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

26 Pages Posted: 18 Mar 2011

See all articles by Sumit Agarwal

Sumit Agarwal

National University of Singapore

Hamid Mohtadi

University of Wisconsin - Milwaukee

Date Written: March 2011


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 tail 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 tail events (Gabaix, et. al, 2006, 2008).

Keywords: Systemic Risk, Heavy Tails, Capital Adequacy, Bank Regulation, Financial Institutions

JEL Classification: G2, G3

Suggested Citation

Agarwal, Sumit and Mohtadi, Hamid, Systemic Risk and Heavy Tails: The Case of Banks’ Loan Portfolio (March 2011). Available at SSRN: or

Sumit Agarwal

National University of Singapore ( email )

15 Kent Ridge Drive
Singapore, 117592
8118 9025 (Phone)


Hamid Mohtadi (Contact Author)

University of Wisconsin - Milwaukee ( email )

Department of Economics
Milwaukee, WI 53211
United States

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