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VaR: Validation & Alternativesintermediate

Dynamic Versus Static VaR

A static VaR fixes its inputs once, using a long unweighted sample so that the volatility and correlation estimates barely move. A dynamic VaR instead updates its inputs over time so the risk number tracks current market conditions. The key input is volatility: dynamic VaR lets it rise in turbulent periods and fall in calm ones. A moving-average rolling window (drop the oldest observation, add the newest) is the simplest implementation, but it is only one option. Exponentially weighted moving average (EWMA, RiskMetrics) and GARCH are richer dynamic schemes that weight recent data more heavily and respond faster to volatility shocks.

Why it matters

Markets switch between calm and stormy regimes, so a risk number frozen on last year’s average is always fighting the last war. Dynamic VaR keeps re-reading the thermometer. The rolling window is the crude version: it forgets old data abruptly and so can lurch when a big day enters or leaves the window. EWMA and GARCH smooth this by fading older observations gradually, which is why they react more sensibly when volatility spikes. The principle is updating inputs, not any single windowing trick.

Formulas

Rolling-window variance (equal weights)
σ^t2=1W∑i=1Wrt−i2\hat\sigma_{t}^{2} = \frac{1}{W}\sum_{i=1}^{W} r_{t-i}^{2}
A simple moving average of the last WW squared returns. Every observation in the window gets equal weight $1/W$, and an extreme return jolts the estimate when it enters and again when it leaves, the "ghosting" effect.
EWMA variance (RiskMetrics)
σ^t2=λ σ^t−12+(1−λ) rt−12\hat\sigma_{t}^{2} = \lambda\,\hat\sigma_{t-1}^{2} + (1-\lambda)\,r_{t-1}^{2}
Weights decay geometrically with the smoothing parameter λ\lambda (RiskMetrics uses λ=0.94\lambda = 0.94 for daily data), so recent returns dominate and the estimate adjusts smoothly rather than ghosting.

Worked examples

Scenario

Volatility has been calm for a year, then a crisis erupts. Compare how a 250-day equal-weighted rolling VaR and an EWMA VaR react over the next week.

Solution

The EWMA estimate jumps within days because the large new squared returns receive weight (1−λ)(1-\lambda) each, lifting VaR quickly. The 250-day equal-weighted window dilutes the shock across 250 observations, so VaR rises sluggishly and understates risk during the most dangerous days. Both are dynamic, but the gradual EWMA decay tracks the regime change far better than the abrupt equal-weight window.

Common mistakes

  • ✗Dynamic VaR just means using a moving-average window. Updating inputs is the principle; the rolling window is one implementation, and EWMA or GARCH are usually better because they weight recent data more.
  • ✗A longer rolling window always gives a better VaR. A long equal-weighted window is stable but slow to react to volatility shifts, so it can badly understate risk just when conditions deteriorate.
  • ✗Static VaR is simply wrong. A static long-window VaR is stable and easy to backtest; it is appropriate when volatility is roughly constant, but it lags in changing regimes.
  • ✗The rolling window has no drawbacks. Equal weighting causes "ghosting": a single extreme return distorts VaR both when it enters the window and abruptly when it drops out.

Revision bullets

  • •Dynamic VaR updates its inputs (mainly volatility) over time
  • •Static VaR fixes inputs on a long, slow-moving sample
  • •Equal-weighted rolling window is the simplest dynamic scheme, not the only one
  • •EWMA and GARCH weight recent data more and react faster
  • •Equal weighting causes "ghosting" when extreme returns enter or leave

Quick check

What fundamentally distinguishes a dynamic VaR from a static VaR?

Compared with an equal-weighted rolling window, why does EWMA respond faster to a volatility spike?

Connected topics

VaR DefinitionVaR Time ScalingFat TailsGARCH VaR

Sources

  1. RiskMetrics (1996)
    J.P. Morgan / Reuters. RiskMetrics Technical Document. 4th ed. J.P. Morgan, 1996.
    Introduces the EWMA volatility model with the daily decay factor 0.94 used in dynamic VaR.
  2. Jorion (2007), Ch. 9
    Jorion, P. Value at Risk: The New Benchmark for Managing Financial Risk. 3rd ed. McGraw-Hill, 2007.
    Compares moving-average, EWMA, and GARCH approaches to time-varying volatility in VaR.
How to cite this page
Dr. Phil's Quant Lab. (2026). Dynamic Versus Static VaR. Derivatives Atlas. https://phucnguyenvan.com/concept/frm-dynamic-var
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