Risk Management
Risk Management tests whether you can identify, measure, and control exposures across market, credit, liquidity, and operational risk. Expect value at risk (VaR), expected shortfall, stress testing, duration and convexity, hedging with derivatives, counterparty risk, and the limits of statistical models.
Core rules and concepts
- Market risk arises from prices, rates, FX, and volatility. Credit risk is default or downgrade risk. Liquidity risk includes funding liquidity and market liquidity. Operational risk covers process, people, systems, and external events.
- VaR estimates the loss threshold not expected to be exceeded at a confidence level over a horizon. It says nothing about the size of losses beyond that threshold.
- Expected shortfall (CVaR) is the average loss conditional on exceeding VaR; it is more sensitive to tail risk.
- Parametric VaR for a single position = value x z x volatility x square root of horizon. Scaling by square root of time assumes independent, identically distributed returns.
- Stress testing applies plausible severe scenarios, including correlation breakdown and liquidity discounts. It complements VaR rather than replacing it.
- Hedging: duration and convexity manage rate risk; beta and index futures manage equity risk; forwards and options manage FX and commodity risk. Basis risk remains when the hedge is not identical to the exposure.
Worked example
A $2 million portfolio has a daily volatility of 1.2%. At 95% confidence, z = 1.645. One-day parametric VaR = $2,000,000 x 1.645 x 0.012 = $39,480. This means that under the model, a loss greater than $39,480 is expected on about 5% of days. For a 10-day horizon, assuming independent returns, VaR = $39,480 x square root of 10 = $124,846. If the portfolio is less liquid and cannot be exited within one day, a 10-day liquidity horizon is more appropriate than a one-day horizon. A stress test might instead assume volatility doubles and correlations rise, producing a much larger loss than the parametric VaR.
Traps that cost marks
Do not describe VaR as the maximum possible loss. Do not confuse the confidence level with the loss probability: 95% VaR uses a 5% tail. Do not scale VaR by 10; scale by the square root of 10 under the independence assumption. Do not ignore basis risk, counterparty risk, or liquidity horizons. Do not treat a model backtest exception as proof that the model is useless; investigate the cause.