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RESEARCH
Low Volatility Strategies
August 2014
Wes Crill
In recent decades, low volatility stocks have enjoyed the benefit of market-like returns.
RESEARCH
However, investors should take caution before extrapolating this performance into the
Associate
Wes earned his BS
and PhD in materials
science engineering
from North Carolina
State University.
future. The historical average returns of stocks with low volatility are well-explained by
known drivers of returns.
INTRODUCTION
A variety of solutions have been designed for investors that wish to reduce volatility risk in the
equity portion of their investments. They include minimum variance, inverse volatility weighting,
and low market beta portfolios. Though differing in name and construction, one common theme
linking many of these strategies is a focus on stocks with low past volatility.
The back-tested performance of low volatility strategies has been particularly appealing in the
past 40 years, reducing volatility relative to the market without any sacrifice in returns. However,
low volatility stocks underperformed the market in earlier periods. This paper shows that wellknown drivers of expected returns can explain the performance in both periods.
Low volatility stocks tend to have low market betas, or low covariances with the market. All
else being equal, this implies lower-than-market expected returns. Only in recent decades has
this been offset with exposure toward value, which allowed low volatility stocks to achieve marketlike returns. Without a systematic focus on the size, relative price, and profitability dimensions
of expected stock returns, it is not clear investors should expect that low volatility portfolios
will have expected returns similar to the market.
The material in this publication is provided solely as background information for registered investment
advisors and institutional investors and is not intended for public use.
DIMENSIONAL FUND ADVISORS
2
LOWERING EXPECTED VOLATILITY
Expected future volatility is unobservable, but past volatility
or past market betas are often used to identify stocks
with low expected volatility. Both metrics provide similar
results, since stocks with low market betas tend to have low
volatility and vice versa. For example, Exhibit 1 shows that
on average over 70% of low market beta stocks are among
the two least volatile quintiles.
Exhibit 1 OVERLAP BETWEEN VOLATILITY
AND MARKET BETA
1928–2013
Exhibit 2 MARKET BETA AND VOLATILITY
Market Beta
Rank
VOLATILITY RANK
Vol 4
Exhibit 2.1 compares market betas and volatilities for
the quintile portfolios formed from sorting on past market
beta. The lowest quintile’s market beta of 0.63 is distinctively
low for an equity portfolio. The low market exposure
was accompanied by a monthly return volatility that
was 1.5 percentage points lower than the market portfolio’s
volatility of 5.4%. Conversely, the high market beta portfolio
amplified market exposure with a market beta of 1.43,
incurring a monthly volatility that was 2.7 percentage
points higher than the market.
Low Vol
Vol 2
Vol 3
High Vol
Low β
52%
19%
12%
9%
8%
β2
30%
32%
18%
12%
8%
β3
12%
29%
30%
18%
10%
β4
4%
17%
29%
33%
17%
High β
1%
3%
11%
29%
57%
Daily stock market betas are estimated using daily returns for one year.
Returns are regressed on the daily market portfolio’s return with five
lags, and the market beta is the sum of the current and lagged slope
coefficients. Stock volatility is measured using standard deviation of
daily returns for the same year as the market beta estimation. Each
December, stocks are ranked on market beta or volatility for that year
to form quintiles, each containing 20% of the market. Included in this
ranking are all common stocks from the NYSE, AMEX, and NASDAQ
exchanges that possess at least 200 return observations in the ranking
period. The percentage of capitalization by volatility rank is measured
for each market beta quintile, and the exhibit reports the time series
averages of these percentages. Stock data and daily market portfolio
from CRSP. Past performance is no guarantee of future results.
1928–2013
Exhibit 2.1: Portfolios Formed on Market Beta
MARKET BETA RANKING
Low β
β2
β3
β4
High β
Market β
0.63
0.79
0.98
1.12
1.43
1.00
Volatility (%)
3.9
4.6
5.5
6.2
8.1
5.4
Market
Exhibit 2.2: Portfolios Formed on Volatility
VOLATILITY RANKING
Low Vol
Vol 2
Vol 3
Vol 4
Market β
0.61
0.82
0.97
1.15
High Vol Market
1.42
1.00
Volatility (%)
3.8
4.8
5.4
6.3
8.1
5.4
At the end of each year, stocks are sorted on daily return volatility or
daily market beta to form quintiles each containing 20% of the market.
Capitalization-weighted average monthly returns are computed for the
portfolios. The tables report post-formation monthly market betas and
return volatility for the market beta-sorted portfolios in Exhibit 2.1 and
the volatility sorted portfolios in Exhibit 2.2. Market returns provided
by Ken French. Filters were applied to data retroactively and with the
benefit of hindsight.
DIMENSIONAL FUND ADVISORS
3
A similar comparison, using past return volatility to form
quintiles, is presented in Exhibit 2.2. Comparing the two
exhibits, post-formation market beta and return volatility
are nearly identical for the low quintile of both sorts and
increase monotonically from low to high. Given the overlap
between the market beta and volatility quintiles and the
similarity of the results in Exhibit 2, the remainder of this
paper uses low market beta as a generalization for low
volatility strategies.1
Exhibit 3 PERSISTENCE OF LOW MARKET BETA
1928–2013
Percent of Low Market
Beta Quintile in Year t
60
50
40
30
20
10
0
Low
2
3
4
High
Market Beta Rank in Year t+1
At the end of each year, stocks are sorted on market beta to form
quintiles, each containing 20% of the market. The chart illustrates
where stocks from the current low market beta quintile tend to rank
the following year. The bars are the average percentage of previous
low market beta quintiles’ capitalization by the subsequent ranking.
Percentages do not sum to 100 due to firms that delist between rank
periods. Filters were applied to data retroactively and with the benefit
of hindsight.
Past market betas can be used as a proxy for future volatility
because market beta rankings are a persistent characteristic,
as shown in Exhibit 3. On average, about 75% of the stocks
in the lowest market beta quintile remain in the lowest two
quintiles the following year. Rankings on return volatility
(not shown) are even more persistent, with almost 90%
remaining in the lowest two quintiles. This suggests that
if a stock has low market beta or volatility relative to other
stocks today, this is likely to remain the case in the future.
UNDERSTANDING MARKET BETA AND RETURNS
Market exposure is an important determinant of expected
return. Under the CAPM assumptions, stocks with low
(high) market betas earn less (more) equity premium and,
all else being equal, should have lower (higher) expected
return than the market. Thus, it may be surprising that
sorting stocks on market beta produced very little spread
in average returns from 1928 to 2013. Exhibit 4 shows that
average returns on high and low market beta portfolios only
differed from the market by about 10 basis points per month.
Breaking the sample into sub-periods reveals differences
in these return comparisons. Prior to 1970, the low market
beta portfolio return was 22 basis points per month less
than the market and 43 basis points lower than that for the
high market beta portfolio, although neither difference is
statistically reliable. However, in the more recent sub-period,
average returns for high and low market beta were essentially
the same, each within two basis points of the market.
The disparity between the recent flat market beta/return
relation and the steeper relation witnessed in the earlier
period can be understood through four-factor regressions
of the portfolio returns. The regression intercepts (alphas)
in Exhibit 5 are within 1.6 standard errors of zero for both
low and high market beta across the entire sample. Hence,
the returns from our sort on market beta are well-explained
by the market, size, value, and momentum factors.
Exhibit 4 AVERAGE RETURN FOR MARKET BETA PORTFOLIOS
HIGH β MINUS LOW β
MARKET MINUS LOW β
Low β
High β
Market
Return
1928−2013
0.82
1.01
0.91
0.19
1928−1969
0.67
1.10
0.89
0.43
1.60
0.22
1.71
1970−2013
0.96
0.92
0.94
-0.04
-0.16
-0.02
-0.15
t-Stat
1.05
Return
0.10
t-Stat
1.15
Capitalization-weighted average returns are computed for the low and high market beta portfolios and compared to the market portfolio.
Time-series averages of the returns are reported in percent for the full sample and two sub-periods. Filters were applied to data retroactively and with
the benefit of hindsight. Returns are not representative actual strategies and do not reflect costs and fees associated with an actual investment. Actual
returns may be lower.
1. Other low volatility strategies were studied, including inverse volatility weighted portfolios and low volatility portfolios formed by sorting on idiosyncratic
volatility and market beta estimated over varying horizons. The results reported here are robust to these alternative specifications of volatility.
DIMENSIONAL FUND ADVISORS
4
Exhibit 5 FOUR-FACTOR REGRESSIONS OF MARKET
BETA PORTFOLIOS
Alpha
t-Stat
Mkt–Rf
SMB
HML
UMD
Low Market Beta
1928−2013
0.09%
1.60
0.65
-0.10
0.07
0.03
1928−1969
0.04%
0.53
0.67
0.00
-0.08
0.03
1970−2013
0.06%
0.79
0.72
-0.13
0.28
0.02
1928−2013 -0.11%
-1.58
1.35
0.28
-0.04
-0.10
1928−1969 -0.12%
-1.45
1.31
0.13
0.23
-0.05
1970−2013 -0.02%
-0.17
1.28
0.33
-0.33
-0.12
High Market Beta
The monthly returns for the low and high market beta portfolios are
regressed on market (Mkt-Rf), size (SMB), value (HML), and momentum
(UMD) factors. Alphas and slope coefficients for the independent
variables are reported for the three time periods. Factor returns provided
by Ken French. Filters were applied to data retroactively and with the
benefit of hindsight.
The factor loadings uncover the driving force behind low
market beta’s recent market-like returns. In the post-1970
period, the low market beta portfolio had a pronounced
value tilt. Thus, despite the low market exposure, low market
beta returns were not lower than the market. In contrast,
the low market beta portfolio had a growth tilt for the first
half of the sample which, combined with the low market
exposure, resulted in lower-than-market average returns.
Exhibit 5 also provides some context to the recent
underperformance of high market beta relative to low
market beta. Over the past 44 years, the high market beta
portfolio had a positive size factor loading and a negative
value factor loading, implying a small cap growth tilt. The
four-factor intercept for small cap growth stocks2 was -17
basis points per month over this period, so small growth
underperformance likely detracted from the returns for
high market beta stocks in the recent sub-period. High
market beta portfolios have also loaded negatively on the
momentum factor, contributing an additional drain on
returns. The performance of the high market beta portfolio
can thus be attributed to exposures to the four factors along
with the poor returns of small cap growth securities.
To further illustrate the role that exposure to low relative
price stocks plays in the relative returns of the low and
high market beta portfolios, two switching strategies were
constructed. Strategy 1 is a low price-to-book strategy.
If, at the beginning of the year, the price-to-book ratio of
the low market beta quintile is less than the price-to-book
ratio of the high market beta quintile, the low price-to-book
strategy invests in the low market beta quintile for that
year. Otherwise, it invests in the high market beta quintile.
Strategy 2 is a high price-to-book strategy and is the
complement of strategy 1.
Exhibit 6 shows the result of this experiment. From 1928
to 2013, the low price-to-book strategy invested in the low
market beta quintile during 52 of the 86 years in the sample
(about 60% of the time). The average monthly return was
1.14%. The average return of the high price-to-book strategy
was 0.68%. The volatilities of the low and high price-tobook strategies were similar. The t-statistic of the difference
in average returns between the strategies is 2.61, implying
this return difference is reliably different from zero. This
is in contrast to the return difference between the low and
high market beta quintiles, which is not reliably different
from zero.
Exhibit 6 MARKET BETA PORTFOLIOS WITH
BOOK-TO-MARKET CONTROLS
1928–2013
Low
Market
Beta
High
Market
Beta
Switching
Strategy 1:
Low Priceto-Book
Switching
Strategy 2:
High Priceto-Book
Monthly Return
0.82
1.01
1.14
0.68
High minus Low
—
0.19
—
0.47
t(High minus Low)
—
1.05
—
2.61
3.88
8.12
6.75
5.95
—
—
52 (60%)
34 (40%)
Standard
Deviation
Years in Low
Market Beta
Two switching strategies are formed. The low price-to-book strategy
invests in the low market beta quintile when its median price-to-book
ratio is less than the median price-to-book ratio of the high market beta
quintile and invests in high market beta otherwise. The high price-to-book
strategy is the complement of this; it invests in the low market beta quintile
when its median price-to-book ratio is greater than the median price-tobook ratio of the high market beta quintile and invests in the high market
beta quintile otherwise. Average monthly returns, monthly volatility, and
portion of years invested in low market beta are reported for these
strategies and the high and low market beta quintiles. The average
monthly differences between high and low market beta and the high and
low price-to-book switching strategies are reported with accompanying
t-statistics. Returns and volatilities are shown in percent. Filters were
applied to data retroactively and with the benefit of hindsight. Returns
are not representative actual strategies and do not reflect costs and fees
associated with an actual investment. Actual returns may be lower.
2. P
erformance for small-cap growth stocks computed using returns on the Fama/French Small Growth Index. See Appendix for index descriptions.
Indices are not available for direct investment.
DIMENSIONAL FUND ADVISORS
5
This simple experiment demonstrates the importance
of the low and high market beta quintiles’ exposure to
low relative price stocks and their subsequent relative
performance. The quintile with greater exposure to
low relative price stocks tended to outperform over the
subsequent year. For example, in years when the low
market beta quintile had lower exposure to low relative
price stocks than the high market beta quintile, the
average monthly return was 0.75% versus 1.57% for the
high market beta quintile. What’s the lesson? Controlling
for relative price is important when informing expectations
about differences in expected returns between low and
high market beta stocks.
betas than higher priced stocks. The shaded regions in
Exhibit 7 indicate periods when large value had the
lowest market betas within large caps. It is apparent that
the tendency for value to have low market beta is a recent
phenomenon occurring predominantly in two stretches,
throughout the 1980s and from the mid-1990s through
the early 2000s.
WHERE IS THE LOW MARKET BETA ANOMALY?
To serve as the foundation of an investment strategy,
an empirical observation should lead to well diversified
and cost-effective portfolios. If the observation is driven
by a small group of tiny stocks, it may be difficult to
construct a well-diversified portfolio that benefits from
the observation. If portfolio turnover must be high to
capture the benefits, there may be little advantage to
investors after implementation costs.
ARE VALUE AND LOW MARKET BETA SYNONYMOUS?
Investors are naturally drawn to the return/volatility
tradeoff achieved by low market beta over the past few
decades, but can this performance be expected in the
future? The sub-period regression analysis shows that
portfolios focused on low market beta stocks have had
inconsistent value exposure. The reverse is also true. Low
relative price stocks do not consistently have lower market
The results presented above are for quintiles of aggregate
market cap that are annually rebalanced and market
cap weighted. Each quintile includes 20% of US market
capitalization and is well-diversified—the quintiles contain
Exhibit 7 MARKET BETAS FOR LARGE CAP STYLE INDICES
1928–2013
Fama/French Large Growth
Fama/French Large Neutral
Fama/French Large Value
1-Year Rolling Market Beta
2.0
1.5
1.0
0.5
0.0
1927
1934
1941
1948
1955
1962
1969
1976
1983
1990
1997
2004
2011
One-year rolling market betas are estimated monthly using daily returns for the past year. The dependent variables in the regressions are daily returns
for the three Fama/French large-cap indices. The independent variable is the daily return on the CRSP Value-Weighted Market Index with five lags.
Shaded area indicates when large value has the lowest market beta. Filters were applied to data retroactively and with the benefit of hindsight. Index
data use for analysis. See Appendix for index descriptions. Indices are not available for direct investment.
DIMENSIONAL FUND ADVISORS
more than 300 stocks on average.3 Weighting by market
cap prevents tiny stocks from dominating the returns,
making the results relevant to real-world implementation.
Due to the annual rebalance frequency, turnover averages
approximately 50%. The historical returns of stocks sorted
on market beta using this reasonable framework are well
explained by known drivers of returns.
It is common for researchers to analyze characteristics of
portfolios that weight stocks equally or in proportion to
their ranking. These tend to produce extreme outcomes
and can magnify the effect being investigated. For example,
in a 100-stock portfolio, the top 10% of securities by rank
weight will represent about 19% of total weight, regardless
of their market caps.
Frequent rebalancing can also boost the magnitude of an
“anomaly.” Trading costs, however, can reduce the returns
actually delivered to investors. Simulated returns that
require a portfolio to be turned over several times per
year can be difficult to capture on an after-cost basis.
If we repeat the exercise above but weight stocks
proportionally to their rank on market beta in each
quintile and rebalance monthly, the outcomes for the
low market beta quintile change substantially. The top
10% of stocks in quintile market beta ranking (by name
count) comprise just 2.5% of market capitalization on
average but account for 18.7% of rank weights. Exhibit 8
indicates rank-weighting over-weights tiny stocks within
the low market beta quintile; the weighted average firm
market cap is under $5 billion, compared to over $180
billion when capitalization weights are employed.
Exhibit 9 reports the performance of the low market beta
quintile with the rank weights. In contrast to the market
cap weighted low market beta portfolio, which has had
returns similar to the market, the rank-weighted quintile
has generated an average return of 35 basis points per
month in excess of the market (over 4% per year). The
four-factor intercept for the portfolio is 41 basis points
6
Exhibit 8 SIZE CHARACTERISTICS OF LOW MARKET
BETA PORTFOLIO
1928–2013
Weighted Average Market Cap
Cap-Weighted
Portfolio
Rank-Weighted
Portfolio
183,714
4,971
Each month, stocks are sorted on market beta, and a low market
beta portfolio is constructed from the lowest quintile of market cap.
The table reports the time series average of the portfolio’s weighted
average market cap, where stocks are weighted in proportion to market
capitalization (cap-weighted) and rank on market beta (rank-weighted.)4
Market caps are shown in USD millions.
per month, indicating that controlling for the four factors
does not completely explain the rank-weighted low market
beta outperformance.
Aside from the extreme security weights produced by
a rank weighting scheme, the final column of Exhibit 9
reveals an additional flaw of this methodology combined
with monthly rebalancing. The average annualized turnover
of 234% is high and would incur large transaction costs
that would likely inhibit the ability of investors to capture
any abnormal returns. Thus, while one can find a “low
market beta anomaly” using an extreme weighting and
rebalancing scheme, the observation may not be useful
for a practical portfolio.
Exhibit 9 PERFORMANCE OF RANK-WEIGHTED LOW
MARKET BETA PORTFOLIO
1928–2013
Low Market Beta
– Market
# Stocks Return
1928−
2013
857
1.26
Return
0.35
t-stat
2.99
Four-Factor
Model
Alpha t-stat Turnover
0.41
5.09
234.1
Time series average monthly return for rank-weighted low market beta and
the average return in excess of the market are reported in percent. Alpha is
the intercept in percent from a regression of the rank-weighted low market
beta portfolio returns on market (Mkt-Rf), size (SMB), value (HML), and
momentum (UMD) factors. Turnover is in percent, annualized. Filters were
applied to data retroactively and with the benefit of hindsight. Returns are
not representative actual strategies and do not reflect costs and fees
associated with an actual investment. Actual returns may be lower.
3. These quintiles are diversified with respect to aggregate market cap and stock count, but not industry; sorting on market beta has tended to produce
portfolios with substantial industry under- and over-weights in the extreme quintiles relative to the market portfolio. Sorting stocks by industry to form
sector-neutral market beta portfolios reduced the spread in volatility between high market beta and low market beta by about 35%.
4. Formula for the market beta rank weight of stock i in an N-stock quintile:
DIMENSIONAL FUND ADVISORS
IMPLICATIONS FOR INVESTORS
Focusing on low volatility or low market beta stocks is
one way of reducing volatility in an equity portfolio. In
recent decades, low market beta portfolios have enjoyed
the additional benefit of market-like returns. However,
investors should take caution before extrapolating this
performance into the future. Low market beta stocks
received a return boost due to a value tilt over the past
few decades. The historical average returns to low market
beta stocks are well-explained by known drivers of returns.
It is not obvious that stocks sorted on past market beta
alone should be expected to consistently deliver the value
premium. If low market beta stocks are not expected to
enjoy the value premium (or other premiums associated
with known dimensions of expected returns), portfolios
targeting low market beta stocks should generally have
lower expected returns than the market portfolio.
APPENDIX
Index Descriptions
Fama/French Small Growth Index
Provided by Fama/French from CRSP (Center for Research
in Security Prices, University of Chicago) securities data.
Includes the lower-half range in market cap and the lower
30% in book-to-market of NYSE securities (plus NYSE
Amex equivalents since July 1962 and Nasdaq equivalents
since 1973). Exclusions: ADRs, investment companies,
tracking stocks, non-US incorporated companies, closedend funds, certificates, shares of beneficial interests, and
negative book values.
7
Fama/French Large Growth Index
Provided by Fama/French from CRSP (Center for Research
in Security Prices, University of Chicago) securities data.
Includes the upper-half range in market cap and the lower
30% in book-to-market of NYSE securities (plus NYSE
Amex equivalents since July 1962 and Nasdaq equivalents
since 1973). Exclusions: ADRs, investment companies,
tracking stocks, non-US incorporated companies, closedend funds, certificates, shares of beneficial interests, and
negative book values.
Fama/French Large Neutral Index
Provided by Fama/French from CRSP (Center for Research
in Security Prices, University of Chicago) securities data.
Includes the upper-half range in market cap and the middle
40% in book-to-market of NYSE securities (plus NYSE
Amex equivalents since July 1962 and Nasdaq equivalents
since 1973). Exclusions: ADRs, Investment Companies,
Tracking Stocks, non-US incorporated companies, Closedend funds, Certificates, Shares of Beneficial Interests, and
negative book values.
Fama/French Large Value Index
Provided by Fama/French from CRSP (Center for Research
in Security Prices, University of Chicago) securities data.
Includes the upper-half range in market cap and the upper
30% in book-to-market of NYSE securities (plus NYSE
Amex equivalents since July 1962 and Nasdaq equivalents
since 1973). Exclusions: ADRs, investment companies,
tracking stocks, non-US incorporated companies, closedend funds, certificates, shares of beneficial interests, and
negative book values.
This information is provided for registered investment advisors and institutional investors and is not intended for public use.
Past performance is no guarantee of future results. There is no guarantee strategies will be successful.
Eugene Fama and Ken French are members of the Board of Directors for and provide consulting services to Dimensional Fund
Advisors LP.
All expressions of opinion are subject to change without notice in reaction to shifting market conditions. International investing
involves special risks such as currency fluctuation and political instability. Investing in emerging markets may accentuate these risks.
Diversification does not protect against loss in declining markets. This article is distributed for informational purposes, and it is not
to be construed as an offer, solicitation, recommendation, or endorsement of any particular security, products, or services.
Dimensional Fund Advisors LP is an investment advisor registered with the Securities and Exchange Commission.
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