Outline why stress testing is used as a risk management tool.
The idea
Stress testing asks what a portfolio or institution would lose if a specified extreme but plausible event occurred. It is used because VaR and expected shortfall, however carefully built, rest on recent history and a chosen confidence level. VaR says nothing about how bad losses are beyond the cutoff, and a calm sample period can understate the risk of rare events. Stress tests are forward looking, can examine exposures with little data, reveal concentrations and hidden correlations, show whether capital and liquidity would survive a crisis, and force managers to think about what could go wrong. They also support limit setting, risk appetite and contingency planning. The usual mistake is to treat a stress loss as a probability-weighted number. Scenarios normally carry no probability, so stress testing complements VaR rather than replacing it.
A practice question
Which statement best explains why risk managers use stress testing alongside VaR?
- It shows the effect of extreme but plausible events that VaR, which depends on a confidence level and recent data, does not fully capture. - correct
- It replaces VaR, because VaR cannot be computed reliably for portfolios that hold many different asset classes, so scenario losses are used for all capital purposes.Why not: VaR can be computed for multi-asset portfolios; stress testing supplements it rather than replacing it.
- It assigns a precise probability to each scenario so that stress losses can be weighted and added to VaR.Why not: Stress scenarios normally carry no probability, so their losses cannot be probability-weighted into VaR.
- It removes model risk because scenario losses do not depend on any assumptions about how risk factors behave.Why not: Stress tests rely on assumptions about shocks and relationships, so they carry model risk of their own.
VaR reports a loss level exceeded with small probability under conditions resembling the sample. Stress tests deliberately examine severe conditions beyond that cutoff, so the two measures answer different questions and are used together.
A harder one
A bank estimates its VaR from the most recent 12 months of data, a period of unusually low volatility. Which is the best argument for adding stress testing?
- A calm sample makes VaR too high, so stress tests are needed to scale the VaR figure back down.Why not: Calm data push VaR down, not up; the concern is understatement of risk.
- Stress tests are cheaper than VaR to run, so they can replace VaR for daily limit monitoring.Why not: Cost is not the reason for stress testing, and stress tests do not replace daily VaR limits.
- A calm sample can understate the risk of rare events, and stress tests examine conditions the sample did not contain. - correct
- Stress tests supply the probability of the crisis, which lets risk managers adjust the VaR confidence level to match how often crises actually occur.Why not: Stress scenarios do not provide probabilities and cannot be used to recalibrate the VaR confidence level.
VaR is only as informative as the data behind it. A calm year contains no crisis, so the VaR is low; stress testing replays or imagines severe conditions to show what that calm number hides.
The hardest tier
A bank has a 99% 10-day VaR of USD 12 million. A hypothetical scenario produces a loss of USD 85 million on the same portfolio, and a colleague says the scenario loss being about seven times the VaR proves the VaR model is wrong. Which response is best?
- The measures answer different questions: the scenario loss shows exposure to a severe event and should be weighed against capital and risk appetite. - correct
- The ratio shows the VaR model is misspecified, so VaR should be multiplied by about seven to match the scenario loss, which then becomes the true measure of risk.Why not: A scenario loss is not an observation of the VaR model failing; scaling VaR by the ratio has no statistical basis.
- Because scenarios carry no probability, the USD 85 million loss can safely be disregarded in decisions.Why not: Absence of a probability does not make a scenario irrelevant; stress losses inform capital, limits and contingency plans.
- The scenario loss is the maximum loss the portfolio can ever suffer, so it should replace VaR as the limit measure.Why not: A scenario is one severe case, not an upper bound on all possible losses, and it does not replace VaR for limits.
VaR is a loss exceeded with 1% probability under typical conditions over 10 days. A scenario loss is conditional on a chosen severe event. A large ratio is information about tail exposure and is judged against capital and risk appetite.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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