Risk Measurement Techniques (VaR, Stress Testing, Scenario Analysis)
What the exam tests
This domain tests the construction, interpretation, and limitations of VaR, expected shortfall, stress testing, and scenario analysis. Expect questions on confidence levels, horizons, backtesting, and the difference between probabilistic and stress measures.
Core rules and concepts
- VaR estimates the loss that will not be exceeded with a given probability over a given horizon. A 95% one-day VaR of PKR 4 million means a 5% chance of losing more than PKR 4 million in one day, assuming the model is correct.
- Parametric VaR uses a normal distribution: VaR = z × volatility × portfolio value.
- Historical simulation revalues the portfolio under past market moves; Monte Carlo simulation generates many scenarios.
- Expected shortfall averages losses beyond the VaR threshold and captures tail severity better than VaR.
- Stress testing applies severe but plausible shocks; scenario analysis examines a coherent set of events. Neither assigns probabilities in the same way as VaR.
- Backtesting compares actual losses with VaR predictions and counts exceptions.
Worked example
A portfolio is worth PKR 200 million with daily volatility 1.2%. For 95% one-day parametric VaR, z = 1.645. VaR = 1.645 × 0.012 × 200 million = PKR 3.948 million. The reasoning: the calculation assumes normally distributed returns and a one-day horizon. If the portfolio has fat tails or illiquid positions, this VaR may understate tail risk; stress testing and expected shortfall should supplement it.
Traps that cost marks
Do not call VaR the maximum loss. Do not compare VaRs with different confidence levels or horizons. Do not scale one-day VaR to ten days by multiplying by 10; under the square-root-of-time rule, multiply by the square root of 10. Do not assume normality for options or illiquid assets. Do not treat a stress scenario as a probability forecast.