How does the EWMA volatility model work and how do I choose the lambda parameter?
I'm studying volatility estimation for FRM Part I. The EWMA model seems simpler than GARCH but I'm not sure how to apply it or what lambda value to use. Can someone walk through a numerical example and explain why RiskMetrics chose lambda = 0.94?
The Exponentially Weighted Moving Average (EWMA) model is the workhorse of practical volatility estimation, made famous by JP Morgan's RiskMetrics system. Let's break it down.
The EWMA Formula:
sigma_t^2 = lambda x sigma_{t-1}^2 + (1 - lambda) x r_{t-1}^2
Where:
- sigma_t^2 = today's variance estimate
- sigma_{t-1}^2 = yesterday's variance estimate
- r_{t-1} = yesterday's return
- lambda = decay factor (0 < lambda < 1)
What Lambda Controls:
Lambda determines how much weight goes to the recent observation vs. the historical average:
- lambda = 0.94 means 6% weight on yesterday's squared return, 94% on the prior variance estimate
- lambda = 0.80 means 20% on yesterday's return — much more reactive
- lambda = 0.99 means only 1% on yesterday — very sluggish
Worked Example — Falcon Asset Management:
Falcon's risk team estimates daily volatility for an equity index.
| Day | Return | Squared Return |
|---|---|---|
| t-2 | — | — |
| t-1 | -2.3% | 0.000529 |
| t | ? | ? |
Previous variance estimate: sigma_{t-1}^2 = 0.000324 (i.e., daily vol = 1.8%)
Using lambda = 0.94:
sigma_t^2 = 0.94 x 0.000324 + 0.06 x 0.000529
= 0.000305 + 0.0000317
= 0.000337
Daily vol = sqrt(0.000337) = 1.835%
The -2.3% shock bumped volatility from 1.80% to 1.835%. With lambda = 0.80, it would jump to 1.91% — much more responsive.
Why Lambda = 0.94?
RiskMetrics chose 0.94 for daily data through backtesting across asset classes. The effective window is approximately 1/(1-lambda) = 1/0.06 = 16.7 days. For monthly data, they used lambda = 0.97 (effective window ~33 months). The choice balances:
- Responsiveness to regime changes (lower lambda)
- Stability to avoid overreacting to noise (higher lambda)
EWMA vs. GARCH(1,1):
| Feature | EWMA | GARCH(1,1) |
|---|---|---|
| Parameters | 1 (lambda) | 3 (omega, alpha, beta) |
| Mean reversion | No | Yes (long-run variance) |
| Simplicity | Very simple | Requires MLE estimation |
| RiskMetrics default | lambda = 0.94 | N/A |
The critical difference: EWMA has no mean reversion. After a volatility spike, EWMA decays slowly but never reverts to a long-run level. GARCH does, through the omega term.
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