In a related paper, see reference , we compute the risk decomposition of a portfolio with respect to a generic homogeneous risk measure. In this paper we extend those results to the risk decomposition of an active portfolio: a portfolio measured against a benchmark. We find that all the results obtained for the portfolio can be extended to the active portfolio. Furthermore, analogously to a similar analysis in portfolio performance attribution, we split active risk according to the investment decision process and obtain a selection risk, an allocation risk, and interaction risk. Finally, we consider risk decomposition and attribution for portfolio with assets in different currencies splitting risk into local components and a currency-exchange component.
Keywords: risk, active risk, risk contributions, value at risk, var,risk decomposition, marginal risk, currency-exchange risk contribution
Pdf file: relative-risk-decomposition.pdfrelative-risk-decomposition