Consider a credit portfolio that consists of default-sensitive instru¬ments such as lines of credit, corporate bonds, and government bonds. The corresponding credit value-at-risk (VaR), is the minimum loss of next year if the worst 0.03 percent event happens. In another words, 99.97 percent of the time the loss will not be greater than VaR. Note that the credit VaR is measured at the time span of one year and is different from the 10-day convention adopted by market VaR. 0.03 percent is chosen because it is a rating agency standard of granting an AA credit rating.
Single instrument
The loss of a single instrument can be decomposed into three components: the default probability of the obligor (PD), the loss given default (LGD), and the exposure at default (EAD). For the sake of simplicity, EAD is assumed to be non-random in the subsequent discussion.
LGD is the portion of EAD that gives negative impact in case of default. LGD is usually less than one because many default obligors are originally backed by securities.
The magnitude of the recovery rate is tied to the collateral properties during or after default. The recovery rate depends on the nature of the instrument: only the loss on principal can be claimed, not the loss on coupon interest.
PD and LGD are positively correlated, meaning PD and the recovery rate are negatively correlated.
Portfolio
The main issue in computing VaR for a credit portfolio is that the joint default probability for two obligors does not follow the law of independence. Companies in the same sector tend to default together. This is known as credit concentration.
Stress testing
Stress testing is the procedure of checking the robustness of VaR under different hypothetical changes. Examples include perturbation of the model parameters, economic downturn of the region, deterioration of the industry environment, or the downgrade of specific obligors’ credit profiles. Another equivalent way is to fix VaR and observe how the tail area of L is affected. A systematic account can be found in the Bank of International Settlement document of “Stress testing at major financial institutions: survey results and practice”.
Implementation details
Some hints on the real complexity of VaR:
• Although many banks have a strong desire to apply credit VaR to both trading and loan books in an integrated manner, some of the cumbersome barriers are the differences in accounting treatment, variation of technology platforms, and illiquidity factors (relating to traditional loans). The banks may involve fundamental changes in organisational structure in order to implement consistent integrated risk management systems.
• Some of the companies involved in a portfolio could have become public very recently and the equity return may not be available before IPO. Statistical techniques, such as EM algorithm of Dempster et al. and data augmentation algorithm of Tanner and Wong, can be employed to impute the missing values and estimate the model parameters.
• Similar to market VaR, backtesting is one of the goals to be achieved in addition to stress testing. However, the time span of credit VaR is typically one year and it is hopeless to collect enough historic credit loss data for validation purpose. Lopez and Saidenberg suggest backtesting by cross-sectional simulation, which is essentially a variation of bootstrap, ie, evaluation based upon resampled data.
This article is an edited version of
an entry in the “Encyclopedia of Quantitative Risk Analysis and
Assessment”, Copyright © 2008 John Wiley & Sons Ltd. Used by
permission.
