Kuantile
Advanced Risk Measurement: Expected Shortfall, VaR Backtesting, EWMA and EVT
VaR is a clean boundary line that tells you how much is at risk; but it leaves two important questions unanswered: how much do I lose when the boundary is crossed, and how do I know the model actually works? The model table in Kuantile's "Advanced risk analysis" section answers exactly these two questions. This article explains every row.
Expected Shortfall: looking beyond the line
99% VaR says "on 99 out of 100 days your loss won't exceed this figure" — it says nothing about the one day it does. Expected Shortfall (ES, also CVaR) measures the average loss on those bad days. The Basel FRTB banking framework moved capital calculations from VaR to 97.5% ES in 2019, precisely because ES sees the tail and VaR does not. In fat-tailed markets like Borsa Istanbul and crypto, the gap between ES and VaR is not cosmetic: the wider it is, the more your bad day looks like a cliff rather than a step.
VaR backtesting: putting the model on trial
Publishing a risk number without ever measuring its accuracy is like selling scales you never calibrate. A backtest asks, for each of the last 250 trading days: "what would VaR have said that morning?" and compares it with the realized return. A loss beyond the VaR line is a violation. At 99% confidence you expect about 2.5 violations in 250 days.
- Kupiec POF test: is the violation count consistent with expectations? Eight violations in 250 days means the model understates risk; the p-value tells you whether that can be chance.
- Christoffersen test: do violations cluster? This is the critical one: four violations spread over a year is fine; four in the same crisis week means the model reacts too slowly to regime change.
- Basel traffic light: the regulators' summary — for 99% VaR over 250 days, 0-4 violations is green, 5-9 yellow, 10+ red. Kuantile shows this badge under the model table.
EWMA: catching regime shifts early
Equal-weighted historical simulation has a weakness: yesterday's shock and a calm day ten months ago carry the same weight, so after a regime change the model keeps describing the old world for weeks. RiskMetrics EWMA volatility fixes this: each day's influence decays exponentially with λ=0.94, so recent weeks dominate. When EWMA VaR rises while historical VaR stands still, the market is hardening and the long window just hasn't noticed yet.
FHS: the best of both worlds
Parametric EWMA VaR assumes normality — dangerous in fat-tailed markets. Filtered Historical Simulation is the elegant middle path: past returns are standardized by that day's volatility, then rescaled by today's. The shape of the empirical distribution (skew, fat tails) is preserved while the level adapts to the current regime. It is arguably the highest value-per-effort statistical upgrade available.
EVT: 99.5% and beyond
At extreme confidence levels historical simulation collapses for lack of data — the worst 0.5% of a 1,000-day sample is five observations. Extreme Value Theory fits a Generalized Pareto distribution to losses beyond the 95% threshold, modeling the tail parametrically. The tail index ξ is informative on its own: the larger it is, the fatter the tail; Turkish assets typically show a visibly higher ξ than developed-market indices.
How to read the table
Five models look at the same portfolio from five angles. If they agree, the regime is calm. EWMA/FHS clearly above historical means the market is hardening; a wide ES-VaR gap means fat tails; a yellow or red backtest means treat all numbers with caution. Disagreement between models is not a flaw — it is a signal.
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