Fast Approximation of Loan Portfolio Loss

Economic capital and Value at Risk are key measures in risk management and risk regulations. The industry practice is to calculate these risk measures based on brute force simulations using market observed index returns as risk factors and some assumed correlation structure. In this paper, we illustrate how the underlying risk factors can be constructed from time series of default probabilities and how Value at Risk and Expected Shortfall can be calculated using a closed form approximation for a multi-factor model. Furthermore, economic capital figures based on risk factors extracted from different sources are compared and analyzed using a large portfolio of over 500 obligors and a small portfolio of 26 obligors. Our findings indicate that observed index returns may not explain default variations well and could lead to an underestimation of risk. Risk neutral default probabilities capture market conditions and changes in market sentiment well, but could lead to an over estimation of risk due to the embedded risk premium.