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[dc]I[/dc]t is certainly easy to find examples of real charts beside randomly generated charts–whether on websites and in books–and most traders know, by now, that it is very difficult to tell which charts are real and which are random. The conclusion that some people draw is that, since technical patterns appear on both real and randomly-generated charts, the entire idea of using price patterns to generate trading ideas is flawed–all forms of technical analysis are invalid. This conclusion is, itself, flawed on several fronts.

Real market prices show at least one very serious departure from simple random walks. A random walk has no memory of what has happened in the past, and future steps are completely independent of past steps. However, we observe something very different in the actual data—large price changes are much more likely to be followed by more large changes, and small changes are more likely to follow small changes. For practical purposes, what is probably happening is that markets respond to new information with large price movements, and these high-volatility environments tend to last for a while after the initial shock. This is referred to in the literature as the persistence of volatility shocks and gives rise to the phenomenon of volatility clustering. The charts below show the absolute value of the standard deviations of daily changes for several years of daily returns in a few different markets with only daily changes > |2.0 stdevs| shown. It might be a bit difficult to see from visual inspection, but these large spikes are not dispersed through the data set randomly—they tend to cluster in specific spots and time periods and tend to follow previous spikes.

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What we see here is autocorrelation of volatility. Even if price changes themselves were random and unpredictable, we can make some predictions about the magnitude (absolute value) of the next price change based on recent changes. Though this type of price action is a severe violation of random walk models (which, by definition, have no memory of previous steps), do not assume that it is an opportunity for easy profits. There is still a lot of random noise, and the market is also aware of this tendency for volatility clustering (even if individual investors sometimes are not); derivatives tend to be priced accordingly so, as always, there is no free lunch.

We’ve looked at practical implications of an autocorrelated volatility environment in this blog and in my book—for instance, in the tendency for large directional moves to follow other large price movements—but it is worth mentioning here that there are also academic models that capture this element of market behavior quite well. Autoregressive conditional heteroskedasticity (ARCH), generalized ARCH (GARCH), and exponential GARCH (EGARCH) are time series models that allow us to deal with the issue of varying levels of volatility across different time periods. A simple random walk model has no memory of the past, but ARCH-family models are aware of recent volatility conditions. ((Though not strictly correct, a good way to think of these models is that they model price paths that are a combination of a random walk with another component added in. This other component is a series of error components (also called residuals) that are themselves randomly generated, but with a process that sets the volatility of the residuals based on recent history. The assumption is that information comes to the market in a random fashion with unpredictable timing, and that these information shocks decay with time. The effect is not unlike throwing a large stone in a pond and watching the waves slowly decay in size.)) If this topic interests you, Campell, Lo, and MacKinlay (1996) and Tsay (2005) are standard references.

From a practical standpoint, volatility clustering is important for everyone to understand: certainly options traders must (the options market already understands and (largely) prices for this effect, so you should too!), but active traders, portfolio managers, and risk managers also need to be aware of this. When a market has a volatile shock, what is the best bet? That, in some way, shape or form, more volatility is around the corner, and do not assume a quick return to quiet markets. An important caveat is that this kind of volatility is non-directional.  A market can make a big move up, and then have a period of volatility that is up, down, or sideways–do not draw the facile assumption that a large price shock up will lead to a further move up–maybe, or maybe not. The key point is that it is unusual for a market to become volatile and then to immediately go dead again.  Volatility shocks tend to persist.  Big moves give rise to more big moves. Volatility begets more volatility.