Market Risk Measurement and Management
Market Risk Measurement and Management
This domain tests whether you can choose the right VaR or ES method, compute a number, and explain why it understates or overstates risk. Expect one numeric VaR question and one interpretation question on backtesting exceptions or model limits.
Methods
- Parametric (variance-covariance): fast, assumes normal returns and linear payoffs; unreliable for options and fat tails.
- Historical simulation: full revaluation on empirical scenarios; captures fat tails present in the window, but is blind to unseen events and slow to react (ghosting).
- Monte Carlo: flexible distributions and path dependence; heavy model and computational cost.
VaR properties and ES
VaR is a quantile, not a coherent risk measure: it can violate subadditivity and says nothing about loss size beyond the threshold. Expected Shortfall, the average of losses beyond the quantile, is coherent. FRTB uses ES at 97.5% one-tail with liquidity horizons of 10, 20, 40, 60 and 120 days, calibrated to a stressed period, with non-modellable risk factors capitalised separately.
Backtesting
250 observations at 99% VaR. Basel traffic light: green 0-4 exceptions, yellow 5-9, red 10 or more, with a multiplier add-on scaling from 0 to 0.65 on top of the base 3.
Worked example
A $10m equity position, daily volatility 1.2%, 99% one-day parametric VaR = 10,000,000 x 2.326 x 0.012 = $279,120. Scaling to 10 days by the square root of 10 gives about $882,700, valid only under i.i.d. returns and a constant position. Two desks show standalone VaRs of $300k and $400k with correlation 0.3: portfolio VaR = square root of (300 squared + 400 squared + 2 x 0.3 x 300 x 400) = square root of 322,000, about $567k, below the $700k sum. That diversification benefit must be allocated back to desks if limits are set on standalone VaR.
Traps
- Multiplying VaR by 10 instead of the square root of 10.
- Adding VaRs arithmetically, or assuming diversification always survives a stress episode.
- Claiming VaR is subadditive or coherent.
- Quoting FRTB ES at 99% rather than 97.5%.
- Forgetting exceptions are counted out of 250 observations, not 100.