Journal of Risk

A stress test to incorporate correlation breakdown

Jongwoo Kim and Christopher C. Finger


The authors introduce the broken arrow stress test, in which they estimate correlation levels in stress situations and apply these correlation levels to arrive at the expected loss for the peripheral assets in the stress test. To identify correlation in stress situations, the joint distribution of core and peripheral assets is specified as a mixture of normals. For the majority of cases, the asset returns are drawn from a normal distribution with lower volatility and one level of correlation; on rarer hectic days, the asset returns are drawn from a different normal distribution, with higher levels of volatility and a second correlation level. In the example presented, stressed correlation levels illustrate significant changes in correlation for four of the 18 markets examined. The broken arrow stress test produces a more reasonable expected loss estimate than other parametric methods and does not present the problem with the idiosyncrasies seen with historical stress tests.

Furthermore, joint distributions estimated over periods without panics will misestimate the degree of correlation between asset returns during panics. Under these circumstances, fear and disengagement by investors often result in simultaneous declines in the values of private obligations, as investors no longer realistically differentiate among degrees of risk and liquidity, and increases in the values of riskless government securities. Consequently, the benefits of portfolio diversification will tend to be overestimated when the rare panic periods are not taken into account.
Remarks by FRB Chairman, Alan Greenspan [4]

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