Compare how stressed VaR and stressed ES are determined with the way traditional VaR and ES are determined, describing the advantages and disadvantages of the stressed measures.
The idea
Traditional VaR and ES are computed on recent market data, for example the latest one to four years, applied to the current portfolio, so they move with current conditions. Stressed VaR and stressed ES use the same method and the current portfolio. They take their market data from a fixed historical window of significant stress, such as one year of crisis data chosen for its relevance to the portfolio. Under Basel 2.5, capital is the larger of the previous day's VaR and a multiplier (at least 3) times the 60-day average 10-day 99% VaR, plus the same construction for stressed VaR. The advantage is that stressed measures stop capital falling in calm markets and reduce procyclicality. The disadvantages are that the window is subjective, it is backward looking, new risk factors lack history, and it cannot be backtested like ordinary VaR.
Formulas
Basel 2.5 VaR plus stressed VaR capital
capital = max(VaRₜ₋₁, mc × VaRavg) + max(sVaRₜ₋₁, ms × sVaRavg)
- VaRₜ₋₁
- the previous day's 10-day 99% VaR
- VaRavg
- the 60-day average of that VaR
- sVaRₜ₋₁
- the previous day's 10-day 99% stressed VaR
- sVaRavg
- the 60-day average of the stressed VaR
- mc
- the VaR multiplier, at least 3
- ms
- the stressed VaR multiplier, at least 3
Each component is a maximum, then the two are added. With 1-day figures, scale to 10 days by √10 first.
A practice question
How does stressed VaR differ from traditional VaR under the usual regulatory approach?
- It uses recent market data but a confidence level of 99.9% instead of 99%.Why not: Stressed VaR changes the data period, not the confidence level.
- It uses hypothetical scenarios written by management rather than historical data.Why not: Stressed VaR is still based on historical data, from a stress window, not management-written scenarios.
- Same method and current portfolio, but market data from a historical period of significant stress instead of the recent period. - correct
- It uses the same recent data as traditional VaR but a horizon of one year in place of 10 days, which is what makes the measure stressed under Basel 2.5.Why not: The horizon is not what differentiates stressed VaR; the data window is.
Traditional VaR is calibrated to current conditions using recent data. Stressed VaR applies the same calculation to the current portfolio but with data from a stressed historical window.
A harder one
Under the Basel 2.5 market risk framework, capital for VaR is the larger of the previous day's 10-day 99% VaR and a multiplier times the 60-day average. The same applies to stressed VaR. A bank reports: VaR previous day USD 7.2 million, VaR 60-day average USD 8.0 million, stressed VaR previous day USD 19.0 million, stressed VaR 60-day average USD 17.5 million, and both multipliers equal 3. The total VaR and stressed VaR capital charge is closest to:
- USD 76.5 million - correct
- USD 78.6 millionWhy not: Applies the multiplier to the previous-day figures (3 x 7.2 + 3 x 19.0) instead of the 60-day averages.
- USD 27.0 millionWhy not: Ignores the multipliers and takes only the larger of previous day and average for each component.
- USD 52.5 millionWhy not: Counts only the stressed component (3 x 17.5) and omits the ordinary VaR component.
VaR component = max(7.2, 3 x 8.0) = 24.0. Stressed component = max(19.0, 3 x 17.5) = 52.5. Total = 24.0 + 52.5 = 76.5. Each component is a maximum of previous-day and multiplier times average.
The hardest tier
A bank's stressed VaR uses a 250-day window from a past financial crisis. The bank now holds large positions in a product that did not exist in that window. Which limitation of stressed VaR does this illustrate?
- Stressed VaR assumes losses are normally distributed, so fat tails in the new product are missed.Why not: Historical-window stressed VaR does not assume normality; the problem is the relevance and coverage of the data.
- Stressed VaR automatically falls when current markets are calm, so it would give the bank too little capital relative to its risks.Why not: Stressed VaR is anchored to a fixed stress window and does not fall when current markets are calm.
- A stressed measure is only as relevant as its window: factors with no history need proxies, and the next crisis may differ. - correct
- Stressed VaR cannot be computed for any portfolio that includes derivatives or structured products.Why not: It can be computed for derivatives portfolios using full revaluation; the issue is missing history for the new product.
Because stressed VaR replays a chosen past period, it inherits that period's limits: new products have no data and proxies must be used, and the choice of window is a judgement that may not match the next crisis.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
Start free →More in Stress Testing
- Outline why stress testing is used as a risk management tool.
- Describe where stress testing sits alongside other risk measures, especially when it is done enterprise-wide.
- Explain what must be weighed, and what proves difficult, when scenarios for stress testing are developed and stress testing models are built.
- Give an example of regulatory stress testing and describe what reverse stress testing is.
- Set out what the internal audit function, senior management and the board of directors each answer for when stress testing is governed.
- Outline how validation, independent review, and policies and procedures each feature in stress testing governance.
- Outline the Basel stress testing principles that apply to banks when they put stress testing into practice.