Exponentially Weighted Moving Average (EWMA): A Practical Guide

The exponentially weighted moving average (EWMA) is a simple but powerful technique for tracking a changing average over time — and in finance it's especially valued as a way of estimating volatility. By giving more weight to recent data, it responds quickly to new information while still drawing on history. This guide explains what an EWMA is, the formula, the role of the decay factor, and its uses — in clear, plain language. It complements our guide to the GARCH model and is relevant to anyone studying quantitative finance, statistics or risk.

What is an exponentially weighted moving average?

An exponentially weighted moving average is an average in which recent observations carry more weight than older ones, with the weights declining exponentially as you go further back in time. A simple moving average treats, say, the last 30 days equally and then drops the 31st day entirely. An EWMA instead lets every past observation contribute, but with steadily shrinking importance — yesterday matters most, the day before slightly less, and so on. This makes it both smooth and responsive: it reacts to new data quickly without lurching, and it never abruptly "forgets" an old observation the way a simple moving average does.

The EWMA formula

For estimating variance (volatility), the EWMA update is:

σ²_t = λ · σ²_t−1 + (1 − λ) · r²_t−1

Here σ²_t is the new variance estimate, σ²_t−1 is yesterday's variance estimate, r²_t−1 is yesterday's squared return, and λ (lambda) is the decay factor, a number between 0 and 1. The beauty of this form is that it's recursive: today's estimate is just a weighted blend of yesterday's estimate and yesterday's new information, so you only need to keep one running figure rather than a long window of data. For example, with λ = 0.94, today's variance is 94% of yesterday's estimate plus 6% of yesterday's squared return — a small but steady nudge toward the latest news.

The role of the decay factor

The decay factor λ controls how quickly old data fades. A high λ (close to 1) means slow decay — the estimate is smooth and stable, putting a lot of weight on history. A low λ means fast decay — the estimate is jumpy and reacts strongly to the latest move. There's a trade-off: too high and the estimate is sluggish to react to genuine changes in volatility; too low and it's noisy. The well-known RiskMetrics approach popularised by J.P. Morgan used λ = 0.94 for daily data as a sensible default, and that value is still a common reference point today.

Why EWMA suits volatility

EWMA is popular for volatility estimation because it naturally captures volatility clustering — the tendency for volatile periods to follow volatile periods. After a large return, the squared-return term pushes the estimate up, and it stays elevated for a while as that observation slowly decays. This produces realistic, time-varying volatility from a very simple rule. In fact, EWMA is a special case of the GARCH(1,1) model — the case where the constant term is zero and the weights sum to one. The main difference is that EWMA has no long-run average to revert to, whereas GARCH adds mean reversion.

What EWMA is used for

EWMA has wide application. In risk management it's used to estimate volatility and feed Value at Risk (VaR) models — the RiskMetrics methodology is built around it. It's also used more generally to smooth noisy time series while keeping them responsive, and in technical analysis, where exponential moving averages of prices are a staple indicator. In quality control and forecasting, EWMA charts track whether a process is drifting. Its blend of simplicity, low data requirements and responsiveness makes it a genuinely versatile tool across many fields.

Frequently asked questions

What is an exponentially weighted moving average?

An average that weights recent observations more heavily than older ones, with weights declining exponentially into the past — smooth yet responsive, and computed recursively from a single running figure.

What is the EWMA variance formula?

σ²_t = λσ²_t−1 + (1 − λ)r²_t−1: today's variance is a weighted blend of yesterday's variance estimate and yesterday's squared return.

What is the decay factor?

The parameter λ (between 0 and 1) controlling how fast old data fades. High λ gives a smooth, stable estimate; low λ gives a reactive one. RiskMetrics used λ = 0.94 for daily data.

How does EWMA relate to GARCH?

EWMA is a special case of GARCH(1,1) with a zero constant and weights summing to one. Unlike GARCH, EWMA has no long-run variance to mean-revert toward.

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