Market Risk: Sensitivities, VaR, and Stress Testing
Core concepts
Market risk arises from movements in prices, rates, spreads, and volatilities. Candidates must understand sensitivity measures: duration and convexity for rates, delta, gamma, vega, and theta for options, and DV01. Know the Value-at-Risk (VaR) framework: confidence level, horizon, and the three main methods-historical simulation, variance-covariance (parametric), and Monte Carlo. Be clear on VaR's limitations: it says nothing about the size of losses beyond the threshold, and it is not sub-additive for all methods. Understand Expected Shortfall (ES), which averages losses beyond the VaR threshold and is coherent. Know backtesting (exceptions, Kupiec-style tests), stress testing, and scenario analysis. Also cover basis risk, volatility risk, and the difference between trading book and banking book treatment.
Traps to watch
A classic trap is interpreting a 99%, one-day VaR of $1 million as "maximum loss." It means losses exceed $1 million on about 1% of days-nothing about severity. Another: parametric VaR assumes normality and understates tail risk; historical simulation depends heavily on the sample window. Watch for questions confusing diversification benefits with guaranteed reduction-correlations can break down in stress. Also distinguish delta (first-order) from gamma (second-order convexity) effects, and remember vega measures sensitivity to implied volatility, not realized volatility.
Worked rule of thumb
For a $50 million position with daily volatility of 1.5%, parametric 99% one-day VaR ≈ 50,000,000 × 1.5% × 2.33 ≈ $1.75 million. The 2.33 multiplier is the one-tailed normal z-score at 99%. If a candidate answer ignores the z-score (giving $750,000), it has confused volatility with VaR.