Friday, April 16, 2010

Correlation as a tool in analyzing performance

As promised in my post on correlation on Tuesday (and, by the way, it's always wise to read comments to these posts), I'm returning to the theme, this time from a practical perspective. The source for today’s post is Kenneth L. Grant’s Trading Risk: Enhanced Profitability through Risk Control (Wiley, 2004). In his chapter on understanding profit/loss patterns he suggests that the trader can often identify areas of strength and weakness in his performance by performing correlation analysis on the time series of his returns.

The first order of business is to choose the time series to analyze. There is no need to be obsessively granular here, except perhaps on rainy weekends when the trader has nothing better to do than look for correlations based on one-minute data. Let’s say the trader chooses a daily P/L time series and a time span of a week or a month.

What kinds of correlations should the trader run? One obvious choice is to see how correlated his daily returns are with the daily returns of market benchmarks. Grant encourages the trader “to be creative, running correlations between your P/L and as many market times series as you can think of—whether they make intuitive sense or not. While you may not find any surprising interdependencies, you may gain one or two insights into the external market patterns that are likely to have the most dramatic impact on your performance. This is particularly true if you perform the analysis over multiple time periods.” (p. 74)

If the trader is pursuing more than one strategy or trading in different accounts, Grant suggests that he do cross correlation analysis. That is, find out how the strategies or accounts correlate with one another. Is the trader really pursuing independent strategies? Or are they just variations on a theme?

Serial correlation can also be a useful, even though lagging, metric. There are two major types of serial correlation. First, autocorrelation “measures the levels at which today’s absolute performance is tied to absolute performance in the recent past.” Do returns exhibit momentum or mean reversion? Second, autoregression measures deviation from the mean of the data set. Unfortunately most discussions of autoregression quickly become very mathematical. Grant says simply: “Suppose you are trading an account that has an average daily P/L of, say, $10,000. The account would be considered autoregressive if it tended to perform excessively well or badly on a routine basis on days after it deviated from this mean significantly.” (p. 77)

And then there are the “kitchen sink” correlations. That is, try correlating any two things that move against one another. Grant urges creativity. For example, try correlating returns with market volume, volatility, time of day or day of the week, length of holding period, transaction size.

It’s easy to become a correlation junkie because running correlations makes performance analysis more transparent and less emotional. Just remember basic statistical principles when running these correlations. And, Grant adds, “gird yourself against the temptation to undertake aggressive modifications of your trading behavior on the basis of a direct interpretation of a single statistic or even a combination of quantitative indicators. . . . Instead, . . . use these statistics as a general diagnostic in your portfolio management tool kit.” (p. 38)

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