Between Christmas and New Year, the familiar roar of events turns staccato and the market is gently buffeted by meager trading volumes; the relentless pursuit of profit that agitates the flight of global capital is sedated. The books are largely closed; the offices of major financial institutions are staffed by fragile acolytes bereft of their titans. Decisions, if any, are postponed.
Considered contemplation (a luxury denied in more urgent times) is apt. What more appropriate position of comfort to consider the very nature of crisis?
Crisis, by our understanding of it, should be extraordinary, yet it seems crises are presented to the capital markets ordinarily. Why (and how) this happens is a deep question, involving not just market structure and probabilities but also human psychology. A simpler question is to ask what how we might comprehend the alarming frequency with which large movements occur in the equity markets: daily swings of over 10% in benchmarks like the S&P 500 are seven times larger than the average variation – theoretically they should be expected only once in billions of years.1 How then, can they occur so frequently?
The dynamics of volatility are the focus of our latest whitepaper, which explains how dispersion and correlation interact to create crises. One of the interesting features we examined was, in particular, how market volatility reacts to high correlations, and what happens if dispersion moves subsequently. The concepts are fairly simply expressed, and the viewpoint can provide a useful insight into the nature of crisis.
Correlations drive market risk
“The market” is made up of a large number of stocks. Each has its own volatility (which may vary) and each stock correlates to some degree (which may vary) with every other stock in the market. All else being equal, market volatility will be higher if the volatility of the average stock rises and if the average stock-to-stock correlation rises. The precise relationship can be derived analytically; the table below illustrates the range of market volatility that can result from a reasonable (and historically realistic) range of input variables.
A very wide range of market volatilities is possible and, viewed from this perspective, the importance of correlations is starkly apparent. In fact, comparing the top left of the table to the bottom right, it seems quite feasible that from one environment to another market volatility might increase by a multiple of over twelve times. An event that a risk manager might previously dismiss as impossible “because it is twelve standard deviations away from the mean” can suddenly become simply “standard.”