Portfolio credit-risk optimization Ian Iscoe a , Alexander Kreinin a , Helmut Mausser a , Oleksandr Romanko a,b,⇑ a Quantitative Research Group, Algorithmics Incorporated, an IBM Company, 185 Spadina Ave., Toronto, ON, Canada M5T 2C6 b Department of Computing and Software, McMaster University, 1280 Main St. West, Hamilton, ON, Canada L8S 4K1 article info Article history: Received 29 July 2011 Accepted 18 January 2012 Available online 28 January 2012 JEL classification: C02 C61 C63 D81 G11 G32 Keywords: Credit risk Optimization Portfolio optimization Risk modeling Value-at-Risk Expected shortfall abstract This paper evaluates several alternative formulations for minimizing the credit risk of a portfolio of finan- cial contracts with different counterparties. Credit risk optimization is challenging because the portfolio loss distribution is typically unavailable in closed form. This makes it difficult to accurately compute Value-at-Risk (VaR) and expected shortfall (ES) at the extreme quantiles that are of practical interest to financial institutions. Our formulations all exploit the conditional independence of counterparties under a structural credit risk model. We consider various approximations to the conditional portfolio loss distribution and formulate VaR and ES minimization problems for each case. We use two realistic credit portfolios to assess the in- and out-of-sample performance for the resulting VaR- and ES-optimized port- folios, as well as for those which we obtain by minimizing the variance or the second moment of the port- folio losses. We find that a Normal approximation to the conditional loss distribution performs best from a practical standpoint. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction For financial institutions, the benefits of managing (portfolio) credit risk include not only reduced monetary losses due to de- faulted or downgraded obligations but also lower capital charges. While individual credit-risky positions can be hedged with credit derivatives such as credit default swaps, imperfectly correlated credit movements among counterparties also provide opportuni- ties for mitigating credit risk at the portfolio level through diversi- fication. In particular, the use of optimization techniques to restructure portfolios of credit-risky positions, is an attractive possibility. However, such procedures face numerous challenges, foremost being the difficulty of representing the portfolio credit loss distribution with sufficient accuracy. This paper formulates several alternative optimization problems that are derived from a structural (Merton) model of portfolio credit risk, and evaluates their effectiveness from the perspectives of risk mitigation and computational practicality. Credit risk refers to the potential monetary loss arising from the default, or a change in the perceived likelihood of default, of a counterparty to a financial contract. Note that a reduction in the default probability, i.e., a transition to a more favorable credit state, results in a monetary gain. However, such gains are generally small relative to the losses that occur due to severe credit downgrades or default. Thus, the credit loss distribution (F) for a typical invest- ment-grade portfolio is positively skewed, the long right tail being consistent with a small likelihood of substantial losses. The complex relationships among asset prices, exposures and credit transitions preclude obtaining a closed-form representation of the actual credit loss distribution. Thus, for risk management purposes, it is necessary to replace F by some approximating distri- bution b F . The form of b F varies depending on the underlying credit loss model. For example, reduced-form models (e.g., CreditRisk+ (Credit Suisse Financial Products, 1997)) provide b F in closed form. However, their underlying assumptions may be viewed as overly simplistic in that they fail to capture the effects of credit-state migrations and correlated movements of risk factors (de Servigny and Renault, 2004). In contrast, structural models (Gupton et al., 0378-4266/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2012.01.013 ⇑ Corresponding author at: Quantitative Research Group, Algorithmics Incor- porated, an IBM Company, 185 Spadina Ave., Toronto, ON, Canada M5T 2C6. Tel.: +1 416 217 4615; fax: +1 416 971 6100. E-mail addresses: Ian.Iscoe@ca.ibm.com (I. Iscoe), Alex.Kreinin@ca.ibm.com (A. Kreinin), Helmut.Mausser@ca.ibm.com (H. Mausser), romanko@mcmaster.ca (O. Romanko). Journal of Banking & Finance 36 (2012) 1604–1615 Contents lists available at SciVerse ScienceDirect Journal of Banking & Finance journal homepage: www.elsevier.com/locate/jbf