Pitfalls in Tests for Changes in Correlations

by Brian H. Boyer of the University of Michigan,
Michael S. Gibson of the Federal Reserve Board, and
Mico Loretan are of the Federal Reserve Board

March 1999

Abstract: Correlations are crucial for pricing and hedging derivatives whose payoff depends on more than one asset.  Typically, correlations computed separately for ordinary and stressful market conditions differ considerably, a pattern widely termed "correlation breakdown."  As a result, risk managers worry that their hedges will be useless when they are most needed, namely during "stressful" market situations.

We show that such worries may not be justified since "correlation breakdowns" can easily be generated by data whose distribution is stationary and, in particular, whose correlation coefficient is constant.  We make this point analytically, by way of several numerical examples, and via an empirical illustration.

But, risk managers should not necessarily relax.  Although "correlation breakdown" can be an artifact of poor data analysis, other evidence suggests that correlations do in fact change over time.

Keywords: risk management, risk measurement, hedging, derivatives, correlation, conditional correlation, normal distribution, foreign exchange.

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