Over the past five years, equity returns in the UK and continental Europe have experienced higher levels of cross-sectional volatility. Here we offer some ways to look at the current situation that may provide helpful insights. We present only our analysis for the UK market for reasons of space, but that for continental Europe is very similar.
The basic measure of cross-sectional volatility is the standard deviation of returns across equities at a point in time. Cross-sectional volatility is sometimes called return dispersion to distinguish it from the volatility of returns to a single security, portfolio, or index over time. Although cross-sectional and time-series volatilities are related, they do not always move in the same direction. For example, an event that moves all stocks in the same direction and then back again will show high time-series volatility but might not show an increased cross-sectional volatility. Conversely, if some sectors move sharply in one direction while others move in the opposite direction, the increased cross-sectional volatility might not also result in increased time-series volatility of a portfolio or index encompassing all sectors.
The trend in increased cross-sectional volatility is documented in Figure 1, which graphs the standard deviation of returns to all shares in the FTSE 350 for each trading day from 1 November 1996–31 October 2001. A 23-day centred moving average is also graphed to better identify trends. Daily volatility has more than doubled over the past five years and shows no sign of returning to pre-1997 levels.
Turning to the events of 11 September, the graph illustrates two interesting features of market reaction. First, volatility was on the rise anyway just before 11 September, increasing from an average of 2% to 3% a day. Second, while there was a predictable increase in volatility in the days following the events, it has since come back down to pre-event levels. So far the episode has had no greater impact than previous high-volatility periods.
There has been much speculation in the financial press about what factors may be driving the increased volatility the market has experienced. We use a regression-based stock-level attribution analysis to permit us to dig deeper and identify some of the key factors. Market-wide, sector and stock-specific factors are estimated by applying cross-sectional regression on each day’s stock returns. (For this analysis, we define cross-sectional volatility as the average squared return rather than the standard deviation. This allows us to identify market-wide movements as an additional volatility factor.)
Figure 2 shows that market-wide shocks were significant factors during the Asian and Russian default episodes. By contrast, the impact of the events of 11 September was only briefly felt across the whole market. In fact, sector volatility has accounted for an increased share of overall cross-sectional volatility in the past year. The usual suspects are the TMT (technology-media-telecommunications) sectors, and transportation, energy and insurance following 11 September.
Indeed the boom and bust of the tech bubble is a large part of what is driving the increase in cross-sectional volatility. Figure 3 plots the ratio of the smoothed daily standard deviations of the TMT and ex-TMT sectors. Prior to early 1998, the ratio hovered around one, which means they were about equal. But from mid-1998 on there has been a steady rise in TMT sector volatility relative to the ex-TMT sectors. This trend was reversed briefly following 11 September as the transportation, energy and insurance sectors were thrown into turmoil, but since then the ratio has been heading back to almost two to one.
The cross-sectional volatility of shares in an equity market is a crucial element in understanding the performance of active managers. To see this, consider the following thought experiment. Suppose all active managers hold securities at weights that were different from the benchmark and different from each other. Now suppose all stocks rose by exactly 5%. What would be the outcome? Cross-sectional volatility as measured by standard deviation would be zero, and all active managers would earn exactly the same return, namely the benchmark return.
Now let just one stock change by something other than 5%. Cross-sectional volatility would be slightly positive and each active manager would have a slightly different return, a return different from the benchmark return. It is easy to extrapolate from this experiment: if all stocks have very different returns, then cross-sectional volatility will be high and active managers will have widely dispersed returns.
That is exactly what we find in Figure 4, in which the cross-sectional dispersion of returns across the Micropal universe of active UK equity managers is superimposed on the daily volatility of the FTSE 350. This is a bit of an apples and oranges comparison as the Micropal returns are monthly while the FTSE are daily. Nonetheless, the correspondence of the two series is striking.
The correlation between the cross-sectional volatility of equities and the dispersion of active returns has important implications for evaluating the performance of active managers. The same set of active over-weight and under-weight security bets will have one outcome in a low volatility environment and a much better (or worse) outcome in a high volatility environment. Thus, for example, the manager who can add 2% alpha in a low volatility market is much more impressive than the manager who can only do it in a high volatility market. Because of this, some analysts have advocated ranking managers on the basis of active returns adjusted for cross-sectional volatility in the market.
The deeper underlying causes of the increase in cross-sectional volatility remain a matter of debate. It is hard to avoid seeing a behavioural aspect as well – fear, greed, and the herd instinct have surely played a role in creating a bubble-like environment. We have seen this before. These high levels of volatility are probably not permanent but the end is not yet in sight.
Portfolio managers have seen their active risk increase without consciously turning the dial up. So the smart (or lucky) managers look smarter and the dumb (or unlucky) look dumber.
Finally, stock-specific volatility is the most consistent potential source of active value-added. The attribution analysis of Figure 2 shows that normally 60–75% of cross-sectional volatility is stock-specific. A 60–75% share of increased volatility means that the scope for adding value through active security bets has increased. The ride is still very bumpy, but the opportunities for active management are greater than ever.
Tom Goodwin is capital markets research analyst with Frank Russell Company in London