Book 2. Credit Risk

FRM Part 2

CR 21. The Evolution of Stress Testing Counterparty Exposure

Presented by: Sudhanshu

Module 1. Counterparty Credit Risk

Module 2. Stress Testing

Module 1. Counterparty Credit Risk

Topic 1. Counterparty Credit Risk (CCR) Exposure Measures

Topic 2. CCR Treatment

Topic 1. Counterparty Credit Risk (CCR) Exposure Measures

• Current Exposure (Replacement Cost): Also known as replacement cost, this is the greater of zero or the market value of a transaction that would be lost if a counterparty defaulted with no recovery. It is the most common measure of exposure at a single point in time.

• Peak Exposure: This measures the distribution of exposures at a high percentile ($95\%$ or $99\%$) at a given future date. It is a forward-looking measure antd is useful for assessing the maximum potential loss over a specific time horizon.

• Expected Exposure: This measures the mean (average) distribution of exposures at a given future date. Expected exposure is also a forward-looking measure and is used in calculating the expected loss for a portfolio.

• Expected Positive Exposure (EPE): EPE is the weighted average of expected exposures over time. It is a key measure used in the calculation of regulatory capital requirements under frameworks like Basel. EPE provides a single value that represents the average expected exposure over the life of a portfolio.

Topic 2. CCR Treatment

• As a Credit Risk:

  • Historically, managed at inception, often through collateral arrangements.

  • This approach treats CCR as a default risk, focusing on the potential for a counterparty to fail to meet its obligations.

  • Because it doesn't actively manage the risk after a trade is set up, it exposes the institution to unexpected changes in Credit Valuation Adjustment (CVA).

  • It is critical to include the CVA when valuing a derivatives portfolio to avoid large, sudden swings in market value.

• As a Market Risk:

  • This allows an institution to actively hedge against market risk losses associated with CCR.

  • However, it leaves the institution exposed to declines in the counterparty's creditworthiness and the ultimate risk of default.

  • This risk can be managed by actively replacing contracts with counterparties whose credit quality is deteriorating, rather than waiting for a default event to occur. This is done by buying new positions in proportion to the counterparty's probability of default.

• The Duality of Risk:

  • It is prudent for financial institutions to treat CCR as both a credit risk and a market risk.

  • However, this approach can be complex to manage and interpret due to the large variety of measurements involved (e.g., current exposure, expected exposure, CVA, VaR of CVA).

Practice Questions: Q1

Q1. Which of the following exposure measures reflects the average distribution of exposures at a specific future date prior to the maturity of the longest maturity transaction within a netting set?
A. Peak exposure.
B. Current exposure.
C. Expected exposure.
D. Expected positive exposure.

Practice Questions: Q1 Answer

Explanation: C is correct.

Expected exposure measures the mean distribution of exposures at a given future date prior to the maturity of the longest maturity exposure in the netting group.

Practice Questions: Q2

Q2. Is the following statement on the treatment of counterparty credit risk (CCR) correct?
“Treating CCR as a market risk does not allow an institution to hedge market risk losses, and it exposes the institution to declines in counterparty creditworthiness and default.”
A. The statement is correct with regard to both hedging market risk losses and counterparty creditworthiness and default.
B. The statement is incorrect with regard to both hedging market risk losses and counterparty creditworthiness and default.
C. The statement is correct with regard to hedging market risk losses only.
D. The statement is correct with regard to counterparty creditworthiness and default only.

Practice Questions: Q2 Answer

Explanation: D is correct.

Treating CCR as a market risk allows an institution to hedge market risk losses; however, it leaves the institution exposed to declines in counterparty credit worthiness and default. CCR can be hedged by the ongoing replacement of contracts with a counterparty instead of waiting for default to occur.

Module 2. Stress Testing

Topic 1. Stress Testing Current Exposure

Topic 2. Stress Testing Expected Loss

Topic 3. Stress Testing Credit Valuation Adjustment (CVA)

Topic 4. Stress Testing Debt Value Adjustment (DVA)

Topic 5. Shortcomings of Stress Testing CCR

Topic 1. Stress Testing Current Exposure

• Process: This involves repricing portfolios under a specific scenario of risk-factor changes, such as an instantaneous $25\%$ decline in the equity market or a sharp rise in interest rates. The goal is to see how the market value of each transaction changes under these stressed conditions.

• Purpose: The primary purpose is to identify which counterparties are most vulnerable to a particular market event. It helps risk managers understand the immediate impact of a market shock on their current exposures.

• Shortcomings:

  • Aggregation is challenging: Simply summing the current exposures across all counterparties under a stressed scenario is not meaningful. This is because the calculation assumes that all defaults happen simultaneously and does not take into account the unique credit quality of each counterparty. A more nuanced approach is required.

  • Limited information: Stress testing current exposure provides a static, one-time view. It does not provide information about how exposure might evolve over the life of the trade, which can lead to significant errors, especially for transactions that are "at-the-money" (where the current market value is close to zero).

• Does not address Wrong-Way Risk: This type of stress testing fails to capture "Wrong-Way Risk," which is a critical element of CCR. This is the risk that a counterparty's exposure to the institution increases at the same time as the counterparty's probability of default. For example, a sharp drop in equity prices might increase a bank's exposure to a hedge fund while simultaneously increasing the fund's likelihood of default.

• Linearity issues: The linearization of delta sensitivities in models can lead to significant errors, as CCR is inherently a non-linear relationship.

Topic 2. Stress Testing Expected Loss

• Loan Portfolios:

  • Expected Loss (EL) is a function of three main components: Probability of Default (       ) Exposure at Default (          ) , and Loss Given Default (           ). This formula is used to calculate the expected loss for each loan in the portfolio and then summed to get the total portfolio EL.

  •  

• Stressed EL (          ) To calculate the stressed expected loss, a firm stresses key macroeconomic variables (like unemployment rates or GDP) which in turn affect the probability of default ($PD$). This is represented by
•  

• Stress Loss: The actual stress loss is the difference between the stressed expected loss (        )  and the current expected loss ($EL$). This provides a measure of how much additional loss the portfolio is expected to incur under the stressed scenario.

• Derivatives Portfolios:

  • For derivatives, the concept is similar to loans, but the exposure is not fixed. Instead, Exposure at Default ($EAD$) is replaced with Expected Positive Exposure (          )  multiplied by an alpha factor (    ). The alpha factor is a regulatory constant that is set to a specific value to account for the potential for exposure to increase over the life of the derivative.

  •  

• Stressed EL (        ): In this case, the stresses are applied to both the Probability of Default ($PD$) and the Expected Positive Exposure ($EPE$), as both are sensitive to changes in market conditions. This is represented by          and
•  

Topic 3. Stress Testing Credit Valuation Adjustment (CVA)

• What is CVA?: The market value of counterparty credit risk. It represents the loss in a portfolio's market value due to a counterparty's default. CVA is a crucial adjustment to the value of a derivatives portfolio, reflecting the potential for a counterparty to default on its obligations.

• Formula: The formula for CVA is the sum of the discounted expected exposures, weighted by the probability of default and the loss given default.

  •  

• Where:
  •            is the Loss Given Default for a specific counterparty.
  •                is the Expected Positive Exposure for a specific counterparty at time
  •                   is the Probability of Default for a specific counterparty between time         and

• Stress Loss on CVA: The stress loss is calculated by subtracting the current CVA from the stressed CVA. This provides a clear measure of the potential losses on CVA that the firm could face in an adverse market scenario.
• CVA as a market risk: CVA can be seen as a market risk because it can be hedged by using a credit default swap (CDS) on the counterparty. The change in CVA can be a significant source of profit and loss for a firm.

Topic 4. Stress Testing Debt Value Adjustment (DVA)

• What is DVA?: The Debt Value Adjustment (DVA) is the value of the financial institution's option to default to its counterparty. It is a credit valuation adjustment that reflects the change in the value of the institution's own debt due to changes in its creditworthiness. When the institution's credit spread widens, its debt becomes less valuable, and DVA increases, which is a gain. DVA is a component of Bilateral CVA (BCVA).

• BCVA vs. CVA:

  • Bilateral CVA (BCVA) is a more comprehensive measure of counterparty risk than CVA alone.

  • BCVA incorporates the Expected Negative Exposure (ENE) from the counterparty's perspective. ENE is the amount the counterparty is exposed to the financial institution.

  • BCVA also includes the probability of the counterparty's survival, which is dependent on credit default swap spreads. The losses, on the other hand, depend on the institution's own credit spread.

• Benefit: Stress testing DVA allows CCR to be treated as a market risk, which enables consistent inclusion in market risk stress tests. This is particularly important for firms that actively manage their own credit risk. The stress loss on DVA is calculated by subtracting the value of the current BCVA from the stressed BCVA.

Topic 5. Shortcomings of Stress Testing CCR

• Lack of Aggregation: A major shortcoming is that stress tests for counterparty credit risk are often performed in isolation. They are not aggregated with stress tests for other types of risks, such as those related to a firm's loan portfolio or trading positions. This makes it difficult to get a holistic view of the firm's total risk exposure under a given scenario.

• Suboptimal Exposure Measure: The use of current exposure as a basis for stress testing is not optimal and can lead to significant errors. Instead, institutions should be using forward-looking measures like expected exposure or expected positive exposure. For derivatives, especially those that are "at-the-money" (where the current market value is close to zero), the current exposure is a poor measure of future risk. In a stressed scenario, the market value can change dramatically, leading to a significant exposure that is missed by a stress test based on current exposure.

• Model Limitations: Many models used for stress testing rely on the linearization of delta sensitivities to approximate changes in the value of derivatives. This is a significant oversimplification. Counterparty credit risk is inherently non-linear, and these models can lead to significant errors, particularly in stressed market conditions where large price movements are common. The actual exposure can be much higher than what the model predicts.

Practice Questions: Q1

Q1. An analyst notes that stress testing current exposure is problematic because aggregating results is typically not meaningful, although it is easy to account for the credit quality of the counterparty.
Are the analyst’s statements correct?
A. The analyst is correct with regard to both aggregating results and credit quality.
B. The analyst is correct with regard to aggregating results only.
C. The analyst is correct with regard to credit quality only.
D. The analyst is incorrect with regard to both aggregating results and credit quality.

Practice Questions: Q1 Answer

Explanation: B is correct.

The analyst is correct to state that aggregating stress results is not meaningful. Simply taking the sum of all exposures only considers the loss that would occur if all counterparties were to simultaneously default. This is an unlikely scenario. The analyst’s statement on credit quality of the counterparty is incorrect since stresses do not factor in the credit quality of the counterparty.

Practice Questions: Q2

Q2. Which of the following statements best reflects the reason why a financial institution does not need to consider aggregating stresses to the expected positive exposure (EPE) with its loan portfolio?
A. Loans are not sensitive to market variables.
B. Stresses to EPE are not sensitive to market variables.
C. The EPE and the loan portfolio are negatively correlated.
D. The EPE and the loan portfolio are positively correlated.

Practice Questions: Q2 Answer

Explanation: A is correct.

A financial institution does not need to consider aggregating stresses to the EPE with its loan portfolio, because loans are not sensitive to market variables and, therefore, will not have any exposure changes from changes in market variables.

Practice Questions: Q3

Q3. Is the following statement on bilateral credit valuation adjustment (BCVA) correct?

“The formula for BCVA is similar to the formula for CVA, except that the BCVA formula uses expected positive exposure (EPE) and it incorporates the probability of the counterparty’s survival.”
A. The statement is correct with regard to both EPE and probability of survival.
B. The statement is correct with regard to EPE only.
C. The statement is correct with regard to probability of survival only.
D. The statement is incorrect with regard to both EPE and probability of survival.

Practice Questions: Q3 Answer

Explanation: C is correct.

The BCVA formula differs from the CVA formula in that BCVA incorporates expected negative exposure (ENE), and the probability of the counterparty’s survival must be included in the BCVA formula.