Market risk measurement and management
Market risk measurement and management
This domain tests the measurement of losses from movements in prices, rates, volatilities and correlations, and the use of limits, hedging and stress testing to manage them. Expect calculations using VaR, duration, DV01 and beta, plus questions on backtesting and the limitations of models.
Core rules and concepts
- VaR estimates the loss that will not be exceeded with a given confidence over a given horizon. It says nothing about the size of losses beyond the threshold.
- Three common methods: variance-covariance assumes normal returns and linear exposures; historical simulation reuses actual past shocks; Monte Carlo simulates distributions and handles non-linearity but is computationally heavy.
- Expected shortfall (ES) is the average loss in the tail beyond VaR and is more coherent for fat-tailed portfolios.
- Sensitivities: delta measures linear price sensitivity, gamma measures curvature, vega measures volatility sensitivity, theta measures time decay; DV01 is the value change for a one-basis-point yield move; modified duration approximates bond price sensitivity.
- Backtesting compares VaR exceptions with the stated confidence level; too many exceptions triggers model review, higher capital or reduced limits.
Worked example
A $10 million portfolio has annual volatility of 20%. For a 95% one-day parametric VaR, daily volatility is 0.20 divided by the square root of 252, about 1.26%. The 95% normal multiplier is 1.645, so VaR is $10m x 1.645 x 0.0126, approximately $207,000. If the bank instead holds a bond position of $50 million with modified duration 5 and yields rise 50 basis points, the approximate loss is $50m x 5 x 0.005 = $1.25 million. The reasoning shows why duration-based measures are local approximations and become less reliable for large yield moves or convex instruments.
Traps that cost marks
- Calling VaR a worst-case loss; it is a threshold, and tail losses can be far larger.
- Scaling VaR by the square root of time without checking that returns are independent and identically distributed.
- Mixing confidence levels or horizons in one comparison, or ignoring that 99% VaR is not directly comparable with 95% VaR.
- Assuming historical simulation captures new regimes; it cannot generate shocks absent from the sample.
- Hedging with futures or swaps removes price risk but creates basis, counterparty and liquidity risk.