Shortfall factor contributions
The risk contribution of a position is the sensitivity of risk to a fractional change in the position. By the Euler formula, the risk contributions add up to the portfolio risk. However, if one wants the contribution of a general ‘risk factor’ to (the systematic part of) the portfolio risk, this idea does not work properly because the risk is not a homogeneous function of the factors. In this article, Richard Martin and Roland Ordovàs introduce a direct generalisation of the Euler formula applicable to any model
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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