Direct Answer
The Hull Moving Average (HMA) is a moving average developed by Alan Hull to reduce lag while staying smooth. It's built from weighted moving averages (WMAs): HMA = WMA( 2 × WMA(price, n/2) − WMA(price, n), sqrt(n) ), where n is the chosen period. The doubling-and-subtracting step is designed to strip out lag that a plain WMA still carries, at the cost of being more prone to overshooting price on sharp reversals than a standard moving average.
Key Takeaways
- HMA = WMA( 2 × WMA(price, n/2) − WMA(price, n), sqrt(n) ), a weighted moving average of a lag-adjusted difference between two other weighted moving averages.
- It's built entirely from weighted moving averages, which already weight recent prices more heavily than a simple moving average.
- The design goal is to reduce lag while keeping the line smooth, a trade-off, not a free improvement, since faster reaction increases the chance of overshooting price on sharp reversals.
- Like other moving averages, the period n is commonly varied; there's no single universal setting for every asset or timeframe.
- Reduced lag doesn't mean fewer false signals, a faster-reacting line can also whipsaw more in choppy, range-bound conditions.
What Is the Hull Moving Average?
The Hull Moving Average is a moving average developed by Alan Hull that is built from weighted moving averages (WMAs) rather than a single simple or exponential average. Its goal is specific: reduce the lag that ordinary moving averages carry, the delay between a real change in price direction and the moving average line reflecting it, without giving up the smoothness that makes a moving average useful for reading trend direction in the first place.
A standard weighted moving average already reduces lag somewhat compared to a simple moving average, because it assigns more weight to recent prices than to older ones. HMA goes a step further: it computes a half-period WMA and a full-period WMA, doubles the shorter one and subtracts the longer one to isolate and amplify the part of the average that's still lagging, and then re-smooths that result with a further WMA calculated over the square root of the period. The result is a line that's designed to turn with price faster than a plain WMA of the same period, while still smoothing out much of the bar-to-bar noise.
The Formula
HMA = WMA( 2 × WMA(price, n/2) − WMA(price, n), sqrt(n) ), where n is the chosen period.
In words: take a weighted moving average over half the period, double it, subtract a full-period weighted moving average, then smooth that result with a further weighted moving average over the square root of the period. Each of the three WMAs in the formula is calculated the same way a standalone WMA is, the difference is what's fed into the final smoothing step.
The doubling-and-subtracting step is the core of the design: it's meant to remove lag that a normal WMA still carries. That same mechanism is also the source of HMA's main trade-off, because the line is built to react faster, it's more prone to overshooting price on sharp reversals than a standard moving average.
Worked Example
Hypothetical example, for education only.
Say a trader is calculating a 9-period HMA (n = 9). The steps in the formula require three separate WMA calculations:
- A WMA over the half period, n/2 = 4 (rounded, since half of 9 isn't a whole number), call this result WMA(price, 4) = $101.20.
- A WMA over the full period, n = 9, call this result WMA(price, 9) = $100.10.
- Double the half-period result and subtract the full-period result: 2 × 101.20 − 100.10 = 202.40 − 100.10 = $102.30.
The final step smooths that $102.30-based series with a WMA over the square root of the period: sqrt(9) = 3, so a 3-period WMA is applied to the most recent values produced by step 3. If that final 3-period WMA works out to, say, $102.05, that value is the 9-period HMA reading for that bar.
Compare that to the plain 9-period WMA in this example, $100.10: the HMA reading sits noticeably closer to the most recent, higher prices, illustrating the lag reduction the formula is designed to produce, while also showing how a HMA reading can sit further from a simple average than traders might expect from a "smooth" line.
How Traders Commonly Use HMA
Slope and direction
Many traders read the HMA the same way they'd read any trend-following moving average: a rising HMA is commonly associated with upward momentum, a falling HMA with downward momentum, and a flattening slope with a possible pause or consolidation. Because HMA is designed to react faster than a comparable SMA or EMA, its slope can change sooner after a genuine shift in price direction, but that same responsiveness means the slope can also flip more readily during choppy, sideways price action.
Price crossing the HMA line
Some traders watch for price crossing above or below the HMA line as a possible trend-change cue, similar to how price-versus-moving-average crossovers are used with SMA or EMA. Because HMA hugs price more closely than a slower average, these crossovers can trigger earlier, which can mean catching a move sooner, or reacting to noise that a slower average would have filtered out.
Color or slope-change coding
On many charting platforms, HMA is plotted with a color that changes based on whether the line is rising or falling, making direction changes easier to scan visually across several charts at once. This is a display convenience, not a separate signal, it reflects the same slope information described above.
Choosing a Period
| Period (n) | Responsiveness | Common use | Trade-off |
|---|---|---|---|
| Short (e.g., single digits) | Very fast | Short-term/active trading | More prone to overshoot and whipsaw |
| Medium | Balanced | General-purpose swing analysis | Still reacts faster than a comparable SMA/EMA |
| Long | Smoother | Longer-term trend reading | Fewer, later signals; less of the lag-reduction benefit is visible bar-to-bar |
As with any moving average, there's no single period that's correct for every asset, timeframe, or purpose. This is a commonly cited framework, not a fixed rule, and the exact behavior of a given period should be verified against your own charting platform rather than assumed, since implementations can round the half-period and square-root-period calculations slightly differently.
Limitations
- Overshoot on sharp reversals, the same doubling-and-subtracting mechanism that removes lag can cause the HMA line to overshoot price when a sharp reversal happens, more so than a standard moving average would.
- Still a lagging calculation at its core, HMA is built entirely from historical price data run through weighted moving averages; reducing lag is a matter of degree, not a change from lagging to leading.
- More whipsaw in sideways markets, a faster-reacting line crosses back and forth more often when price isn't trending, which can generate more false signals in range-bound conditions than a slower moving average would.
- Implementation differences, because the formula involves rounding a half period and a square-root period, exact HMA values can differ slightly between charting platforms; always verify the calculation your platform uses.
Common Mistakes
- Assuming "less lag" means "more accurate", HMA is designed to reduce lag, not to improve predictive accuracy; a faster line can still be wrong, and can be wrong sooner.
- Trading every slope change or crossover in isolation, like other moving averages, HMA signals are commonly paired with price structure, volume, or another indicator rather than acted on alone.
- Ignoring the overshoot trade-off, treating HMA as a strictly "better" version of SMA or EMA without accounting for its greater tendency to overshoot on sharp reversals.
- Assuming one period works across assets and timeframes, the period that suits a fast-moving asset on a short timeframe won't necessarily suit a slower one on a daily chart.
Buying Responsiveness With Overshoot
The Hull moving average reduces lag through a weighting scheme that responds quickly to recent price. That responsiveness is genuine and it is not free: the same construction causes the line to overshoot at turning points, continuing briefly in the prior direction's smoothed path before catching up.
The consequence for signals is specific. Crossover systems built on this average trigger earlier than those on conventional averages, which helps in sustained trends and hurts in choppy conditions where the earlier trigger simply means more false signals. Which effect dominates depends on the instrument rather than on the average.
The mistake is substituting it into an existing system without retesting. Parameters tuned around a slower average assume a certain signal frequency, and swapping in a faster one changes that frequency substantially while leaving the rest of the rules calibrated for the old behaviour.
The line also inherits the fundamental limitation of every moving average, which is that it summarises past prices. Reduced lag narrows the gap between the summary and the present; it does not close it, and no weighting scheme can.
HMA FAQs
What does the Hull Moving Average do differently from a normal moving average?
It combines a half-period weighted moving average, doubled, minus a full-period weighted moving average, then smooths that result with a further weighted moving average over the square root of the period. The doubling-and-subtracting step is designed to strip out lag that a standard weighted moving average still carries, at the cost of being more prone to overshooting price on sharp reversals.
What is the HMA formula?
HMA = WMA( 2 x WMA(price, n/2) - WMA(price, n), sqrt(n) ), where n is the chosen period. Take a weighted moving average over half the period, double it, subtract a full-period weighted moving average, then smooth that result with a further weighted moving average over the square root of the period.
Who created the Hull Moving Average?
Alan Hull developed it as a moving average designed to reduce lag while staying smooth, building it out of weighted moving averages rather than a single simple or exponential average.
Does a smoother, less-lagging moving average mean fewer false signals?
Not necessarily. Reducing lag is a design trade-off, not a guarantee of accuracy. An indicator built to react faster is, by design, also more prone to overshooting price on sharp reversals, which can itself create false signals in choppy conditions.
What period is commonly used for HMA?
There is no single universal setting. As with other moving averages, shorter periods react faster with more noise and longer periods smooth further with more lag; the right period depends on the asset, timeframe, and what the indicator is being used for, and should be verified against your own charting platform rather than assumed.
Can the Hull Moving Average be used alone?
It can be viewed on its own, but like any single moving average it only describes one aspect of price behavior. Traders commonly pair it with price structure, volume, or another indicator rather than trading its signals in isolation.
What is the cost of the reduced lag in this moving average?
The construction achieves responsiveness by combining weighted averages in a way that can overshoot, so the line sometimes extends beyond the price move that produced it and then corrects. In choppy conditions that overshoot produces direction changes the underlying price did not really make. Reduced lag and reduced false signals are not the same property, and this design trades one for the other.
How should the direction changes of this average be used?
Because the line is smooth, a change in its slope is visually clear, and many implementations colour the line by direction. Treating each slope change as a signal produces frequent reversals in ranging markets. It is more workable as a trend filter, where the slope determines which direction of trade is permitted, than as an entry trigger in its own right.
Does the square root step in the calculation have a theoretical basis?
The construction uses a final smoothing over the square root of the chosen period, which is a design choice made to balance smoothness against responsiveness rather than a result derived from a model. It works in the sense that it produces the intended behaviour. Presenting it as a mathematical necessity would overstate what the derivation establishes.
References
- CMT Association: Technical Analysis Body of Knowledge and Research
- CFA Institute Research and Policy Center: Investment Research
- TA-Lib: Technical Analysis Function Library Documentation
- Alan Hull developed the Hull Moving Average as a weighted-moving-average-based indicator designed to reduce lag while maintaining smoothness.
- SEC Investor.gov: Introduction to Investing