intuitive sense; therefore, equities should carry the expectation of a return premium that compensates the investor for the increased risk. 14 The market (equity risk) premium is the key input in the CAPM. Under the CAPM, as long as the market risk premium is expected to be positive, more risk (market beta) results in greater expected return.
Popularity and the Equity Premium Puzzle. Mehra and Prescott (1985) coined the expression “equity premium puzzle” and argued that the equity premium has been too large relative to academic models of investor behavior, including the CAPM. They maintained that the observed historical equity premium is consistent with relative risk aversion that is approximately 30 times greater than theoretical estimates. Working with a version of Kahneman and Tversky’s (1979) prospect theory (in which losses hurt far more than equivalent gains help), Benartzi and Thaler (1995) claimed to have solved the equity premium puzzle. Mehra and Prescott (2003) reviewed the various explanations for why the equity premium has been so large, including Benartzi and Thaler’s, and concluded that the equity premium remains a puzzle.
Ang (2014 , pp. 242–52) provided an overview of the four primary explanations for the equity premium puzzle: Aversion to market risk is sometimes very high (Campbell and Cochrane 1999 ), disaster risk is feared (Rietz 1988 ; Jorion and Goetzmann 1999 ), long-run risk is undesirable (Bansal and Yaron 2004 ), and investors are heterogeneous (Jerison 1984 ; Kirman 2006 ). 15 Interestingly, while discussing the risk-free-rate puzzle of Weil (1989) , Ang stated, “It turns out that the question, ‘why are equity returns so high?’ is the flip side of the question, ‘why are risk-free rates so low?’ ” (p. 245).
Idzorek (2015) offered a popularity-based explanation for the yin and yang of the risk-free and equity premium puzzles:
[E]quity investing has been substantially democratized—with the creation of the first modern mutual fund in the 1920s, steady decreases in trading costs, the first index funds in the 1970s, and more recently the advent of exchange-traded funds. This democratization has increased equity investing’s relative popularity. An increase in its popularity seems to have corresponded with a substantial return premium over bonds. (p. 48)
That is, a long, steady increase in the relative popularity of equity investing may have contributed to the high realized , historical equity premium (demand increasing faster than supply). In the future, unless further gains in the popularity of equity investing occur, the expected equity premium is likely to be lower than it has been. This explanation would also imply that the equity premium is not the result of a stationary process.
Goetzmann and Ibbotson (2008) documented the historical equity premium in the United States between 1792 and 1925 and between 1926 and 2004. They found a significantly higher realized premium between 1926 and 2004. Proving that the democratization of equity investing contributed to the increased realized historical equity premium would be difficult, but the relationship seems plausible. Consistent with the shifting relative popularity of stocks versus bonds, nearly 90 years ago Fisher (1930) wrote,
… investment trusts and investment council tend to diminish the risk to the common stock investor. This new movement has created a new demand for such stocks and raised their prices, at the same time it has tended to decrease the demand for, and to lower the price of, bonds. (p. 221)
Fisher (1930) made this observation during a time of euphoric stock market popularity. Almost three-quarters of a century later, Duca (2001) chronicled the further democratization of the US capital markets, including an increase in the number of households owning stock, which went from 25% in the 1960s to 50% in the 1990s.
Premiums and Anomalies within Equity Markets
Although risk may be the main driver of return differences among asset classes (bills vs. bonds, bonds vs. stocks, and so on, as illustrated in Figure 2.1 ), increasing evidence indicates that risk is not the primary driver within asset classes. Frazzini and Pedersen (2014) and others demonstrated that in the equity asset class, low-beta and low-volatility portfolios have done better than high-beta or high-volatility portfolios, which Asness, Frazzini, and Pedersen (2012) attributed to leverage aversion. Ibbotson and Kim (2017) showed that the risk and return dimensions are surprisingly reversed for most of the factors that affect stock returns. We show this result in Figure 2.2 . 16
Figure 2.2. Risk and Return for Factor-Based Equity Portfolios, 1972–2016
Sources: Ibbotson and Kim (2017) ; Ibbotson (2018) .
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To some degree, Figure 2.2 focuses on a single plot point from Figure 2.1 : US equities. In the US equity asset class, sorts based on beta, volatility; size of companies measured by accounting data; value measures; momentum; various factor loadings; and so on show the seemingly perverse result that within the US stock market, the lower risk characteristics are associated with higher returns. The regression line in Figure 2.2 depicts this result. This line is in contrast to the capital market line, which is positively sloped and runs through the points representing the m
arket portfolio and the risk-free asset. 17
If risk is not the single driver of returns, what is? Investors do not like risk. Therefore, they need to be compensated for taking on risk, especially for the betas or systematic risks that they cannot collectively avoid. Unfortunately, the term “risk” has become a catch-all for any attribute that investors do not like even though the attribute may not be directly linked to risk.
The compensation for risk makes sense, but compensation should also apply to other characteristics that investors do not like. Asset prices should also reflect the characteristics that investors like “too much.” Stated simply and broadly, if an asset has characteristics that investors really like, its price will be high. If the asset has characteristics that investors do not like, its price will be low, all other things being equal. Thus, the asset with the more desirable characteristics should have lower expected relative returns, whereas the asset with less desirable characteristics should have higher expected relative returns.
Risk is only one dimension of popularity. Popularity can include all sorts of other characteristics that do not fit well into the risk–return paradigm. Following the preference for less risk, the next most obvious characteristic that investors nearly uniformly desire is liquidity. For a given level of expected return and risk, investors prefer high liquidity.
Just as avoiding risk is not free, however, neither is avoiding illiquidity. Both often come at the expense of lower expected returns. Assets with high liquidity are coveted and thus more expensive than assets with low liquidity, even though the differences in liquidity or transaction costs might appear minor. Liquidity cannot easily be squeezed into a risk–return paradigm because the less liquid assets are not necessarily more volatile, nor do they necessarily have higher betas.
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