# LO 18.4: Explain expected loss, unexpected loss, VaR, and concentration risk, and

LO 18.4: Explain expected loss, unexpected loss, VaR, and concentration risk, and describe the differences am ong them.
Expected loss (EL) calculates the average loss in the long run generated from credit facilities. The EL rate is a percentage of the EAD. EL can be determined on a financial basis, defined as a decrease in market value resulting from credit risk, or on an actuarial basis, ignoring credit risk and considering only losses from the EAD.
EL can be calculated as:
EL = PD x LGD x EAD
EL is determined based on expectations and is a cost that is incorporated into business and credit decisions. However, actual losses may be different from expectations, resulting in unexpected losses (ULs). ULs are problematic because they can jeopardize the viability of a bank as a going concern. Banks can prepare for ULs by holding sufficient equity capital to cover all risks, not just credit risks. Capital can be replenished from profits in good times, which can absorb ULs. Credit risk models and credit ratings are important in determining the overall credit contributions needed by banks.
In measuring UL, standard deviation is not an adequate measure since it assumes a symmetrical loss distribution. In practice, risks are often not symmetric, so other credit
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2018 Kaplan, Inc.
Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2
measures, such as value at risk (VaR), are more useful. VaR is defined as a percentage of EAD and is calculated as the difference between the maximum loss at a certain confidence level and the EL at a given time horizon. For example, VaR at a 99% confidence level defines the capital that a bank must put aside to cover ULs in 99% of the cases. The banks insolvency (due to catastrophic losses) is therefore confined to events whose probability does not exceed 1%.
As mentioned, credit risk probability distributions are asymmetric, where events with small probabilities (e.g., insolvency) may significantly impact a banks profitability. Credit risk models can help estimate probability density functions. Loss distributions and calculating VaR measures can be done by (1) adopting a parametric closed-form distribution, (2) using numerical simulations, or (3) using discrete probability solutions.
Despite the usefulness of VaR and EL measures, these measures do not factor in portfolio concentration and typically ignore diversification between assets. Diversification reduces risk; therefore, the aggregate of individual risk measures does not equal portfolio risk. As a result, analyzing credit risk from a portfolio perspective should account for concentration risk. Concentration risk arises in credit portfolios where borrowers all face common risk factors, including interest rates, exchange rates, and changes in technology. Facing common risks is problematic since they simultaneously affect a borrowers willingness and ability to repay their obligations.
Banks traditionally avoided concentration risk by limiting their exposures to individual customers, and, thus, minimizing risk through higher granularity (i.e., a well-diversified portfolio). When analyzing with quantitative credit risk management, the need for granularity is already integrated into default correlations. Full portfolio credit risk models look at how much individual borrower risk factors contribute to concentration. They also enable segmentation of portfolio risk or viewing the entire portfolio risk profile as a whole. Portfolio credit risk models are critical in quantifying how much marginal risk can be attributed to various credit exposures. Without these models, it is not possible to properly quantify risks.
Default codependencies can be modeled through (1) asset value correlations and (2) default correlations. When modeling with asset value correlations, portfolios could be affected by external events, which influence counterparty values and could cause asset values to drop below the value of outstanding debt. Diversification is measured by considering the debt outstanding between two borrowers and by looking at the correlation among asset values.
Modeling with default correlations looks at historical correlations of data among homogenous borrower groups Since default correlations are generally not perfectly positively correlated, banks will have to separately address their potential losses in changing financial periods. This would allow banks to address risks in a more organized fashion, with less committed capital and smaller fluctuations in provisioning.
2018 Kaplan, Inc.
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Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2