Market Risk Measurement and Management
Market Risk Measurement and Management asks you to quantify loss from adverse price moves and to judge whether the number is trustworthy. Core topics are VaR under parametric, historical-simulation, and Monte Carlo approaches; expected shortfall; volatility forecasting; backtesting; and stress testing.
Core rules
- VaR is the loss not exceeded with probability c over horizon T; it says nothing about the severity of losses beyond the threshold.
- Parametric (delta-normal): VaR = z × σ × portfolio value; scale by √T only under i.i.d. returns.
- Historical simulation reuses the empirical distribution; it cannot produce a loss larger than the worst in the sample and adapts slowly to new volatility.
- Expected shortfall (average loss beyond VaR) is coherent and subadditive; VaR is not subadditive.
- Basel backtesting counts exceptions over 250 days at 99%: green 0–4, yellow 5–9, red 10 or more; the multiplier is 3 plus a plus factor in the yellow and red zones.
- EWMA and GARCH capture volatility clustering; correlations rise in stress, shrinking diversification benefits.
Worked example
A USD 10 million portfolio has daily volatility of 1.2%. At 99%, z = 2.326. 1-day VaR = 10,000,000 × 2.326 × 0.012 = USD 279,120. 10-day VaR = 279,120 × √10 ≈ USD 882,700. If the loss distribution has fat tails, the true 99% quantile exceeds this normal-based figure, so parametric VaR understates tail risk.
Traps
- Scaling by √10 when returns are autocorrelated or volatility is time-varying.
- Presenting VaR as a maximum possible loss.
- Using a normal z for portfolios with short options, where delta-normal misstates non-linear payoffs.
- Forgetting that backtesting requires a consistent P&L series and the 99%/1-day Basel standard.