Hull Moving Average & Concavity

The Problem With Traditional Moving Averages

Traditional moving averages (SMA, EMA) have a fundamental trade-off: the longer the lookback, the smoother the line — but the greater the lag. A 200-period SMA is extremely smooth but trails price by hundreds of bars. A 5-period EMA is very responsive but generates excessive false signals from noise. This lag makes it difficult to detect early trend transitions.

The Hull Moving Average

The Hull Moving Average (HMA), developed by Alan Hull, addresses lag by using a weighted moving average of weighted moving averages. The formula essentially calculates two WMAs of different lengths, then takes the WMA of their difference — creating an average that is both smoother than a short-period MA and more responsive than a long-period MA.

The result: the HMA tracks price more closely in trending conditions while still filtering out most noise during consolidation. This makes it substantially better than traditional MAs for trend identification.

What Is Concavity?

Concavity is the mathematical concept of the "second derivative" of a curve — it measures the rate of change of the direction of the curve, not just the direction itself.

• First derivative (slope): Is the HMA going up or down? (Are we in an uptrend or downtrend?)
• Second derivative (concavity): Is the slope increasing or decreasing? (Is the trend accelerating or decelerating?)

Think of it like driving: if your speed is 60 mph but you're pressing the accelerator, you're accelerating. If you're at 60 mph but pressing the brake, you're decelerating — even though you're still moving forward. Concavity tells you whether the trend is pressing the accelerator or the brake.

Why Concavity Flips Are More Useful Than Crossovers

Traditional MA crossover systems wait for a slow MA to cross a fast MA — by definition a lagging signal. Concavity flips happen earlier: when the HMA stops accelerating in the current direction, it's a warning that trend momentum is fading — often before a traditional crossover would signal anything.

This gives traders an earlier exit signal and earlier entry timing in new trends.

Practical Interpretation

TDL Connection

HMA Concavity Pro applies this analysis automatically with color-coded trend states that change based on both direction and concavity, plus flip signals that appear at the moment concavity changes — giving you the earliest possible warning of trend momentum transitions.