### Stress Testing and other Risk Management Tools

After completing this reading, you should be able to:

• Describe the relationship between stress testing and other risk measures, particularly in enterprise-wide stress testing.
• Describe the various approaches to using VaR models in stress tests.
• Explain the importance of stressed inputs and their importance in stressed VaR.

## The Relationship between Stress Testing and Other Risk measures

Stress testing plays a large role in the assessment of banks’ capital adequacy as a result of the 2007-2009 financial crisis. However, banks continue to use other risk-management tools such as VaR in conjunction with stress testing.

### Similarities between Enterprise-wide stress-testing and Economic Capital/VaR

• Both stress testing and EC-VaR are used by financial institutions for purposes of risk management.
• For both enterprise-wide stress tests and VaR, the inputs used are scenarios and data. Both involve the translation of scenarios into loss estimates.

### Differences

• While stress test losses take an accounting view, EC losses take a market view.
• While stress tests examine a long period, typically spanning several years, EC models focus on losses at a given point in time, say, the loss in value at the end of year $$t$$.
• While stress testing largely doesn’t involve probabilities, EC models are founded on probabilities. For example, a 99.9% VaR can be viewed as a 1-in-1,000 event.
• Stress testing focuses on the conditional expected loss (EL) while EC-VaR measures the unconditional unexpected loss

#### Stress Testing

Measure of unexpected loss

Measure of expected loss

Typically unconditional or TTC (through-the-cycle)

Typically conditional or PIT (point-in-time)

Typically one-year horizon

Typically beyond one-year horizon

Typically doesn’t identify causal risks

Reveals the causal (underlying) risks

Economic value-based

Accounting-based

Corresponds to a specific probabilistic loss level, not a macroeconomic scenario

Corresponds to a macroeconomic scenario, not a specific probabilistic loss level

Focus on a very large number of scenarios

Focus on just a few scenarios

## Using VaR Models in Stress Tests

One of the approaches that have been used to incorporate stress tests in VaR models involves trying to assess whether the stress test loss is part of the loss distribution developed in the VaR/EC estimation. This way, a hypothetical/historical stress scenario can be associated with a given probability.

For example, suppose a scenario’s loss magnitude translates into a $${ 95 }^{ th }$$ percentile loss on the VaR loss distribution. In such a case, the $${ 95 }^{ th }$$ percentile loss in the EC model could be taken as an approximation to the stressed loss for market risk.

A different approach used to incorporate stress testing in VaR involves the use of stressed inputs. According to Basel market rules released in 2011, banks should calculate a stressed VaR based on the 10-day, 99th percentile, one-tailed confidence interval value-at-risk measure of the current portfolio with model inputs calibrated to historical data from a continuous 12-month period of significant financial stress relevant to the bank’s portfolio.

The goal is to replicate a VaR calculation that would be generated based on a bank’s current portfolio if the relevant market factors were to be subjected to stress.

The market risk framework also demands the incorporation of stress tests. Banks that use the internal models approach, in particular, are required to have a rigorous stress testing program in place. In the revisions to Basel Ill (BCBS 2011b), stressed parameters are required to determine the default risk capital charge for counterparty credit risk.

Stressed inputs are also important in the capital charge for credit valuation adjustment (CVA).

A risk metric with a stressed input is usually more conservative, meaning that the capital set aside is likely to be sufficient even if a shock/stress event occurs.

On the downside, however, such a risk metric loses its responsiveness to current market conditions. Instead, the metric primarily depends on portfolio composition.

## Questions

### Question 1

Hardik and Simriti compare and contrast stress testing with economic capital and value at risk measures. Which of the following statements regarding differences between the two types of risk measures is most accurate?

1. Stress tests tend to calculate losses from the perspective of the market, while EC/VaR methods compute losses based on an accounting point of view
2. While stress tests focus on unconditional scenarios, EC/VaR methods focus on conditional scenarios
3. While stress tests examine a long period, typically spanning several years, EC models focus on losses at a given point in time, say, the loss in value at the end of year $$t$$.
4. Stress tests tend to use cardinal probabilities while EC/VaR methods use ordinal arrangements

A is inaccurate. Stress tests tend to calculate losses from the perspective of accounting, while EC/VaR methods compute losses based on a market point of view.

B is inaccurate. While stress tests focus on conditional scenarios, EC/VaR methods focus on unconditional scenarios.

D is also inaccurate. Stress tests do not focus on probabilities. Instead, they focus on ordinal arrangements like “severe,” “more severe,” and “extremely severe.” EC/VaR methods, on the other hand, focus on cardinal probabilities. For instance, a 95% VaR loss could be interpreted as 5-in-100 events.

### Question 2

One of the approaches used to incorporate stress testing in VaR involves the use of stressed inputs. Which of the following statements most accurately represents a genuine disadvantage of relying on risk metrics that incorporate stressed inputs?

1. The metrics are usually more conservative (less aggressive)
2. The metrics are usually less conservative (more aggressive)
3. The capital set aside, as informed by the risk metrics, is likely to be insufficient
4. The risk metrics primarily depend on portfolio composition and are not responsive to emerging risks or current market conditions.