Exponentially Weighted Moving Average (EWMA): A Practical Guide

What Is EWMA?

The Exponentially Weighted Moving Average (EWMA) is a statistical method for calculating a weighted average of historical data points where more recent observations receive greater weight than older ones. In finance, EWMA is most commonly used for estimating volatility and correlation — key inputs for risk models, option pricing, and portfolio management.

How EWMA Works

Unlike a simple moving average (which weights all observations equally), EWMA applies a decay factor (lambda, λ) that determines how quickly the influence of past observations diminishes. A lambda close to 1 (e.g. 0.97) means older data retains influence for longer — a smoother estimate. A lower lambda (e.g. 0.94) makes the estimate more responsive to recent changes. The RiskMetrics methodology, popularised by JP Morgan in the 1990s, used λ = 0.94 for daily data.

EWMA Volatility Formula

The EWMA variance estimate for day t is: σ²t = λσ²t-1 + (1-λ)r²t-1, where rt-1 is the return on the previous day. This recursive formula means each new estimate incorporates all historical returns with exponentially declining weights.

Advantages Over Simple Moving Average

EWMA responds more quickly to sudden market movements — volatility spikes are picked up faster. It avoids the "ghost effect" of simple moving averages, where an extreme return causes a sharp drop in the estimated volatility exactly N days later when it rolls out of the window.

Relevance for Finance Professionals

Risk managers, quantitative analysts, and finance professionals working with market risk models will encounter EWMA as a core component of VaR (Value at Risk) models and regulatory capital calculations.

Further Reading

• Risk Management Careers
• Treasury CPD
• CPD for Finance Professionals

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