CVaR and Credit Risk Measurement - Edith Cowan University

CVaR and Credit Risk Measurement By Robert J. Powell1 and David E. Allen1 1School of Accounting, Finance and Economics, Edith Cowan University School of Accounting, Finance and Economics & FEMARC Working Paper Series Edith Cowan University August 2009 Working Paper 0905 Correspondence author: Robert J. Powell School of Accounting, Finance and Economics Faculty of Business and Law Edith Cowan University Joondalup, WA 6027 Australia Phone: +618 6304 2439 Fax: +618 6304 5271 Email: r.powell@ecu.edu.au ABSTRACT The link between credit risk and the current financial crisis accentuates the importance of measuring and predicting extreme credit risk. Conditional Value at Risk (CVaR) has become an increasingly popular method for measuring extreme market risk. We apply these CVaR techniques to the measurement of

credit risk and compare the probability of default among Australian sectors prior to and during the financial crisis. An in depth understanding of sectoral risk is vital to Banks to ensure that there is not an overconcentration of credit risk in any sector. This paper demonstrates how CVaR methodology can be applied in different economic circumstances and provides Australian Banks with important insights into extreme sectoral credit risk leading up to and during the financial crisis. Keywords: Conditional Value at Risk (CVaR); Banks; Structural modelling; Probability of default (PD) 1 1. Introduction Value at Risk (VaR) has become an increasingly popular metric for measuring market risk. VaR measures potential losses over a specific time period within a given confidence level. The concept is well understood and widely used. Its popularity escalated when it was incorporated into the Basel Accord as a required measurement for determining capital adequacy for market risk. VaR has also been applied to credit risk through models such as CreditMetrics (Gupton, Finger, & Bhatia, 1997), CreditPortfolioView (Wilson, 1998), and iTransition (Allen & Powell, 2008). Nevertheless, despite its popularity, VaR has certain undesirable mathematical properties; such as lack of sub-additivity and convexity; see the discussion in Arztner et al (1999; 1997). In the case of the standard normal distribution VaR is proportional to the standard deviation and is coherent when based on this distribution but not in other circumstances. The VaR resulting from the combination of two portfolios can be greater than the sum of the risks of the individual portfolios. A further complication is associated with the fact that VaR is difficult to optimize when calculated from scenarios. It can be difficult to resolve as a function of a portfolio position and can exhibit multiple local extrema, which makes it problematic to determine the optimal mix of positions and the VaR of a particular mix. See the discussion of this in Mckay and Keefer (1996) and Mauser and Rosen (1999). Conditional Value at Risk (CVaR) measures extreme returns (those beyond VaR). Allen and Powell (2006; 2007) explored CVaR as an alternative method to VaR for measuring market and credit risk. They found that CVaR yields consistent results to VaR when applied to Australian industry risk rankings, but has the added advantage of measuring extreme returns (those beyond VaR). Pflug (2000) proved that CVaR is a coherent risk measure with a number of desirable properties such as convexity...

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