Shortfall factor contributions

Shortfall factor contributions

The notion of the contribution of a position to the risk of a portfolio is well understood as the sensitivity of risk to a fractional change in position (for comprehensive reviews, see Tasche, 2007 and 2008). By the Euler formula, these contributions add up to the risk, as the risk is a homogeneous function of the asset allocations. It is also known that when risk is to be understood as the standard deviation or expected shortfall (ES) then, in the context of a factor or conditional-independence

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