Measuring Default Risk for a Portfolio of Equities

Abstract

This work evaluates some changes proposed by the Basel committee (BCBS) regulation for capital allocation in the trading book due to a company default in an equities portfolio. In the last decade, some measures were designed to account for the risk of default of a company, which were not caught by a 10-day value at risk measure. The first and more conservative measure designed to capture the effect of defaults was the incremental risk charge. With time, this measure went through some changes until it became the default risk charge. To design these measures, we used a Merton model to compute the probability of default. This probability is compared with the simulated asset returns to compute a 1-year value at risk. The idea is to capture the risk of a company defaulting. The results shown are based in a portfolio of Ibovespa companies and a portfolio of S\&P 500 companies. Additionally, we propose a manner to account for the correlation in the companies, and we compare the effects of the standard method of capital allocation to the models developed in this study.

Keywords: FRTB; default risk; equities; multi-factor model