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1 Risk and Return Within the Stock Market: What Works Best? Roger G. Ibbotson * and Daniel Y.-J. Kim ** January 14, 2014 Abstract This paper studies return-predictive characteristics of U.S. securities, including beta, volatility, size, value, liquidity, and momentum. Value and low liquidity have the largest impact on returns, while low beta, low volatility, and low liquidity have the best performance when measured on a risk adjusted basis. Contrary to the conventional wisdom on risk and reward, most portfolio sorting metrics exhibit an inverse risk-return relationship, with lower risk portfolios outperforming higher risk portfolios. A broad theme that emerges from the empirical evidence is that popularity underperforms. * Roger G. Ibbotson is a Professor in Practice at Yale School of Management and Chairman & CIO of Zebra Capital Management, LLC. ** Daniel Y.-J. Kim is Research Director at Zebra Capital Management, LLC.

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1

Risk and Return Within the Stock Market:

What Works Best?

Roger G. Ibbotson* and Daniel Y.-J. Kim**

January 14, 2014

Abstract

This paper studies return-predictive characteristics of U.S. securities,

including beta, volatility, size, value, liquidity, and momentum. Value and low

liquidity have the largest impact on returns, while low beta, low volatility, and

low liquidity have the best performance when measured on a risk adjusted

basis. Contrary to the conventional wisdom on risk and reward, most portfolio

sorting metrics exhibit an inverse risk-return relationship, with lower risk

portfolios outperforming higher risk portfolios. A broad theme that emerges

from the empirical evidence is that popularity underperforms.

* Roger G. Ibbotson is a Professor in Practice at Yale School of Management and Chairman & CIO of Zebra Capital Management, LLC. ** Daniel Y.-J. Kim is Research Director at Zebra Capital Management, LLC.

2

It is well known that across asset classes, more risky asset classes beat

less risky assets. Over the long run, stocks outperform bonds in the U.S.1 and

worldwide for almost all extended periods. For example, Dimson, Marsh, and

Staunton (2013) examine equity risk premiums starting in 1900, and find that

stocks outperform bonds in all 20 developed countries studied.

Instead of across stock markets, we look within a single market, the U.S.

stock market. We study the risk and return relationships when categorizing

stocks by various characteristics including beta, volatility, size, value, liquidity,

and momentum. We determine which characteristics have the largest impact

on returns and observe whether higher risk always accompanies higher

returns. Relative to the conventional wisdom on risk and reward, many of the

empirical results are surprising; we offer the underperformance of popularity

as a common explanation for several of these unexpected results.

The Data Set

We use the CRSP (market data) and Compustat (accounting data)

datasets on U.S. stocks, as accessed through the WRDS website2. Portfolios

are constructed annually on the final trading day of each calendar year

between 1971 and 2012, using trailing 12-month (“selection year”) data. In

each selection year, the universe is limited to a maximum of 3,000 stocks, but

1 See Ibbotson SBBI 2013 Classic Yearbook, Market Results for Stocks, Bonds, Bills, and Inflation 1926-2012, Morningstar Inc. Stocks had a compounded annual return of 9.8% over the full period while long-term U.S. Government bonds returned 5.7% and U.S. Treasury Bills returned 3.5%. 2 CRSP (Center for Research in Security Prices) data is from the University of Chicago, Booth School of Business, and Compustat is a trademark of Standard & Poor's, a division of the McGraw-Hill Companies. WRDS (Wharton Research Data Services) is available at wrds-web.wharton.upenn.edu.

3

in about half of the sample period years, the universe consists of fewer than

3,000 stocks, after culling the sample for low capitalizations, low stock prices,

or missing data3. We make use of selection-year data on revenue, earnings,

book equity, and assets when available. Selected portfolios are passively held

in the following calendar year (the “performance year”) to determine the total

returns of portfolios.

In Table 1 we list the equally weighted and capitalization weighted

benchmarks, derived from the universe of stocks in the study. The period

consists of 42 performance years from 1972-2013 (1971 is only used as a

selection year), over which the average number of stocks in the universe

portfolio is 2,602. This period covers several economic cycles, including the

recessions of 1973-74, 1980-81, 1991-92, 2000-2001, and the financial crisis

of 2008. It also includes the strong bull markets of the 1980s and 1990s, so

that the overall returns are still reasonably high and are far in excess of

riskless rates. Thus there is a substantial equity risk premium over the period.

Table 1. Benchmark returns, 1972-2013.

Portfolio Weighting Result

Universe

Equal weight

geom 12.98%

arith 15.22%

SD 22.03%

Cap weight

geom 10.72%

arith 12.27%

SD 17.86% 3 The inclusion criteria for stocks are: common stocks listed on the NYSE, AMEX, or NASDAQ markets, but excluding REITs, warrants, ADRs, ETFs, Americus Trust Components, and closed-end funds. Data for trading volume, total returns, earnings, shares outstanding, and price must be available for the 12 months of the selection year. The stock price at the end of the selection year must be at least $2. Finally, the market capitalization of included companies must both rank within the largest 3,000 for the year, and also exceed a fixed fraction of the total universe market cap at year end, equal to that of a $100 million company at the end of 2011.

4

We will examine the general categories of beta & volatility, size, value,

liquidity, momentum, Fama & French betas, and factor betas of portfolios,

where each of these categories includes various sorting metrics with which the

stock universe is ranked in the selection year by quartiles, with total returns

measured in the following performance year.

In Table 2 as an illustration, we list the median metric values of all

quartile portfolios constructed on the last trading day of selection year 2012.

For example, the row labeled “CAPM beta” lists the median beta of the 4

quartile portfolios constructed by sorting each stock in the universe by beta (as

calculated from daily stock returns during 2012.) Likewise, the row labeled

“Market cap [$B]” shows the median market cap of the 4 size quartiles

constructed using year-end 2012 market cap data.

Accounting data is lagged by 2 months beyond the end of the accounting

reporting period, in order to reflect reporting delays. Thus, in Table 2, the sort

metrics for total assets, revenue, net income, book/market, earnings/price,

and ROE for selection year 2012 are measured using accounting data from

reporting periods ending between November 2011 and October 2012. In

contrast, market cap, market turnover, and momentum are ranked using

calendar year 2012 data.

In Table 2, our naming convention for the quartile portfolios is that the

geometric mean of portfolio Q1 over the 42-year study period always

outperforms that of portfolio Q4.

5

Table 2. Median metric values of all quartile portfolios selected in 2012.

Category Portfolio Sort Metric Q1 Q2 Q3 Q4

Beta & Volatility

CAPM beta 0.714 1.049 1.308 1.738

Daily volatility 0.013 0.018 0.023 0.033

Monthly volatility 0.045 0.071 0.097 0.151

Size

Market Cap [$B] 0.211 0.620 1.792 8.977

Total Assets [$B] 12.712 2.622 0.878 0.224

Revenue [$B] 7.399 1.572 0.506 0.109

Net Income [$B] 0.510 0.085 0.021 -0.023

Value Book/Market 1.099 0.661 0.402 0.175

Earnings/Price 0.099 0.061 0.038 -0.054

ROE 0.236 0.123 0.068 -0.096

Liquidity Amihud [10-6] 0.057 0.007 0.001 0.000

Turnover 0.436 1.041 1.718 3.303

Momentum 12-month 0.577 0.242 0.080 -0.145

2-12 month 0.530 0.204 0.048 -0.173

Fama & French Factor Coefficients

FF Market beta 0.612 0.912 1.155 1.574

FF SMB small size beta -0.046 0.501 0.986 1.604

FF HML high value beta 0.864 0.362 -0.025 -0.529

Single Factor Coefficients

SMB small size beta 0.622 1.207 1.702 2.368

HML high value beta 0.695 0.231 -0.106 -0.606

WML high momentum beta -1.541 -0.997 -0.690 -0.320

LMH low liquidity beta -0.529 -0.877 -1.203 -1.784

6

Comparing the Quartile Portfolios Across Characteristics

Portfolios constructed using selection-year (1971-2012) metrics are

passively held in the subsequent performance year (1972-2013). During the

performance year, no rebalancing takes place, so the position weights are

allowed to float throughout the performance year. The end of each calendar

year thus marks both the end of the performance year for the portfolios

selected one year previously, as well as the construction date for a new set of

selection-year portfolios using recalculated sort metrics listed in Table 2. In

effect, the 84 quartile portfolios listed in Table 2 last for the entire study period

and are rebalanced annually.

We report the annualized geometric mean, the annualized arithmetic

mean, and the annualized monthly standard deviation in the tables that follow.

In Figures 1-8 and Figure 10, we plot the annualized geometric mean

during the study period on the vertical axis and the annualized standard

deviations on the horizontal axis.

Beta and Volatility. We first look at the impact of beta and volatility upon

returns over the period. According to the Sharpe (1964) and Lintner (1965)

capital asset pricing model, there should be a positive relationship between

beta and returns. Even according to more general theories of capital markets,

there should be a positive relationship between risk and return. Thus higher

volatility should also be associated with high returns.

7

In Table 3, we report the long-term performance-year returns for each

quartile portfolio within the Beta & Volatility category of sort metrics. We list

the annualized geometric mean, arithmetic mean, and annualized standard

deviation that were realized during the study period. Again, portfolios Q1

through Q4 are in either strictly increasing or strictly decreasing order in the

portfolio sorting metric, and Q1 denotes whichever extreme in the sorting

metric outperformed over the study time period. For this category of return-

predictive metrics, the Q1 outperforming quartiles are associated with low beta,

low daily volatility, and low monthly volatility from the selection year.

Table 3. Beta & Volatility Quartile portfolio returns, 1972-2013.

Portfolio sort metric Result Q1 Q2 Q3 Q4

CAPM beta Q1 = low

geom 14.42% 14.50% 12.93% 8.80%

arith 15.99% 16.52% 15.41% 12.97%

SD 18.52% 21.16% 23.24% 29.99%

Daily volatility Q1 = low

geom 14.01% 14.53% 13.85% 7.84%

arith 15.27% 16.36% 16.47% 12.79%

SD 16.60% 19.97% 23.86% 33.08%

Monthly volatility Q1 = low

geom 14.41% 14.66% 13.37% 8.00%

arith 15.76% 16.53% 16.05% 12.56%

SD 17.33% 20.23% 24.04% 31.68%

Graphing the quartiles in Figure 1 illustrates these results on an annual

geometric mean vs. annual standard deviation plot. The Q1 quartiles are

shown with pointed up triangles, while the Q4 quartiles are shown with the

pointed down triangles. The middle quartiles Q2 and Q3 are shown with

smaller dots. The risk and return of the equally weighted universe and

capitalization weighted universe portfolios are shown in diamonds. Note that

8

for the Q4 portfolios, high beta, high monthly volatility and high daily volatility

had by far the lowest realized returns, even though they had the most risk.

The Q1 and Q2 portfolios had the highest returns, but with a risk less than the

equally weighted universe portfolio.

Other researchers have previously found that a positive beta and

volatility risk and return relationship do not hold. For example, Black, Jensen,

and Scholes (1972) and Frazzini and Pedersen (2011) find that high beta stocks

are associated with low excess returns, while Haugen and Baker (1991) and

Ang, Hodrick, Xing and Zhang (2006) find that high volatility stocks

consistently underperform.

Figure 1. Beta & Volatility Quartile Portfolios

9

Frazzini and Pedersen (2011) show that leverage aversion on the part of

some market participants results in the popularity of high-volatility, high-beta

securities; this popularity in turn bids up prices and reduces returns.

Size of Companies. The size portfolios are presented in Table 4.

Comparing the quartiles, the small cap premium is positive in that the

geometric mean of small-cap Q1 is 14.08% vs. 11.70% from large-cap Q4, with

small caps having a higher standard deviation.

When we measure company size by total assets, revenue, or net income,

however, it is the larger companies that outperform the smaller companies.

The differences in arithmetic mean return between the Q1 and Q4 portfolios

are not significant, a result that is consistent with previous results (Berk 1997)

that examine accounting-based measures of company size as a predictor of

expected returns.

Table 4. Size Quartile portfolio returns, 1972-2013.

Portfolio sort metric Result Q1 Q2 Q3 Q4

Market Cap Q1 = small cap

geom 14.08% 12.65% 12.92% 11.70%

arith 17.36% 15.18% 15.03% 13.32%

SD 26.98% 23.63% 21.38% 18.33%

Total Assets Q1 = high assets

geom 12.85% 14.36% 13.08% 11.27%

arith 14.63% 16.21% 15.43% 14.78%

SD 19.38% 20.19% 22.58% 27.86%

Revenue Q1 = high revenue

geom 13.79% 13.66% 13.59% 10.68%

arith 15.56% 15.78% 15.98% 13.90%

SD 19.52% 21.39% 22.80% 26.80%

Net Income Q1 = high income

geom 12.83% 13.63% 14.01% 10.76%

arith 14.39% 15.48% 16.48% 14.80%

SD 18.14% 20.12% 23.20% 29.79%

10

Regardless of the metric used, we find that the standard deviation of

returns is much higher for the smaller companies than the larger companies.

As shown in Figure 2, high volatility is associated with small size, however

defined. For small caps, high risk is associated with high returns, while for

small companies, high risk is associated with low returns.

Figure 2. Size Quartiles

11

Value Measures. It is well known in the financial literature (Stattman 1980,

Basu 1983) that value seems to outperform growth over longer periods, even

when defined in different ways. Our results in Table 5 confirm these results for

portfolio quartiles using stocks reflected on ranked book to market, earnings to

price, and return on equity during the selection years. In each case the

outperforming Q1 quartile has a high value ratio, and the underperforming Q4

portfolios are the growth (or anti value) portfolios.

Table 5. Value Quartile portfolio returns, 1972-2013.

Portfolio sort metric Result Q1 Q2 Q3 Q4

Book/Market Q1 = high

geom 16.32% 14.45% 11.89% 8.57%

arith 19.03% 16.48% 13.99% 11.51%

SD 24.69% 21.46% 21.06% 25.06%

Earnings/Price Q1 = high

geom 16.74% 14.09% 11.17% 8.87%

arith 19.14% 15.87% 13.24% 12.65%

SD 23.17% 19.98% 20.89% 28.54%

ROE Q1 = high

geom 13.52% 13.83% 13.50% 10.38%

arith 15.81% 15.65% 15.52% 14.02%

SD 21.99% 19.80% 21.06% 28.09%

In Figure 3 we plot the four value quartiles, for each of these measures of

value. Note that while the Q1 value portfolio clearly outperforms in each case,

it is usually the Q4 growth portfolio that is most risky, even though the Q4

portfolio has the lowest returns. Thus value premiums appear to be positive,

but are not necessarily risk premiums as they are usually referred to.

Since high-growth companies (whether characterized by low B/M, low

E/P, or low ROE) tend to be newsworthy, up-and-coming “hot” companies,

12

within the category of value metrics, popularity is again associated with

underperformance in the long term.

Figure 3. Value Quartiles

Liquidity. We measure returns from portfolios formed by ranking two

different measures of liquidity premiums. One measure is the Amihud (2002)

“ILLIQ” metric, defined as the absolute value of the daily return divided by the

daily dollar value of shares traded, averaged over the course of the selection

year. Stocks are ranked during the selection year by this metric, and are

placed into the four quartile portfolios for each performance year. Another

measure of liquidity is the turnover rate (Datar, Naik and Radcliffe 1998), for

which we calculate the monthly ratios of the number of shares traded to the

13

number of shares outstanding, with the twelve monthly turnover rates summed

over the selection year to get the annual turnover rate for each stock. The

stocks are then ranked and placed into the four quartile portfolios.

In Table 6 we show the returns for liquidity according to the two

methods. The low liquidity portfolios are labeled Q1 and the high liquidity

portfolios Q4. For both measures, the low liquidity portfolios outperform by a

wide margin.

Table 6. Liquidity Quartile portfolio returns, 1972-2013.

Portfolio sort metric Result Q1 Q2 Q3 Q4

Amihud Q1 = low liquidity

geom 14.85% 12.31% 12.35% 11.43%

arith 17.74% 14.92% 14.60% 13.17%

SD 25.54% 23.94% 22.11% 18.99%

Turnover Q1 = low liquidity

geom 15.51% 14.42% 12.80% 8.27%

arith 17.33% 16.34% 15.18% 12.05%

SD 20.18% 20.66% 22.74% 28.35%

In Figure 4 we graph the four liquidity quartiles from the Amihud and

turnover measures. Although for both measures the low liquidity Q1 portfolios

outperform, the two measures have completely different risk characteristics.

The low liquidity Amihud measure is the most risky portfolio, whereas the low

turnover portfolios exhibit less risk.

Idiosyncratic liquidity is a multifaceted concept. Since turnover

measures the fraction of a company that changes owners, it encodes popularity

through trading volume, whereas the Amihud metric measures the price

impact of trading and thus is a more “pure” measure of liquidity. Like the

14

categories of beta and volatility previously discussed, here we find that the

quartile portfolios associated with less popularity outperform with lower risk.

Figure 4. Liquidity Quartiles

Momentum. In Table 7 we measure the returns from the portfolios formed

from ranking the returns of the last 12 months and from the last 11 months (2-

12) as of calendar year end. This second measure is often used since the near-

in month is usually considered a reversal month (Jegadeesh 1990). The results

show that both measures of momentum predicted returns over the period.

15

Table 7. Momentum Quartile portfolio returns, 1972-2013.

Portfolio sort metric Result Q1 Q2 Q3 Q4

12-month momentum Q1 = high

geom 13.58% 14.73% 13.85% 8.69%

arith 16.10% 16.48% 15.80% 12.52%

SD 23.48% 19.65% 20.73% 29.14%

2-12 month momentum Q1 = high

geom 13.76% 14.84% 13.43% 8.92%

arith 16.22% 16.70% 15.32% 12.65%

SD 23.27% 20.24% 20.41% 28.69%

When we plot the momentum results in Figure 5, it is clear that the

momentum results are driven by the poor performance of the loser Q4

portfolios. These loser portfolios not only have the worst performance, but also

the highest risk.

Figure 5. Momentum Quartiles

16

Fama & French Factors. We obtain Fama and French (1993) factors on the

market, size, and value from Kenneth R. French’s website.4 We regress our

universe of stocks from the selection year on the factors, using daily return

data from each selection year. We then rank the stocks according to their

market, size, and value factor loadings and assign them into quartile portfolios.

From Table 8, we can see that the low beta portfolio outperforms, similar

to CAPM beta result from Table 3. The Fama & French Q1 value portfolio also

outperforms the Q4 growth portfolio, similar to the results in Table 5 for the

book/market characteristic. Surprisingly, when sorting by the Fama & French

SMB size coefficient, the portfolio with low SMB size coefficients (associated

with large cap stocks) outperforms the portfolio with high SMB size coefficients

(associated with small cap stocks).

Table 8. Fama & French Factor Coefficient quartile returns, 1972-2013.

Portfolio sort metric Result Q1 Q2 Q3 Q4

FF Market beta Q1 = low beta

geom 14.23% 13.99% 12.71% 10.20%

arith 15.73% 15.87% 15.13% 14.16%

SD 18.03% 20.15% 22.86% 29.52%

FF SMB size beta Q1 = large cap beta

geom 12.94% 14.13% 13.80% 10.37%

arith 14.49% 16.14% 16.21% 14.06%

SD 18.08% 20.76% 22.87% 28.73%

FF HML B/M beta Q1 = high value beta

geom 14.00% 14.09% 13.67% 9.39%

arith 16.45% 16.10% 15.61% 12.73%

SD 23.27% 21.12% 20.49% 26.88%

4 We used Kenneth French’s labels for the following factors: SMB (small minus big) for size, HML (high minus low back-to-market ratio) for value. See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

17

Figure 6 illustrates the impact of the Fama & French ranked coefficient

portfolios. The underperforming Q4 coefficient portfolios (high market beta,

small cap beta, high growth beta) not only have the lowest returns, but also the

highest risk.

Figure 6. Fama & French Factor Coefficient Quartiles

Single Beta Factors. We create our own long-short daily liquidity factor

(Ibbotson, Chen, Kim and Hu 2013) by taking the difference of the Q1 (low

turnover) portfolio returns versus Q4 (high turnover) returns. We then regress

our universe of stock returns on each of these factors individually, and rank

the coefficients. The stocks are then placed into one of the four quartile

portfolios according to their ranking.

18

We then repeat this procedure using the Fama-French size and value

daily factors described in the previous section, as well as the Fama-French

daily momentum factor as obtained from Kenneth R. French’s website.

The performance year results are shown in Table 9. As anticipated, the

factor coefficient portfolios associated with high value and less liquidity both

outperform. Surprisingly, the factor coefficient portfolios associated with small

caps and high momentum both underperform. The negative coefficient on

momentum suggests that the use of factor analysis in portfolio selection (a

popular strategy among many quant investment firms) may be leading to bad

bets.

Table 9. Single Factor Coefficient quartile portfolio returns, 1972-2013.

Portfolio sort metric Result Q1 Q2 Q3 Q4

SMB size beta Q1 = large cap beta

geom 13.11% 13.98% 14.04% 10.07%

arith 14.79% 16.11% 16.43% 13.57%

SD 19.16% 21.49% 22.78% 27.31%

HML B/M beta Q1 = high value beta

geom 15.58% 14.74% 12.88% 7.39%

arith 17.53% 16.82% 15.14% 11.40%

SD 20.65% 21.57% 22.27% 29.36%

WML momentum beta Q1 = loser beta

geom 13.58% 14.54% 13.08% 9.71%

arith 16.75% 16.68% 15.08% 12.38%

SD 26.02% 21.68% 20.90% 23.59%

LMH turnover beta Q1 = low liquidity beta

geom 14.62% 14.12% 13.27% 8.41%

arith 16.17% 16.03% 15.76% 12.94%

SD 18.58% 20.42% 23.29% 31.39%

19

Figure 7 illustrates the results of Table 9 in graphical form. The

outperformers are the high value beta, low liquidity beta, large cap (low SMB)

beta, and the loser (low WML) momentum betas. The three highest risk

portfolios are the small cap beta, high growth beta, and high liquid betas, even

though these portfolios have the lowest returns.

Figure 7. Single Factor Coefficient Quartiles

20

What Works Best?

In Figure 8 we present a summary of the compound annual returns and

annualized standard deviation for the top-performing quartile (Q1) of each sub

category. Value is observed to be the highest returning category with high

earnings/price and high book to market ranking #1 and #2, with value beta

and low turnover close behind. On a risk adjusted basis, the best performers

are the low volatility, low beta, and low turnover portfolios. These portfolios

not only outperform, but also are less risky than the universe equally weighted

portfolio.

Figure 8. Risk & Return: Top Quartiles5

5 To maintain legibility in the figure, we do not label every data point.

21

The results in Figure 8 contrast with the popularity of return-predictive

characteristics as measured by citation counts in the academic literature.

Green, Hand, and Zhang (2013) find that seminal papers of predictive factors

with higher citation counts are associated with lower long-term returns: in

terms of citations, the most popular signal is momentum.

Figure 9 shows all quartile portfolios for all metric categories in risk and

arithmetic mean return space. Here, rather than clustering along the Capital

Market Line as one might expect from classical theory, a negative relationship

between return and risk within the stock market is clearly seen.

Figure 9. Risk vs. Arithmetic Return Within The Stock Market Capital Market Line (solid line), OLS fit6 of all quartile portfolios (dashed line).

6 The slope of the arithmetic-return regression line is –0.201 with a t-statistic of –4.9. The constant term is 0.198, and the adjusted R-squared is 0.21.

22

One disadvantage of arithmetic mean returns is that they ignore the

detrimental effect of volatility on long-term realizable returns. Since the

geometric mean is more relevant to real stock investors, Figure 10 shows a

geometric mean return version of Figure 9. In geometric space, the Capital

Market Line becomes curved, and the regression line tilts even more strongly

negative, since portfolios with a higher standard deviation drop farther in

geometric mean relative to their arithmetic mean.

Figure 10. Risk vs. Geometric Return Within The Stock Market

Capital Market Line (solid line), OLS fit7 of all quartile portfolios (dashed line).

7 The slope of the geometric-return regression line is –0.423 with a t-statistic of –9.9. The constant term is 0.225, and the adjusted R-squared is 0.53.

23

Conclusions

We have ranked stock characteristics on beta & volatility, size of firms,

value measures, liquidity, and momentum, and formed quartile portfolios. We

have also ranked stock coefficients on the Fama and French factors, as well as

on our own factors created by taking the difference between top and bottom

quartile returns. These were all done in the prior selection year, with the

ranked quartile portfolios returns measured in the following performance years

(out of sample) for the years 1972-2013.

Relative to the popular wisdom that greater reward comes with greater

risk, the results presented here include many surprises. Contrary to theory,

low beta and low volatility portfolios outperform high beta and high volatility

portfolios. Small capitalization stocks outperform, but not small companies,

since large companies measured by assets, revenue, and income outperform.

Less liquid stocks outperform on both Amihud and turnover measures, but

these less liquid portfolios are more risky by the Amihud measure, and less

risky by the turnover measure. High momentum portfolios outperform as

anticipated, but it is the low momentum portfolios which are more risky.

There are also surprising results when we regress the stocks on Fama &

French and our own created factors. The coefficients do not always line up

with the factors, even by direction. The Fama & French market beta gets a

negative return, and so does the size coefficient, indicating the companies that

are negatively sensitive to their SMB factor. Portfolios ranked by loadings on

single factors also do not always work as anticipated. The coefficients on value

24

and low liquidity are positive, but the coefficients on small size and high

momentum turn out to be negative.

Overall the best returning characteristics are high earning/price, high

book to market, and low turnover. On risk adjusted basis, the best

performances were low beta, low volatility, and low turnover.

When considered individually, the results presented here mainly confirm

previously reported results. However, by presenting these results together in a

common framework, we have shown that there has been a clear negative

relationship between risk and return within the U.S. stock market.

Within this anomaly, a common theme emerges. Whether it be through

factors that encode popularity among investors (turnover, growth), academic

popularity (citations), or popularity caused by leverage aversion (beta,

volatility), popularity underperforms.

25

References

Amihud, Yakov. 2002. “Illiquidity and Stock Returns: Cross-Section and Time-Series Effects,” Journal of Financial Markets, vol. 5, no.1 (January): 31-56.

Ang, Andrew, Robert J. Hodrick, Yuhang Xing, and Xiaoyan Zhang. 2006. “The Cross-Section of Volatility and Expected Returns.” Journal of Finance, vol. 61, no. 1 (February):259-299.

Basu, Sanjoy. 1983. “The Relationship Between Earnings Yield, Market Value, and Return for NYSE Common Stocks: Further Evidence,” Journal of Financial Economics, vol. 12, vol. 1 (June):129-156.

Berk, Jonathan B. 1997. “Does Size Really Matter?” Financial Analysts Journal, vol. 53, no. 5 (September-October):12-18.

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