Risk Measurement and Quantification
Core measures
Quantification converts exposures into comparable numbers. Candidates must understand value at risk (VaR) and its limitations: VaR states a loss threshold not exceeded with a given confidence over a horizon, but says nothing about the size of losses beyond it. Expected shortfall (CVaR) addresses tail severity and is preferred under modern standards. Know stress testing and scenario analysis as complements to statistical models, and backtesting as validation of model performance.
Credit and operational measurement
Credit measures include probability of default (PD), loss given default (LGD), exposure at default (EAD), and expected loss = PD × LGD × EAD. Unexpected loss relates to the tail of the loss distribution and drives capital. Operational risk is often measured with loss distribution approaches (frequency and severity) or scenario-based capital. Traps: confusing expected loss (priced into margin) with unexpected loss (covered by capital); assuming diversification benefits in stress; treating model output as truth.
Model risk and assumptions
Every measure embeds assumptions - historical correlations, distributional form, liquidity horizons. Model risk arises from bad data, flawed design, or misuse. Questions often test that models require independent validation, documentation, ongoing monitoring, and governance approval, and that a model's sophistication does not eliminate judgment.
Worked example and rule of thumb
A portfolio has a one-day 99% VaR of 10 million. This means roughly one day in a hundred should exceed 10 million, but not how much. If expected shortfall at the same confidence is 18 million, tail losses average 18 million when VaR is breached. Rule of thumb: report VaR with stress and expected shortfall, and always state confidence, horizon, and portfolio scope - mismatched parameters are the most common exam trap.