HMA: Hull Moving Average and Lag Reduction

Key Takeaways

• HMA Hull moving average chains three weighted moving averages, two short and one at the square root of the period.
• The construction cancels most of the lag that a length-N WMA would otherwise carry on a trending series.
• The most common mistake is reading every direction change of the HMA as a reversal signal in choppy markets.
• HMA is widely used by short-term trend traders who want responsiveness without the noise of a fast EMA.

What It Is

The Hull Moving Average is a smoothed combination of weighted moving averages built to reduce lag. Alan Hull published it on his personal site in 2005, and major charting platforms have carried it as a built-in study since.

Unlike adaptive averages that change their effective length based on volatility, the HMA uses fixed-length WMAs in a particular nested order. The result tracks price more closely than a same-length WMA or EMA and reverses direction with less delay.

The Intuition

Lag in a moving average is built into the math: any average centered on the past trails the present. Hull noticed that if you take two WMAs, one short and one long, and combine them in the right way, you can produce a line whose midpoint is closer to the current bar.

The trick is to subtract the long WMA from twice the short WMA. That projection sits ahead of either input. Then a final shorter WMA, of length equal to the square root of the original period, smooths the projection so it stays visually clean.

How It Works

The published formula, available on alanhull.com and reproduced by StockCharts and Fidelity, is:

HMA(N) = WMA( 2 * WMA(N/2) - WMA(N), sqrt(N) )

Step by step:

1. Compute a WMA of price over N/2 bars and call it WMA_half.
2. Compute a WMA of price over N bars and call it WMA_full.
3. Form the projection: 2 * WMA_half - WMA_full.
4. Smooth that projection with a WMA of length sqrt(N), rounded to an integer.

The square-root smoothing is the part that makes the HMA usable. Without it, the 2*WMA_half - WMA_full step produces a fast but jittery line. The sqrt(N) WMA suppresses the noise while keeping most of the lag reduction.

Hull suggested length 16 as a typical setting for daily charts, which gives WMA_half(8), WMA_full(16), and a final smoothing WMA(4). Longer periods are common for swing trading and shorter ones for intraday.

Worked Example

Take a 16-period setting on a strong uptrend. Suppose at a given bar:

• WMA(8) = 102.0 (closer to current price)
• WMA(16) = 100.5 (further back in time)

Compute the projection:

projection = 2 * 102.0 - 100.5
           = 204.0 - 100.5
           = 103.5

That value sits above both inputs, leaning toward where the recent prices have been pulling. Now smooth with WMA(4) over the most recent four projection values. Suppose the last four projection prints are 102.8, 103.1, 103.3, 103.5. The WMA(4) uses weights 1, 2, 3, 4 with divisor 10:

HMA = (102.8*1 + 103.1*2 + 103.3*3 + 103.5*4) / 10
    = (102.8 + 206.2 + 309.9 + 414.0) / 10
    = 1032.9 / 10
    = 103.29

The HMA prints 103.29, well above the 100.5 of the slower input WMA(16), so the line tracks the trend closely. On a turn, the same construction reverses faster than a plain WMA(16) because the projection step moves first.

Common Mistakes

1. Trading every direction change. The HMA does reverse faster than a WMA or EMA, which is the point. In sideways markets, that speed produces more false turns. Pair it with a volatility regime or a longer trend filter.

2. Confusing the HMA with a leading indicator. The HMA reduces lag; it does not eliminate it. The line still depends only on past prices and cannot predict the future. Marketing copy that calls HMA "leading" is wrong.

3. Changing the period without re-rounding sqrt(N). Some implementations leave sqrt(N) as a fractional value or floor it inconsistently. Round once and document the choice; otherwise back-test results drift.

4. Substituting EMAs or SMAs for the WMAs. The lag-cancellation in 2*WMA(N/2) - WMA(N) only works cleanly with linear WMAs. Swapping in EMAs changes the bias and breaks the published behavior.

5. Using HMA on illiquid or gappy series. The HMA reacts fast on purpose. On thin stocks or pre-market data, a single bad print can swing the line meaningfully. Filter out gaps or use a smoothed input series.

Frequently Asked Questions

What is HMA Hull moving average in simple terms? The HMA Hull moving average is a nested chain of weighted moving averages that cuts lag while keeping the line smooth. Alan Hull published it in 2005.

How does HMA affect investment decisions? Short-term trend traders use HMA crosses and direction changes for entries that would arrive late on a plain EMA. Many discretionary traders watch the HMA color or slope as a regime gauge.

What is a real-world example of HMA use? HMA is a default overlay on TradingView, Fidelity Active Trader Pro, and many MetaTrader templates. Period-16 HMA on a daily chart of a liquid ETF is a common starting point.

How can investors use HMA effectively? Tie the length to your horizon, confirm signals with another filter, and avoid trading single direction changes in sideways markets. Use HMA as one input among several rather than as a standalone system.

How is HMA different from ALMA? HMA uses nested WMAs with square-root smoothing and fixed weights. ALMA uses a Gaussian distribution of weights with an offset and sigma parameter that the user can tune.

Sources

1. Hull, Alan. "The Hull Moving Average." https://alanhull.com/hull-moving-average
2. StockCharts ChartSchool. "Hull Moving Average (HMA)." https://chartschool.stockcharts.com/table-of-contents/technical-indicators-and-overlays/technical-overlays/hull-moving-average-hma
3. Fidelity Learning Center. "Hull Moving Average." https://www.fidelity.com/learning-center/trading-investing/technical-analysis/technical-indicator-guide/hull-moving-average
4. Incredible Charts. "Hull Moving Average (HMA)." https://www.incrediblecharts.com/indicators/hull-moving-average.php

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.