# LO 18.6: Define risk-adjusted pricing and determine risk-adjusted return on risk-

As VaR increases, so does the expectation of higher returns and economic capital. The cost of capital multiplied by VaR needs to be incorporated into lending decisions as a cost for banks that are price takers, or as a lending cost (to be included in credit spreads) for banks that are price setters.
Economic capital is important from a pricing perspective and should, therefore, be incorporated into loan pricing decisions. While, in theory, price is an external factor and banks are price takers in an integrated market, in reality, markets are segmented, so pricing decisions vary. For example, in the wholesale market, banks are typically price takers,
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Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2
whereas in retail markets, banks are price setters (due to information asymmetries and costs). Regardless of the market, prices are an important component of credit decisions and loan pricing. For banks, risk-based pricing policy is important for (1) active portfolio management (by using credit derivatives), (2) integrating credit, market, and operational risks into risk budgeting, and (3) setting management objectives.
The risk-adjusted return on capital (RAROC) has been widely used by banks in measuring risk-adjusted performance. A common variant of RAROC is the risk-adjusted return on risk-adjusted capital (RARORAC). Both of these measures are used by business lines to assess whether returns generated exceed the market risk premium required by capital. The market risk premium should be in proportion to the credit spread. Transactions create value if RARORAC exceeds a minimum target, for example, a target return on equity (ROE):
RARORAC > ROEr
, target
Applied in the context of economic value added (EVA), which is a measure of the firms economic profit, EVA can be determined as the risk premium of economic capital, where Ke is the cost of shareholder capital:
EVA = (RARORAC – Ke) x economic capital
The pricing of credit products should include fundamental variables, including costs and potential losses. Therefore, RARORAC should incorporate funding cost, EL (to cover loan provisions), allocated economic capital, and excess return required by shareholders (with respect to the cost of funding). In simple form, RARORAC can be calculated as:
RARORAC =
spread + fees EL cost of capital cost of operations
economic capital
Firms can make certain exceptions to override credit decisions for relationship or reputational reasons. For example, a bank may decide to maintain ties with an otherwise unprofitable customer for reputational or relationship reasons. These decisions should be made at the senior management level.
In general, credit decisions and outcomes, as well as customer profitability analysis, should be communicated to senior management. The goal of such analysis is to generate a comprehensive view of customer profitability, costs, revenues, and risks by segmenting customers, with the aim of identifying profitable and unprofitable relationships. Capital currently set aside for unprofitable or marginally profitable customers could then be freed up and allocated to more profitable opportunities. The relative risk-adjusted profitability models of customers are important in optimizing the risk-return decisions regarding bank portfolios. These models have gained more traction recently because of the growth in investor sophistication, and the growth in size and complexity of banking groups, which now have a greater need for risk-adjusted performance measures.
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Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2
K e y C o n c e p t s
LO 18.1
Credit ratings measure a borrowers creditworthiness. Ratings enable borrowers to access capital markets and properly manage risks.
LO 18.2
There are several classifications of credit risk. Risks relating to default include default risk, recovery risk, and exposure risk. Risks relating to valuation include migration risk, spread risk, and liquidity risk. Credit risk also encompasses concentration risk and can be correlated with pure financial risks.
LO 18.3
Determining default probability can be based on (1) analysis of historical default frequencies of a borrowers homogenous asset classes, (2) mathematical and statistical tools, (3) a hybrid approach that combines mathematical and judgmental analyses, and (4) implicit default probabilities from market prices of publicly listed counterparties.
Default risk is typically measured over one year. However, cumulative default rates extending beyond one year are important. Shorter exposures, such as overnight lending, are also exposed to default risk.
Recovery risk is a conditional metric assuming that default has already occurred. The amount of recovery depends on (1) the type of credit contracts used and the relevant legal system, (2) general economic conditions, and (3) covenants. Estimating the recovery rate on ex ante basis is challenging due to the difficulty in collecting recovery rate data, uniformity of information, and challenges in creating a comprehensive model.
Exposure risk is easily determined for term loans. For revolving credit facilities, exposure depends on borrower behavior and external events. In this case, exposure risk [i.e., exposure at default (EAD)] can be calculated as:
EAD = drawn amount + (limit drawn amount) x loan equivalency factor
LO 18.4
Expected loss (EL) is the average loss generated from credit facilities. EL can be calculated as:
EL = PD x LGD x EAD
Unexpected losses (ULs) result from actual losses that may be different from expectations. The risk of ULs can be mitigated by holding sufficient equity capital.
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Value at risk (VaR) measures are more useful in measuring unexpected losses than traditional volatility measures since loss distributions are not symmetric. VaR is computed as the difference between the maximum loss at a certain confidence level and the EL at a given time horizon.
Traditional risk measures, like VaR, do not account for concentration risk, which arises when borrowers are exposed to common risk factors which could simultaneously affect their willingness and ability to repay their obligations.
Concentration was traditionally mitigated by minimizing exposure to a single borrower. Portfolio credit risk models specifically factor in a borrowers risk contribution to concentration, and allow for segmentation of portfolio risk or viewing the portfolio risk profile as a whole.
Default codependencies can be modeled with (1) asset value correlations, which look at the influence of external events on asset values, and (2) default correlations, which look at historical correlations among homogenous borrower groups.
LO 18.5
Marginal VaR calculates the incremental portfolio risk from an individual exposure. Marginal VaR is useful in calculating betas, which can be interpreted as the marginal risk contribution from a loan to average portfolio risk. A beta greater than one implies concentration risk, while a beta less than one indicates diversification.
LO 18.6
The risk-adjusted return on risk-adjusted capital (RARORAC) is an important risk- adjusted performance measure used to assess whether returns generated exceed the market risk premium required by capital. Transactions add value as long as RARORAC exceeds a minimum target (e.g., a target return on equity).
Economic value added (EVA) measures economic profit and looks at the additional return generated relative to the cost of capital:
EVA = (RARORAC – Ke) x economic capital
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Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2
C o n c e p t C h e c k e r s
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Which of the following credit risks best reflects the risk that an entity may have to accept lower-than-expected values for credit exposures that must be sold? A. Recovery risk. B. Exposure risk. C. Spread risk. D. Liquidity risk.
During a conversation about credit risk, a colleague mentions that the typical measure of default risk is the probability of default (PD) over a one-year horizon, because overnight lending has a zero PD. Is your colleague correct with respect to her statements? A. She is correct with respect to both statements. B. She is correct with respect to default risk over a one-year horizon only. C. She is correct with respect to overnight lending only. D. She is not correct with respect to either statement.
A credit analyst notes that value at risk (VaR) is a more useful measure than volatility of losses, because loss distributions tend to be asymmetric. The analyst further notes that VaR does not account for portfolio concentration risk. Is the analyst correct with respect to his statements? A. The analyst is correct with respect to both statements. B. The analyst is correct with respect to VaR as a more useful measure only. C. The analyst is correct with respect to concentration risk only. D. The analyst is not correct with respect to either statement.
Which of the following risks is most likely associated with marginal value at risk (marginal VaR)? A. Recovery risk. B. Spread risk. C. Concentration risk. D. Exposure risk.
A bank estimated that its risk-adjlisted return on risk-adjusted capital (RARORAC) is 13%. The banks marginal cost of capital is 7%, and its economic capital is $100 million. What is the banks economic value added (EVA)? A.$7 million B. $8 million. C.$15 million. D. $22 million. Page 36 2018 Kaplan, Inc. Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2 C o n c e p t C h e c k e r A n s w e r s 1. D Liquidity risk measures the risk that asset liquidity and values deteriorate during adverse market conditions, resulting in lower market value. 2. B The colleagues statement with respect to the PD being measured over a one-year time horizon is correct. She is incorrect with respect to her statement on overnight lending, which has a non-zero PD. 3. A The analyst is correct with respect to both of his statements. Value at risk (VaR) is a more useful measure than the standard deviation of losses, since loss risk distributions tend to be asymmetric. VaR, however, does not account for portfolio concentration risk. 4. C Marginal VaR is a measure of concentration risk, which measures the probability of loss arising from a borrowers exposure to common risk factors. 5. B EVA measures economic profit as the additional return generated relative to the cost of capital. EVA is calculated as: EVA = (RARORAC – K J x economic capital EVA = (0.13 – 0.07) x$100 million = \$8 million
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The following is a review of the Credit Risk Measurement and Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in:
Ra t in g A s s i g n m e n t M e t h o d o l o g i e s
Topic 19
E x a m F o c u s
The focus of this topic is on the assessment of default risk and assigning ratings as a means of quantifying this risk. For the exam, be comfortable with the relationship between default probability and ratings. Also, understand how ratings are derived for issues and issuers, how ratings migrate over time, how various default probabilities are calculated, and what defines a good ratings system. Default is predicted using many different approaches: experts-based (heuristic), reduced form (statistical and numerical), structural (the Merton model), linear discriminant analysis, logistic regression models, cluster analysis, principal component analysis, and cash-flow simulations. You should be familiar with the advantages and limitations of each of these approaches as well as the similarities and differences among them. These approaches are heavily quantitative, so it is critical to also factor qualitative information into any analysis of default probability.
R a t i n g S y s t e m s