In this paper we generalize Vasicek's Asymptotic Single Risk Factor (ASRF) solution to multiple factors organized with a particular hierarchical structure. We use this model to investigate credit portfolio loss. In this hierarchical factor model, asset returns of a company depend on a global factor, a sector factor, and an idiosyncratic risk factor. All companies share the same global factor and all companies within a sector share the same sector factor. Using the central limit theorem, we

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... e closed form solutions for the Value-at-Risk (VaR) and expected shortfall (ES) under the assumptions that the number of sectors in the portfolio is large, and the exposures scale as the reciprocal of the number of sectors. Our results for the VaR agree well with Monte-Carlo simulations 1 providing the sector factor loadings and variance of systematic risk are not too large.