Evaluating Design Choices in Economic Capital Modeling: A Loss Function Approach

Abstract

This paper considers issues relating to the segmentation or grouping of credit exposures and the potential impact upon economic capital allocation and attribution. When discussing capital allocation, we refer to the assessment of total capital at the portfolio level, while our discussion of capital attribution focuses on getting capital assigned appropriately at the bucket level.

We emphasize that a loss or value function must be specified so as to quantify the gains and losses from choosing a more or less granular asset segmentation scheme. Our chosen loss function considers the trade-off between the decrease in sampling variance obtained by combining data to increase sample size and the bias resulting from characterizing unlike assets with the same default probability.

The implications are illustrated with several numerical examples that consider accuracy in the estimation of both portfolio-level and asset-level capital requirements. The suggested technique can be used to quantify whether a loss in accuracy from grouping or segmentation is outweighed by the decrease in variance of estimated capital. That is, the loss from grouping is small when the evaluation criterion is the accuracy of estimation of the required total capital; grouping is of more concern when we are interested in getting capital attributed correctly at the bucket level.

Keywords: Economic Capital, Basel, Rating System, Granularity, Loss Function

JEL Classification: C15, E58, G21, G28