Systemic Risk and Heavy Tails: The Case of Banks’ Loan Portfolio

Abstract

We estimate a Pareto distribution for loan losses, as an alternative to the commonly used Vasicek distribution, using simulated data. A key assumption in the construction of Vasicek distribution is that firm-level risk is idiosyncratic. It also assumes that firm exposure to systemic risk is constant across firms (captured by R1/2). But profitability may decline differently across firms in a recession in ways that are both systematic and related to firm characteristics, such as size, sector, or firm-level fixed effects. Finally, when calculating expected loss under the Vasicek framework, the probability of default (PD) and loss given default (LGD) of loans are assumed to be uncorrelated. Yet, evidence points to correlations between PD and LGD especially when systemic risk is dominant. (c.f. Miu and Ozdemir, 2006, Altman, Reti and Sironi, 2005). Its possibility has also been discussed in the BASEL final rule (Federal Register 2007 p. 69309). We use a Pareto distribution to overcome these restrictions. We find a higher probability of large losses than has been understood thus far. We examine our findings, based on simulated data that reproduce a bank’s mean PD and LGD values. The findings do show that the Pareto distribution predicts a higher likelihood of events and fits the data more closely, when compared with the Vasicek distribution. The threshold or cross-over point at which this tail result obtains corresponds to PDs ranging from 1% to 2%, a range found in the mid to mid-high risk segments for many banks' portfolios. The use of Pareto distribution is consistent with the new thinking about the role of Power Law in explaining events (Gabaix, et. al, 2006, 2008).