We found the correlations between the various factors to be relatively low. Moving across the measures of brand value, competitive advantage, and reputation, representing three dimensions of popularity, we see that the arithmetic and geometric mean returns of the less popular quartiles nearly monotonically outperformed the more popular quartiles. The higher returns for the quartiles based on brand power had no discernible relationship to risk. The higher returns based on sustainable competitive advantage had a strong relationship to risk (more risk/more return), and those based on company reputation had a mild relationship to risk.
Assuming that a powerful brand, a sustainable competitive advantage, and a good reputation are characteristics that investors like or admire, from the popularity perspective, some investors (the willing or unknowing losers) are simply willing to give up some level of return or overpay for a characteristic they like.
The results based on sustainable competitive advantage and company reputation are consistent with the risk–return paradigm, but the results from all three data sets are consistent with the theory of popularity.
We performed empirical analyses for negatively coskewed stocks and lottery-like stocks. Stocks with negative coskewness were expected to command a higher expected return than those with positive coskewness because negatively skewed returns are less desirable or less popular. Lottery-like stocks have a relatively small probability of a large payoff and are preferred. Consistent with the popularity hypothesis, we found that stocks with more negative coskewness (those less popular) tend to have higher risk-adjusted returns and lottery-type stocks (those more popular) tend to have lower risk-adjusted returns.
Overall, we carried out five extended analyses (brand, competitive advantage, reputation, tail risk, and lottery-like stocks). For each, we analyzed both equally weighted composites and market cap–weighted composites. Of the 10 views, 10 out of 10 were highly consistent to moderately consistent with the popularity thesis, whereas only 5 out of 10 were consistent with the risk– return paradigm.
Finally, for each dimension of popularity analyzed in the chapter, we created what one might label “a popularity factor series” by subtracting the most popular portfolio from the least popular portfolio, resulting in a zero-dollar factor for investment brand, competitive advantage, reputation, tail risk, and lottery-like stocks. We carried out this approach for both the equally weighted composites and the market cap–weighted composites. We created correlation matrixes so we could see how correlated the various factors were with one another and with the Fama–French size and value factors. We found the correlations between the various factors to be relatively low.
7. Empirical Evidence of Popularity from Factors
Throughout this book, we have touched on the idea that popularity helps to explain most, if not all, of the well-known premiums and anomalies. We have even been able to put forth popularity as a potential explanation for the equity premium puzzle, the underdiversification puzzle, momentum, and bubbles and crashes. In this chapter, we take a closer look at various return premiums and anomalies through the popularity lens.
This chapter is largely based on Ibbotson and Kim (2017 ; hereafter, IK) with an overlay of the popularity framework of Ibbotson and Idzorek (2014) and Idzorek and Ibbotson (2017) , which has been advanced throughout this book. Specifically, IK studied the risk and return relationships that are revealed when stocks are sorted by beta, volatility, size, value, liquidity, and momentum. All of the tables and figures in this chapter are based on the tables and figures in IK, with some recasting, reordering, and reformatting.
As the reader will see, the conventional wisdom that more risk means more return does not always hold. We believe that popularity serves as a good explanation for this.
Returns and Factors
IK used the CRSP data set (market data) and Compustat data set (accounting data) for US stocks as accessed through the WRDS website. 46 They constructed portfolios annually on the final trading day of each calendar year between 1971 and 2016 and used trailing 12-month (“selection year”) data. For each year, the universe was limited to a maximum of 3,000 stocks, but in about half of the sample period years, the universe consisted of fewer than 3,000 stocks after the sample was culled for small-capitalization stocks, low stock prices, or missing data. 47 We made use of selection-year data on revenue, earnings, book equity, and assets when available. Selected portfolios were passively held for the following calendar year (the “performance year”) to determine the total returns of the portfolios.
Table 7.1. Composite Returns for the Universe, 1972–2016
Weighting
Statistics
Equally weighted
Geometric mean return
12.52%
Arithmetic mean return
14.66
Standard deviation
21.56
Cap-weighted
Geometric mean return
10.56
Arithmetic mean return
12.02
Standard deviation
17.34
Source: Ibbotson and Kim (2017) .
______________________________
Table 7.1 presents summary statistics for the equally weighted and cap-weighted composites derived from the universe of stocks in the IK study. The period consists of 45 performance years from 1972 to 2016 (1971 was used only as a selection year), during which the average number of stocks in the universe portfolio was 2,603. This period covered several economic cycles, including the recessions of 1973–1974, 1980–1981, 1991–1992, and 2000–2001 as well as the financial crisis of 2008. It also includes the strong bull markets of the 1980s, 1990s, and 2009–2016, so the overall returns are still reasonably high and are far in excess of riskless rates. Relative to the returns on cash and bonds (not reported), a substantial equity risk premium was realized over the period regardless of the weighting scheme. As Table 7.1 shows, the equally weighted composite produced a higher geometric return, albeit with a higher standard deviation, than the cap-weighted composite and is thus consistent with the risk–return paradigm.
IK examined beta, volatility, size, value, liquidity, momentum, and other factors based on these variables. From this list, we examined those variables that are most relevant to empirical tests of popularity. 48 From our perspective, among active managers, high beta, high volatility, and high liquidity are popular characteristics. High volatility is popular among active managers because of the commonly held belief that a portfolio of high-beta stocks should outperform a portfolio of low-beta stocks in most markets since the stock market goes up most years. Portfolio managers know that most investors focus primarily on returns and return comparisons and often ignore risk-adjusted returns or treat them as less important than pure returns. Of the IK factors, we viewed momentum as a change or a series of changes in relative popularity.
For each factor, IK sorted all stocks in the universe in the selection year and formed quartiles. They then measured the total returns of the quartile portfolios in the following performance year.
IK numbered the quartiles on the basis of ex post performance over the 45-year period, so Quartile 1 outperformed Quartile 4. For consistency with Chapter 6 , we renumbered IK’s quartiles, where possible, on the basis of popularity so that Quartile 1 contains the most popular stocks and Quartile 4 contains the least popular stocks.
Table 7.2 presents the median factor values for the various quartile portfolios constructed on the last trading day of selection year 2015. For example, the row labeled “Beta” lists the median beta of the four quartile portfolios constructed by sorting each stock in the universe by beta (as calculated from daily stock returns during 2015). Similarly, the row labeled “Market cap” shows the median market cap (in billions of dollars) of the four size quartiles constructed using year-end 2015 market-cap data. In some rows, we have reversed the order of the values shown by IK to conform to our convention for numbering the quartiles.
______________________________
Table 7.2. Median “Factor” Metric of All Quartile Portfolios Selected in 2015
Factor(s)
Portfolio Sorting Metric
Q4
(least popular)
Q3
Q2
Q1
(most popular)
Beta & volatility
Beta
0.667
0.885
1.042
1.310
Daily volatility
0.013
0.017
0.023
0.036
Monthly volatility
0.051
0.072
0.101
0.162
Size
Market cap ($ billions)
0.259
0.792
2.273
11.577
Total assets ($ billions)
0.240
1.017
3.229
15.735
Revenue ($ billions)
0.099
0.529
1.793
8.211
Net income ($ billions)
–0.042
0.019
0.094
0.559
Value
Book/market
0.983
0.559
0.315
0.126
Earnings/price
0.084
0.053
0.028
–0.066
Return on equity
–0.223
0.057
0.115
0.250
Liquidity
Amihud illiquidity
2.948
0.432
0.085
0.013
Momentum
12-month
–0.373
–0.114
0.064
0.319
2–12 months
–0.319
–0.070
0.101
0.358
Note: Amihud illiquidity is the Amihud (2002) measure, defined as the absolute value of the daily return divided by the daily dollar value of shares traded, averaged over the course of a period. Source: Ibbotson and Kim (2017) .
IK lagged accounting data two months beyond the end of the accounting reporting period to reflect reporting delays. Thus, in Table 7.2 , the metrics of total assets, revenue, net income, book/market, earnings/price, and return on equity for selection year 2015 were based on accounting data from reporting periods ending between November 2014 and October 2015. In contrast, we used calendar year 2015 data to rank market cap and momentum because these variables are immediately available at the end of the year.
IK constructed portfolios on the last day of the selection year (1971–2015) and then measured performance in the subsequent year (1972–2016). During the performance year, they did not rebalance, so the position weights floated throughout the performance year. Therefore, the end of each calendar year marked both the end of the performance year for the portfolios selected one year previously and the construction date for a new set of selection-year portfolios based on the recalculated sorting metrics listed in Table 7.2 . All of the quartile portfolios listed were rebalanced annually.
We report the annualized geometric mean, the annualized arithmetic mean, and the annualized monthly standard deviation in the tables that follow. In the figures that follow, we show the annualized geometric mean during the study period plotted on the vertical axes and the annualized standard deviations plotted on the horizontal axes. In the sections that follow, we focus on beta and volatility, size, value, and liquidity.
Beta and Volatility
According to the capital asset pricing model (CAPM), a positive relationship should exist between beta and returns. In general, a positive relationship should exist between risk and return. Thus, higher volatility and systematic risk should also be associated with higher returns.
Table 7.3 reports the long-term performance-year returns for each quartile portfolio based on beta and also based on volatility. For the reasons that we discussed in Chapter 2 , we regard high-beta and high-volatility stocks as being popular and low-beta and low-volatility stocks as being unpopular.
IK showed the annualized geometric mean, arithmetic mean, and annualized standard deviation that were realized during the study period. For all but one sorting metric (daily volatility), Quartile 4 (Q4) outperformed the other quartiles, in terms of geometric mean return, over the study period. In each case, Q4 represents the most unpopular stocks (low beta, low daily volatility, and low monthly volatility) from the selection year.
Table 7.3. Beta and Volatility Quartile Portfolio Returns, 1972–2016
Portfolio Sorting Metric
Statistic
Q4
(least popular, low)
Q3
Q2
Q1
(most popular, high)
CAPM beta
Geometric mean return (%)
14.20
13.99
12.45
8.24
Arithmetic mean return (%)
15.70
15.92
14.82
12.20
Standard dev. (%)
18.15
20.67
22.72
29.24
Sharpe ratio
0.60
0.53
0.44
0.25
Daily volatility
Geometric mean return (%)
13.94
14.18
13.24
7.12
Arithmetic mean return (%)
15.15
15.91
15.78
11.81
Standard dev. (%)
16.25
19.47
23.51
32.21
Sharpe ratio
0.63
0.57
0.46
0.22
Monthly volatility
Geometric mean return (%)
14.28
14.27
12.78
7.35
Arithmetic mean return (%)
15.56
16.07
15.35
11.67
Standard dev. (%)
16.93
19.84
23.57
30.90
Sharpe ratio
0.63
0.56
0.44
0.22
Source: Ibbotson and Kim (2017) .
______________________________
In Table 7.3 , the less popular quartiles monotonically outperformed the more popular quartiles from a Sharpe ratio perspective. The same is nearly true from a geometric return perspective. The quartiles based on CAPM beta, daily volatility, and monthly volatility are all consistent with the popularity paradigm, while none of them is consistent with the risk–return paradigm. In fact, the breakdown of the risk–return relationship in Table 7.3 is dramatic.
Figure 7.1 plots the annual geometric mean versus the annualized standard deviation of the quartile portfolios in Table 7.3 . The equally weighted stock universe reported in Figure 7.1 and in the rest of the figures in this chapter is labeled “Universe Equal,” and the cap-weighted stock universe is labeled “Universe Cap.”
By a relatively large margin, Figure 7.1 shows that the three Q1 portfolios (high CAPM beta, high monthly volatility, and high daily volatility) have the lowest realized returns and highest standard deviations. The Q3 and Q4 portfolios have the highest returns and lower standard deviations.
Other researchers have found similar results in which the expected relationship—more risk/more return—seems to break down. For example, Jensen, Black, and Scholes (1972) and Frazzini and Pedersen (2014) found that high-beta stocks are associated with low excess returns; Haugen and Baker (1991) and Ang, Hodrick, Xing, and Zhang (2006) found that high-volatility stocks consistently underperform.
Figure 7.1. Performance of Beta and Volatility Quartile Portfolios, 1972–2016
Notes: Squares indicate Q4 (least popular, low), and diamonds indicate Q1 (most popular, high). Small dots indicate Q2 and Q3.
Source: Ibbotson and Kim (2017) .
______________________________
As we discussed in Chapter 2 , building on the idea of leverage aversion put forth by Black (1972) , Frazzini and Pedersen (2014) argued that leverage aversion on the part of enough market participants results in demand for high-volatility, high-beta securities. 49 The reason is that investors who cannot or do not wish to leverage may buy high-beta securities as a substitute. The popularity of high-beta stocks, in turn, bids up prices and reduces returns. To the extent to which leverage is highly unpopular and investors are averse to it, Frazzini and Pedersen’s results are consistent with the theory of popularity.
The results that we present in Figure 7.1 show that the CAPM risk–return relationship does not hold. Although risk is usually unpopular, especially across asset classes, in some situations, taking risk is the popular thing to do, especially in the stock market. Thus, we see that beta and volatility have had an inverse empirical relationship to stock returns, with high-beta and high-volatility stocks having lower returns.
Size
Table 7.4 presents results for the size quartile portfolios. Because the geometric return of the Q4 (small-cap, least popular) portfolio is higher than that of the Q1 (large-cap, most popular) portfolio, we conclude that the small-cap premium is positive. Additionally, small-cap stocks have a higher standard deviation than large-cap stocks; thus, the size dimension as measured by market cap is consistent with a positive risk–return trade-off. If we interpret market cap as a relative dollar-based popularity vote, this result is perhaps an indirect measurement of popularity. Relative to small-cap stocks, more people own large-cap stocks and own more of them, and large-cap stocks are more liquid, are better known, and are covered by more equity analysts. Hence, large-cap stocks have a number of popular characteristics.
Popularity Page 14