Market Risk
Core Concepts
Market risk is the risk of loss from movements in market prices: interest rates, equity prices, FX rates, and commodity prices. Candidates must know value at risk (VaR) and its limitations: it is a quantile measure, says nothing about tail losses beyond the confidence level, and can be gamed. Expected shortfall (ES) measures average loss beyond VaR. Stress testing and scenario analysis complement VaR. Greeks measure sensitivity: delta (price), gamma (delta change), vega (volatility), theta (time), rho (interest rate). Backtesting compares VaR to actual losses. Model risk arises from incorrect assumptions. Liquidity risk can amplify market risk.
Traps in Questions
- Assuming VaR captures tail risk; it does not.
- Confusing 99% VaR with 1% probability of loss; it is the loss threshold.
- Forgetting that VaR is not sub-additive; ES is coherent.
- Overlooking that historical simulation assumes the past represents the future.
Worked Example
A portfolio has 1-day 99% VaR of $1 million. This means there is a 1% chance the loss exceeds $1 million in one day. If the firm holds $50 million capital, the VaR is 2% of capital. A stress test might show a $10 million loss in a severe scenario, revealing tail risk beyond VaR.
Rule of thumb: VaR tells you the minimum loss in the worst x% of cases; ES tells you the average of those worst losses.