We look at the problem of constructing multivariate distributions consistent with given marginal distributions and dependence measures. Although copulas, rank correlations and other dependence concepts have been known for a long time they are of recent use in risk management. In the case of multivariate normal distributions linear correlation determines the dependence structure in a unique way. However, it is not an appropriate dependence measure in the case of non-normal multivariate distributions and it can be very misleading.

We discuss potential shortcomings and pitfalls.

VaR is not a coherent measure for non-normal risks because it does not satisfy the sub-additivity property. We give examples when VaR for risk aggregation is larger the sum of the individual VaRs in the aggregation.

Reference Books

• H.Joe, "Multivariate Models and Dependence Concepts", 1997
• R.B.Nelsen, "An introduction to Copulas", 1999.
• P.Embrechts, A. McNeil, and D.Straumann, "Correlation and dependence in risk management: properties and pitfalls", 1999 CorrelationPitfalls.pdf.

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