Hull Moving Average (HMA)

What is the Hull Moving Average (HMA)?

The Hull Moving Average (HMA) is a moving average that combines three linearly weighted moving averages to follow price closely while staying smooth. It doubles a half-period WMA, subtracts a full-period WMA, and smooths the result with a WMA whose length is the square root of the period. Alan Hull introduced the construction in 2005 to reduce the delay behind price.

Each component WMA gives the newest of k observations weight k, the next k − 1, and the oldest 1. Divide the weighted total by k(k + 1) / 2.

How is the Hull Moving Average calculated?

Select full length n, integer half-length m and integer square-root smoothing length q. Compute WMA(m) and WMA(n), form the intermediate series 2 × WMA(m) − WMA(n), then apply WMA(q) to that series.

For HMA(4), use m = 2 and q = 2. The closes $100, $102, $101, $105 and $108 produce an intermediate value of 104.63 at bar 4 and 108.90 at bar 5. Their two-period WMA is $107.48.

The calculation needs n + q − 1 observations when every component uses a full window and m is no greater than n. HMA(4) starts on observation 5; HMA(16) starts on observation 19.

Why the HMA lags less and can overshoot price

A k-period WMA trails a straight price ramp by (k − 1) / 3 bars. Combining the three stages gives HMA a coefficient-weighted delay of (2m − n + q − 2) / 3.

At n = 16, m = 8 and q = 4, the delay is two thirds of a bar. At n = 4, m = 2 and q = 2, it is zero. These values describe a straight ramp with the required history in place.

HMA(16) has 19 price coefficients. They sum to one, and 11 are negative. The heaviest weight, 0.2411, falls on the third newest observation and the newest carries 0.1307, so the line leans hardest on the last few bars rather than the latest print.

Negative coefficients allow the line to extend beyond the input price range. In the chart, HMA(4) peaks at $127.38 after a $127 price high and later reaches $115.89 when the lowest input close is $116.

HMA turning points as trading signals

A rising HMA has a current value above its preceding value. A downward turn changes that slope from positive to negative. Alan Hull recommends reading these turns as the event for an HMA rule.

Specify the decision bar. A rule using a completed close acts on the completed value; an intrabar rule acts on the developing value.

Match any plotted displacement with the bar that produced the value. Select the platform’s integer-length convention explicitly for periods whose half or square root is fractional.

How traders use the Hull Moving Average

Compare the turn with swing levels, a breakout or a pullback. Define the entry, invalidation and position size around the complete setup.

Swapped in as a channel centerline, the HMA moves the bands with a quicker line, while ATR-based bands keep the same width.

The HMA turns early, so look for fresh buying in the new direction in Options Flow, then price an expiration that matches the swing’s length in the Options Profit Calculator.

Limitations of the Hull Moving Average

• Set stops and targets from price, not from the line. Negative coefficients push the HMA beyond the input range at turns, as the $127.38 peak above a $127 high shows.
• Pair each turn with a swing level in a choppy market. The responsive line turns often there and reverses within a few bars.
• Expect more lag and overshoot on curved paths. The two-thirds-bar delay holds on a straight ramp, and a curved or reversing path changes both.
• Check the rounding convention. When a period’s half or square root is fractional, platforms that round differently plot different values.
• Trade turns on completed bars. The developing bar keeps updating, and an intrabar turn that reverses before the close disappears from the line.

Bottom line

The Hull Moving Average follows a steady trend with much less delay than a simple or exponential average of the same length, at the cost of overshooting turns. Read it through slope changes on completed bars, record the platform’s integer-length convention, and confirm each turn with swing levels before trading it.