The highly publicized Fed report last week (see previous posting) on hedge fund risk gives a useful lesson on the potential folly of using only one variable to asses “risk”.

It’s often said that “correlation goes to 1″ in times of distress. The report acknowledges the materiality of cross-strategy correlation in assessing hedge fund risk.

“A key determinant of hedge fund risk is the degree of similarity between the trading strategies of different funds. Similar trading strategies can heighten risk when funds have to close out comparable positions in response to a common shock. For example, many funds had to close out positions during the LTCM crisis to meet margin calls and satisfy risk management constraints.”

Tobias Adrian, author of the report, says that covariance is a better risk measure than correlation because it “*captures the extent to which their returns move together (or apart, in the case of negative covariance) in dollar terms”.*

Correlation, says Adrian, is less relevant when measuring risk since it only indicates the propensity of strategies to move in the same direction – not the scale of those moves. In his words:

“…it matters little if two funds tend to gain or lose at the same time if such joint gains and losses are only a small fraction of the funds’ total returns.”

He describes, in refreshingly plain English, that correlation is essentially “normalized” by dividing the covariance by the volatilities of the two securities in question. In other words, correlation is a ratio of covariance (in dollars) to volatility (in dollars). So, when volatility drops, correlation rises – even if the actual quantum of the covariance is unchanged.

Recently, both equity markets and hedge funds have had a relatively low volatility. So Adrian wonders if a drop-off in volatility has simply not been matched by a commensurate drop-off in covariance. Such a situation would lead to a rise in correlation. His hypothesis:

“…the distinction is more than a mere technicality: the correlation of hedge fund returns rose both in the period prior to the LTCM crisis and in recent timesâ€”but for different reasons. An increase in the comovement of dollar returns was the leading cause of rising correlation in the 1990s, but a decline in overall volatility explains the recent rise.”

First, the report shows the chart that has everyone worried. As you can see, it shows that hedge funds are more “correlated” then ever:

But wait, says Adrian. The two components of correlation, covariance and volatility, give us more insight into what is going on. We are now experiencing a low covariance and an *even lower* volatility.

To conclude, Adrian looks specifically at the months surrounding September 1998 and the LTCM crisis. He compares the correlation of equities to the cross-correlation of hedge funds in the fall of 1998 and finds that it is actually *equities*, not hedge funds that are more prone to show a lot of comovement in times of distress.

“Our finding that the onset of the LTCM event was not associated with an increase in hedge fund correlations contrasts with other results showing how asset returns behave during financial crises…

“The behavior of equity correlations contrasts strongly with that of hedge fund correlations during the LTCM crisis. As we observed earlier, hedge fund correlations did not spike during either the Russian default or the LTCM event. Taken together, these results suggest that the investment strategies of hedge funds differ substantially from those of marginal equity investors. In particular, the spike in hedge fund cross-sectional volatility in August 1998 illustrates the heterogeneity of hedge fund investment strategies.”

And so a story that began with the headline “Hedge Fund Risk Highest Since 1998″ actually ends up arguing A) that hedge fund comovement is actually quite low, and B) that hedge fund correlation is more likely to remain low in a crisis than equity market correlation.

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