EWMA and RiskMetrics [/ˈewma ənd ˈriskmetriks/] n - An exponentially weighted moving average is a one-parameter contrivance for granting recent observations the greater voice. Recent days govern the estimate, while older ones fade like writing on a palimpsest:

EWMA weight decay

The recursion is:

$${\hat{\sigma }}_t^2=\lambda {\hat{\sigma }}_{t-1}^2+(1-\lambda )r_{t-1}^2$$

$\lambda$ is the decay factor, commonly close to one. A value of 0.94 implies a half-life of roughly eleven days. A smaller $\lambda$ renders the estimate more responsive to recent events; a larger one makes it smoother.

RiskMetrics made EWMA famous for the management of risk. A portfolio covariance matrix may be updated in the same manner:

$${\hat{\Sigma }}_t=\lambda {\hat{\Sigma }}_{t-1}+(1-\lambda )r_{t-1}{r}_{t-1}^T$$

The matrix update is swift and asks for no optimization, which commends EWMA for high-dimensional portfolios where fitting a full GARCH model would prove slow or unstable.

The defect is rigidity. EWMA knows no mean reversion; after a volatility spike, the forecast decays exponentially toward the long-run average at a fixed pace. GARCH adds a long-run variance target and can reckon more truly over longer horizons. See Volatility Modeling with GARCH for the comparison.

EWMA also weighs positive and negative shocks alike. In equities, a large negative return commonly raises future volatility more than a positive return of equal size, so a desk concerned with downside risk may find EWMA understating the left tail.

The decay parameter should be chosen for the horizon, not for the modeler’s intuition; a one-day risk forecast and a one-month risk forecast want different lambdas. Walk-forward testing is the only honest way to choose. In practice, a decay factor of 0.94 for daily variance endures as a starting point because it works, not because it is optimal.