What Is EWMA Volatility? A Plain-English Primer

Open any risk textbook's chapter on volatility and three names appear in a row: the plain rolling standard deviation, EWMA, and GARCH. The rolling window is the one most chart users already know. EWMA is the next step up, and it changes exactly one thing: how much each past day is allowed to count.

EWMA stands for exponentially weighted moving average. Applied to volatility, it is an estimate of how large a market's moves have recently been in which yesterday matters most, the day before matters a little less, and older days fade smoothly instead of all counting equally and then vanishing. Everything here is descriptive: a volatility estimate measures the size of recent moves and says nothing about direction.

The idea in one sentence

EWMA volatility is a running estimate that blends the previous estimate with the newest squared return, so recent days carry the most weight and the weight on older days shrinks by a constant fraction for each step back in time.

Unlike a rolling window, which counts the last n returns equally and drops everything older, EWMA has no hard edge: every past day still counts, a little less as it ages.

The formula, in words

The update rule has two ingredients, yesterday's variance estimate and yesterday's squared return, and a number λ (lambda) between 0 and 1:

today's variance = λ × yesterday's variance + (1 − λ) × yesterday's squared return

Volatility is the square root of that variance. The two weights, λ and (1 − λ), add to one, so the result is a proper weighted average. Unrolling the recursion shows the "exponential": the newest squared return gets weight (1 − λ), the one before it (1 − λ) × λ, the one before that (1 − λ) × λ², and so on, each weight the previous one multiplied by λ. A practical consequence is that only one running number needs to be carried forward, because the whole history is already folded into yesterday's estimate.

The decay factor: a memory dial

λ is the single dial. Close to 1, the estimate keeps most of its previous value each step, so it moves slowly and remembers for a long time. Smaller, the newest return counts for more, so the estimate moves quickly and forgets sooner.

A useful way to read a given λ is its half-life, the number of days after which an old observation's weight has fallen to half, which is ln(0.5) ÷ ln(λ). By that arithmetic, λ = 0.90 has a half-life of about 6.6 days, λ = 0.94 about 11.2 days, λ = 0.97 about 22.8 days, and λ = 0.99 about 69 days. By convention, RiskMetrics®-style daily volatility uses λ = 0.94, and that is the usual textbook reference point. It is a convention, not a law of markets, and nothing here recommends a value.

For scale, with λ = 0.94 the weights on the most recent 60 returns add up to about 98% of the total, so its reach is of the same order as a 60-bar window, though front-loaded rather than flat. As with window length in the rolling-volatility primer, short memory is reactive and noisier; long memory is steadier and slower.

A worked example, side by side

The numbers below are hypothetical arithmetic that shows the mechanics. They are not market data and not output from any indicator.

Suppose a quiet market has a daily volatility estimate of 1.0% (a variance of 0.0001) under both a 60-bar rolling window and an EWMA with λ = 0.94. One day then closes 3% from the previous close, a squared return of 0.0009. Treating average returns as zero for simplicity, the EWMA's new variance is 0.94 × 0.0001 + 0.06 × 0.0009 = 0.000148, so its volatility rises from 1.00% to about 1.22%. In the rolling window, the 3% day replaces the oldest day, so variance rises by about (0.0009 − 0.0001) ÷ 60 and volatility rises from 1.00% to about 1.06%.

The same shock moved the EWMA several times as far on the first day, which is the "recent days count more" property at work. Now let the market return to ordinary 1% days. The EWMA eases down gradually: about 1.12% after ten calm days, about 1.07% after twenty, about 1.04% after thirty, approaching 1.00% without a break. The rolling estimate behaves differently. It stays near 1.06% as long as the 3% day remains inside the window, then falls back to 1.00% in a single step on the day that bar leaves, even though nothing happened that day. That step is the window's "cliff", a feature of any equal-weighted window. EWMA has no such step.

EWMA versus a rolling window

The two differ structurally. Rolling weights are flat inside the window and zero outside; EWMA weights are front-loaded and never reach zero. Rolling has a window length in bars; EWMA has a decay factor and, through it, a half-life. Because EWMA puts more weight on recent returns, it reacts faster than an equal-weighted window to a sudden jump in volatility, as the example shows. That follows from the construction and does not depend on any dataset. And a rolling estimate can be recomputed by hand from the last n returns, while an EWMA depends on the chain of earlier estimates, so reproducing it needs the same λ and the same starting value.

Which is better depends on the task. For a risk desk, the faster reaction is often the point. For the narrower job of keeping a chart band calibrated one bar ahead, Oisigma's working paper scored a rolling estimate, a GARCH model, and a RiskMetrics®-style EWMA inside the same return-space band construction and found the three statistically indistinguishable on average one-day calibration. The simple vs sophisticated volatility models article covers that comparison and its limits, and the Proof page summarizes it. It is a result about average calibration for those three estimators, not a claim that they are interchangeable in every respect.

What EWMA does not do

First, EWMA has no long-run anchor. Nothing in the update rule pulls the estimate back toward a historical average, so a multi-day forecast from an EWMA is simply today's estimate carried forward flat. GARCH-family models add exactly that missing term, and EWMA is mathematically a stripped-down GARCH(1,1) with no long-run variance term.

Second, it is not a forecast of direction. A high reading says moves have recently been large, not which way the next one goes.

Third, it still reacts only after the fact. It reacts faster than a flat window, but an estimate built from past returns can only register a shock once it has happened. The crisis-onset article describes how that plays out for Oisigma's own rolling-window band, the only onset figure Oisigma has published; none has been published for EWMA.

Underneath both approaches sits the same observation, that calm tends to follow calm and large moves tend to follow large moves, known as volatility clustering. EWMA is one simple way to track that persistence with a single parameter.

The takeaway

EWMA volatility is a weighted average of squared returns whose weights fade geometrically into the past, with one number, λ, setting how long the estimate remembers. It reacts to fresh moves faster than an equal-weighted window and avoids the window's step when an old shock drops out, at the cost of a parameter that must be stated. On the one-day calibration task, Oisigma's published comparison found it statistically indistinguishable from the plain rolling estimate on average; Oisigma's own band uses the rolling estimate, with a window of typically about 60 bars. Past behavior is not a guarantee of future results.

Frequently asked questions

What lambda is normally used for EWMA volatility? The usual reference point is λ = 0.94 for daily data in RiskMetrics®-style models, and 0.97 is often quoted for monthly data. These are conventions rather than universal optima, and the best value for a given purpose is an empirical question. Oisigma's published sensitivity work covers rolling window lengths, and it makes no claim about a best λ.

Is EWMA volatility the same as the exponential moving average on a price chart? No. The familiar EMA line on a chart averages prices. EWMA volatility applies the same exponential weighting to squared returns, so it measures the size of recent moves rather than the level of price. The weighting idea is shared; the quantity being averaged is different.

Do past EWMA values change when a new bar arrives? Not by construction. Each day's estimate is built only from earlier data through the recursive rule, so a value computed for a closed bar is not revised by later bars. The one place an EWMA depends on a choice is its starting value, which affects the first stretch of output before the early observations have faded.

Can an EWMA be used to draw bands on a chart? Mechanically, yes: it supplies the volatility estimate that a band multiplies and projects. Whether the resulting band is calibrated is a separate, testable question that each construction has to answer for itself. Oisigma's working paper put a RiskMetrics®-style EWMA inside the same return-space construction as its rolling estimate and found them statistically indistinguishable on average one-day calibration, as covered in the model comparison.

If you would like to see a deliberately plain, calibrated expected range on your own charts, the Behavioral Transform Model runs on TradingView with a free 30-day trial, then $15 per month.