Risk Measurement and Quantification
Building blocks
Quantification converts risk into distributions of loss. Candidates must understand exposure, probability, severity, expected loss, unexpected loss, and confidence levels. Expected loss is probability times exposure times loss given default in credit settings; unexpected loss is the dispersion around that mean and drives capital. Value at risk (VaR) states a loss threshold not exceeded with a given confidence over a horizon; expected shortfall (ES) is the average loss beyond VaR and is more sensitive to tail events.
Key traps
- VaR says nothing about the size of losses beyond the threshold; it is not sub-additive in general.
- Diversification assumptions break down in stress conditions when correlations rise.
- Model output is not truth: backtesting, validation, and documented assumptions are essential.
- Correlated inputs must be handled with care; multiplying independent probabilities is a classic error.
Stress testing and scenarios
Stress tests apply severe but plausible scenarios, including historical and hypothetical ones, and are used alongside statistical models because tails are under-sampled.
Worked rule of thumb
A portfolio has a 99% one-day VaR of 5 million. This means that on roughly one trading day in a hundred, losses are expected to exceed 5 million; it does not cap the loss at 5 million. If expected shortfall at the same confidence is 12 million, the average loss on those breach days is about 12 million. When a question asks which measure better captures tail severity, expected shortfall is the answer.