Download Cross-sectional volatility and return dispersion

Cross-sectional volatility and return dispersion
Ernest M Ankrim; Zhuanxin Ding
3,574 words
1 September 2002
Financial Analysts Journal
67
Volume 58, Issue 5; ISSN: 0015-198X
English
Copyright (c) 2002 ProQuest Information and Learning. All rights reserved. Copyright Association
for Investment Management and Research Sep/Oct 2002
In the past few years, the return spread between successful and unsuccessful active managers has
increased dramatically. We analyzed how levels of cross-sectional volatility correspond to active
manager dispersion in the U.S. and other equity markets. We demonstrate that changes in the level
of cross-sectional volatility have a significant association with the distribution of active manager
returns. We further show that these observations are neither unique to U.S. equities nor merely a
product of the "technology bubble"; they are observable in several equity markets.
Cross-Sectional Volatility and Return Dispersion Ernest M. Ankrim and Zhuanxin Ding
In the past few years, the return spread between successful and unsuccessful active managers has
increased dramatically. Moreover, many investors have experienced manager and fund tracking
errors that far exceeded expectations. These phenomena are not so much a result of managers
taking larger bets or becoming more diverse in their skill levels but, rather, of the riskiness of the
bets being magnified by an increase in cross-sectional volatility in the equity markets. Crosssectional volatility, in contrast to the more common volatility measure of variability of a given return
series through time, measures variations in returns across market sectors or individual stocks in a
given time period.
We illustrate the magnitude of the recent expansion in the gulf between the good and bad manager
performances in various equity markets. In the study we report, we first used return data on the
S&P 500 Index from November 1989 to December 2000 and calculated the cross-sectional volatility
for each month. We then analyzed how levels of cross-sectional volatility correspond to dispersion in
the returns of active managers in the U.S. large-cap market. Intuitively, the active risks in portfolios
are functions of both the aggressiveness and the cross-sectional volatility of security/industry/sector
returns. Our empirical study shows that the recent widening of manager dispersion appears to be
linked to the increase in cross-sectional volatility in the U.S. large-cap equity market without a
commensurate increase in the aggressiveness of portfolios.
We extended our study to address three issues. First, we demonstrate that these observations are
not unique to U.S. equities. Similar increases are occurring in the U.S. small-cap and other
countries' markets. Second, we suggest that this experience is not entirely new; in fact, the highest
value of cross-sectional volatility in Japan occurred in 1987, not 2000. Finally, we show that the
increases are not solely a product of the technology "bubble" but are still observable when
technology sectors are removed from the broad equity markets.
Observations for 2001 indicate that the level of cross-sectional volatility has declined in some
markets, but current levels are still well above historical norms. In the future, therefore, portfolio
managers must decide whether, knowing that rewards and penalties will be amplified, they are
comfortable with the current magnitude of their bets. If higher active risk is beyond their objectives
(or tolerance for business risk), they will have to reduce the portfolio's aggressiveness. The
corollary risk is that the cross-sectional volatility will revert to its historical levels and leave portfolio
managers who lowered the aggressiveness of their bets with indexlike returns at active fees.
For investors, this environment poses a different sort of risk. In an environment where active bets
generate large results (good and bad), active dispersion will be higher. Therefore, some mutual
funds will generate astoundingly good returns and some will report astoundingly bad returns. The
effect is heightened temptation for investors to chase the most recent winners in the mutual fund
market. When the difference between the best and worst mutual funds in the market expands twoor threefold, the behavior of the average investor is not difficult to predict. But plenty of research
warns against such behavior. The best response for individual investors in this environment is to
stick with whatever well-developed investment strategy they already have. The investors who avoid
the temptation to chase after the astonishing returns should look back on this wild period with
better-than-average performance. N
Keywords: Portfolio Management: private client focus; Portfolio Management: equity strategies;
Portfolio Management: asset allocation
The differences between the best and worst performances of equity portfolio managers have
increased dramatically in the past two years. The cause is not so much that managers are taking
larger bets or becoming more diverse in their skill levels but that the riskiness of those bets is being
magnified by an increase in cross-sectional volatility in the equity markets.
We illustrate the magnitude of the recent expansion in the gulf between good and bad manager
performances in various equity markets. We define the concept of cross-sectional volatility and
show how its pattern in these markets explains many of the differences we have observed between
the best and worst performances of active managers. We then address some typical questions that
arise from our results. Finally, we suggest what a manager and an individual investor should do in
this environment.
What Has Been Happening
The returns of the top- and bottom-performing active equity managers will always vary. Different
styles will be in favor at different times, ensuring that managers will take turns being near the top.
The range between the best and worst performances of active managers, however, is usually fairly
steady-except recently.
Using a U.S. equity universe as an example, Figure 1 illustrates the difference in annual returns
between the 95th percentile manager and the 5th percentile manager in The Frank Russell
Company's large-cap market-oriented universe from the quarter ending July 1988 through the
quarter ending December 2000. These differences ranged between 10 percentage points (pps) and
30 percentage points for almost all periods between 1988 and 1998.1 In 1999, however, the range
increased to slightly more than 40 pps, and by March 2000, the range had soared to 66 pps. This
magnitude is not in line with the previous 13 years' experience. In fact, the 44 pp difference for the
year ending December 1998 was the widest range in the 51 different rolling four-quarter
observations from the second quarter of 1986 through the fourth quarter of 1998. Yet, that 44 pp
range increased by half only five quarters later. Clearly, something different has been going on.
Cross-Sectional Volatility
Observers and students of investment markets and asset allocation are familiar with the term
"intertemporal volatility." Most of its applications relate to the variability of daily, monthly, or
quarterly returns for some market or asset-class average over a long horizon (years or, preferably,
decades). For example, a 60-month window is widely used as a measure of intertemporal
volatility.2 In contrast, cross-sectional volatility measures the variability in stock or sector returns in
a market within a given time period. Cross-sectional volatility is interesting because it helps
describe how the environment for strategies driven by country, stock, or sector selection is
changing.
Although the long-run volatility of market returns may look quite different from the one-timeperiod
cross-sectional volatility of a market, the two measures are related. As shown in Appendix A, the
expected change of cross-sectional volatility is a combination of three factors. The first is the
change in the average volatility in the sectors making up the market; the second is the change in
overall market volatility; and the third is the change in the sector mean dispersion. If sector mean
dispersions are relatively stable over time, which we think is reasonable, then change in crosssectional volatility is mainly attributable to changes in average sector volatility and overall market
volatility. The result is that cross-sectional volatility will rise with (1) a general increase in sector
volatilitywhile the correlation of returns between sectors is held constant-or (2) decreases in crosssector correlations-while the level of sector volatility is held constant. As Campbell, Lettau, Malkiel,
and Xu (2001) observed, the recent experiences of the U.S. equity markets have included an
increase in the level of sector volatility and reductions in crosssector correlations. Thus, both
possible sources of a rise in cross-sectional volatility have occurred simultaneously, causing the
dramatic jump displayed in Figure 1.
Academic and media writers have been paying attention to the growing risks in equities. Some have
characterized it as a rise in "firm-level volatility relative to market volatility" (Campbell et al.).
Appendix A shows why this firm-level volatility is nearly equivalent to a rise in cross-sectional
volatility. Others have observed that many money managers and asset advisors are currently
examining their risk models or developing new ones because recent realized return dispersion has
been far beyond what they expected on the basis of their history-based models (Riley 2000). But
why is manager return dispersion related to the prevailing level of cross-sectional volatility?
Volatility and Dispersion
Active portfolio managers create portfolios designed to beat a particular benchmark by choosing to
hold securities in proportions (weights) that are different from those in the benchmark. The larger
the differences in security weights, the more aggressive the bets the manager is making and the
greater the active risks. The magnitude of the active risk is also influenced, however, by variability
in the payoffs among securities (cross-sectional volatility). The most obvious illustration of this
truism is a simple but extreme example: Imagine that all the securities in a given benchmark had
identical returns for a month (that is, the cross-sectional volatility was zero). Assuming all active
portfolio managers held securities that were in the benchmark in whatever weights they chose,
clearly the returns of all active portfolios and the benchmark would be identical. This example is
quite unrealistic, of course, but it illustrates how the active risks in portfolios are functions of both
the aggressiveness of the portfolio bets and the cross-sectional volatility of security/industry/sector
returns. As the cross-sectional volatility rises from zero, portfolio returns begin to diverge from the
benchmark. For a given set of bets, the rewards or penalties increase as the variations in returns
among subsets of the market increase. Therefore, we would expect a wider dispersion of active
returns during periods of high cross-sectional volatility. Figure 2 illustrates this point.
In Figure 2, we combined cross-sectional (across-sector) volatility values for each month over 12month windows (to smooth them out) and superimposed that line over the manager dispersion
shown in Figure 1 (scaled on the right axis).3 For 1986 through 1997, the average value of this
cross-sectional volatility was 2.6 percent. For the same 12 years, the dispersion between the 95th
percentile managers' returns and 5th percentile managers' returns averaged 20.7 pps. For the year
ending in December 1999, the cross-sectional volatility was 5 percent and the 95th percentile to 5th
percentile difference grew to 50 pps. Six months later, for the 12 months ending June 2000, these
values had grown to, respectively, 6.1 percent and 61.6 pps. Clearly, active managers' bets were
having magnified effects on their performance. Figure 1. Figure 2. Table 1. Table 2.
Three Questions
In the process of reviewing this research, our colleagues raised three natural and important
questions:
* Is the recent dispersion a phenomenon seen solely in the U.S. large-cap market?
* Has it happened before?
* Is this effect simply another version of the technology boom (and bust) story?
U.S. Large-Cap Market Only? To answer this question, we need to examine two elements: Has the
growth of active manager return dispersion occurred in U.S. markets other than large-cap equity?
And has a similar pattern of high crosssectional volatility occurred in equity markets outside the
United States?
As Table 1 shows, the recent experiences of higher active dispersion are not unique to U.S. largecap equities. The widening range between the good and poor active returns is evident in the U.S.
small-cap, Canadian, Japanese, and U.K. markets. The annual difference between 95th percentile
and 5th percentile managers for the nine years from 1990 through 1998 was 16-34 pps, but for the
four quarters ending in June 2000, the range grew to 3097 pps. Being a good (or lucky) active
manager in 2000 paid off handsomely; being bad (or unlucky) really hurt.
The source of much of this rising dispersion among active managers is no doubt rising
crosssectional volatility. The volatility phenomenon has been widespread among markets. As the
averages in Table 2 show, the 1999-2000 period brought a significant increase in cross-sectional
volatility across all the markets we considered. A revisit at the end of 2001 showed that volatility
has stayed near the 1999-2000 averages.
In addition to the similar pattern of average cross-sectional volatilities, the time paths of these
cross-sectional volatilities are in lockstep. Figure 3 tracks the rolling 12-month average crosssectional volatility for the five markets we studied for the time periods spanned by our available
data. Clearly, all of these markets experienced substantial increases in cross-sectional return
volatility in 1999 and 2000.
Has the Phenomenon Happened Before? Figure 3 also provides an answer to the second question.
Our data go back only to the late 1980swith one fortunate exception. As Figure 3 shows, the
Japanese equity data (from Russell/Nomura) extend back to 1980. This long data set for Japan
demonstrates that the recent rise in cross-sectional volatility is not unique in the past 20 years. In
fact, the cross-sectional volatility experienced in early 2000 is not even the highest ever measured
in Japan. For the 12-month average ending June 1987, the Japanese market had a 12-month
average crosssectional volatility of 9.47 percent (compared with the highest recent 12-month
period, which ended in 2000, of 8.64 percent). Although we do not have data going back to the
early 1980s for the other markets, the levels at the end of 1987 were not appreciably higher than
average for these markets; so, if they have been following the same pattern as Japanese equities,
we can be reasonably sure that such an event has happened before in these markets. Figure 3.
Is the Phenomenon Another Technology Story? The dramatic boom and bust of the U.S. technology
sector in 1999 and 2000 coincided with the rise of cross-sectional volatility in U.S. large-cap stocks.
To discover whether the observed crosssectional volatility was higher only because of higher
volatility in the technology sector, we calculated cross-sectional volatility values for the five markets
we studied for each month in the 1998-99 and 1999-2000 periods with and without returns to
technology stocks.5 Table 3 summarizes the results of these calculations and compares them with
results for the total markets for the 1990-98 period.6 Clearly, some of the observed increases in
these values can be attributed to volatile returns in the technology sectors. A recent check of these
values for 2001 reveals values similar to the 1999-2000 averages, still at levels materially above
volatility values for 1990-1998.
Nevertheless, the differences between the 1990-98 and the 1999-2000 periods are substantial,
even when the technology influence has been removed. With the technology sector excluded from
both periods, across all the markets in Table 3, the increases in cross-sectional volatilities range
from 54 percent to 116 percent. The story is not only about technology.
Possible Causes
What in the markets has changed that might be causing this increase in cross-sectional volatility?
Honestly, we do not know. The growing importance of individual investors and increasing access to
inexpensive trading opportunities might be having an impact. Indeed, the most logical explanations
we found are contained in Campbell et al. These authors proposed that day trading and financial
innovation in general play a part. Other factors that might be influential are the current tendency to
break up conglomerates into more focused companies, the trend of issuing stock early in the
corporate life cycle, changes in executive compensation, increases in leverage, and shocks to the
discount rates investors apply in valuing companies. No doubt, many lines of research are being and
will be pursued in an effort to understand the sources of higher cross-sectional volatility. Table 3.
However, although these recent developments may turn out to be contributing factors, readers
should remember that the period encompassing the late 20th and early 21st century is not the first
time that such levels of cross-sectional volatility have been observed. Moreover, given the evidence
of behavior in three non-U.S. markets, explanations that concentrate solely on U.S. markets are
insufficient.
Conclusion
Whatever the causes of the recent environment, it clearly poses challenges for portfolio managers
and investors. For portfolio managers, the active risk in their portfolios has increased without an
explicit increase in the aggressiveness of their bets. The managers lucky enough to have been
"smart" during such a period have been rewarded beyond reasonable expectations. Those
unfortunate enough to have made the wrong calls have been penalized harshly.
In the future, portfolio managers must decide whether, knowing that rewards and penalties will be
amplified, they are comfortable with the current magnitude of their bets. If higher active risk is
beyond their objectives (or tolerance for business risk), they will have to reduce the portfolio's
aggressiveness. The corollary risk is that the crosssectional volatility will revert to its historical
levels and leave portfolio managers who lowered the aggressiveness of their bets with indexlike
returns at active fees. Cross-sectional volatility has shown some degree of persistence, and recent
levels seem to be near their earlier highs. In any case, current levels are well above historical
norms. Thus, the emerging pattern clearly warrants monitoring by all involved in the management
of active portfolios.
For investors, this environment poses a different sort of risk. In an environment where active bets
generate large results (good and bad), active dispersion will be higher. Thus, some mutual funds
will generate astoundingly good returns and some will report astoundingly bad returns. The effect is
heightened temptation for investors to chase the most recent winners in the mutual fund market.
When the difference between the best and worst mutual funds in the market expands two- or
threefold, the behavior of the average investor is not difficult to predict.
But plenty of research warns against such behavior.7 The best response for individual investors in
this environment is to stick with whatever well-developed investment strategy they already have.
The investors who avoid the temptation to chase after the astonishing returns should look back on
this wild period with better-than-average performance. Some things never change.
The authors thank Paul Bouchey, David Carino, Leola Ross, and Mike Ruff for helpful comments and
suggestions. Appendix A. Cross-Sectional Volatility (Dispersion)
Ernest M. Ankrim and Zhuanxin Ding
Ernest M. Ankrim is director of portfolio strategy at The Frank Russell Company, Tacoma,
Washington. Zhuanxin Ding is senior research analyst at The Frank Russell Company, Tacoma,
Washington.
Footnotes:
1. We used the difference between the 95th and 5th percentile managers, rather than the maximum
and minimum, because this difference is less likely to be distorted by individual outliers in the
universe.
2. Intertemporal volatility in 60-month windows is the most common observation structure used in
equity risk models, such as those offered by Barra and Vestek.
3. For the U.S. market, we used the 12 sectors of the Russell 1000 Index. For our analysis of the
Canadian, U.K., and Japanese markets, we used the sectors used by, respectively, the Tokyo Stock
Exchange 300 Index, the Financial
Times Stock Exchange Index, and the Russell/Nomura Index.
4. Charts showing the patterns of cross-sectional volatility and active manager dispersion for the
U.S. small-cap, Canadian, Japanese, and U.K. markets are available from the authors.
5. For markets where technology is grouped into one sector (such as the U.S. large-cap and smallcap markets), excluding technology was simple. For deciphering what was and was not "technology"
in the United Kingdom, Canada, and Japan, we were aided by our colleagues Jennie Tyndall,
Christopher Caspar, and Tim Hicks. For the United Kingdom, technology included telecommunication
services, information technology hardware, software and computer services, media and
photography, information technology, electricity, and electronic and electrical equipment. For Japan,
technology included precision instruments, electrical appliances, and communications. For Canada,
technol
ogy included industrial products and communications/ media.
6. Individual charts comparing cross-sectional volatilities before and after the exclusion of the
technology sectors are available from the authors.
7. See Nesbitt (1995), Ankrim (1997), and Financial Research Corporation (2001).
References:
Ankrim, Ernest M. 1997. "Past Performance Is No Guarantee of PAST Results!" Russell Research
Commentary (August). Campbell, John Y., Martin Lettau, Burton Malkiel, and Yexiao Xu. 2001.
"Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk."
Journal of Finance, vol. 56, no. 1 (February):1-43.
Financial Research Corporation. 2001. Investors Behaving Badly. Investing Essentials, Phoenix
Investment Partners.
Nesbitt, Stephen L. 1995. "Buy High, Sell Low: Timing Errors in Mutual Fund Allocations." Journal of
Portfolio Management, vol. 22, no. 1 (Fall):57-60.
Riley, Barry. 2000. "Coping with the Market's Mood Swings." Financial Times, Euro Markets section
(September 27).
Document fia0000020021029dy9100005