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. Cross-sectional 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 two- or 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 cross-sectional 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 cross-sector 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 12-month 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. large-cap 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 cross-sectional 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.