Shortfall: who contributes and how much?

Understanding risk contributions is a key part of successful risk management and portfolio optimisation. Richard Martin extends the discussion from value-at-risk to expected shortfall and shows that saddlepoint approximation preserves the convexity proper

The properties and analytical derivation of risk measures and their sensitivities to asset allocations is now established as an important issue for portfolio management and optimisation. This is particularly so for credit portfolios, where the risk is highly asymmetrical (Artzner et al, 1999, Gouriéroux, Laurent & Scaillet, 2000, Martin, 2004, Martin, Thompson & Browne, 2001, Martin & Ordovás, 2006).

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