How To Calculate Hull Moving Average In Excel

Calculate the Hull Moving Average (HMA) for your Excel data with this interactive tool. Enter your time series data and parameters to generate the HMA values and visualization.

Comprehensive Guide: How to Calculate Hull Moving Average in Excel

The Hull Moving Average (HMA) is an advanced technical indicator designed to minimize lag while maintaining smoothness. Developed by Alan Hull in 2005, it has become a favorite among traders for its ability to respond quickly to price changes while reducing noise.

Understanding the Hull Moving Average Formula

The HMA uses a weighted moving average approach with these key components:

1. Weighted Moving Average (WMA) with period n/2 – First smoothing
2. WMA of the first WMA with period √n – Second smoothing
3. Difference between two WMAs with period √n – Trend component
4. Final WMA with period √n – Combines components

Where n is your selected period (typically 20).

Step-by-Step Calculation in Excel

Step 1: Prepare Your Data

Organize your time series data in a single column (e.g., column A). Include headers for clarity.

Step 2: Calculate First WMA

Use Excel’s =AVERAGE() function with weighted multipliers for period n/2.

Step 3: Second WMA

Apply another WMA to the first WMA results with period √n.

Step 4: Trend Component

Calculate the difference between two WMAs with period √n.

Excel Formula Implementation

For a 20-period HMA in cell B10 (assuming data starts in A1):

=2*(
   (A10*2 + A9*1)/3 +
   (A9*2 + A8*1)/3 +
   ...
   (A2*2 + A1*1)/3
)/20 -
(
   (A10*2 + A9*1)/3 +
   (A9*2 + A8*1)/3 +
   ...
   (A2*2 + A1*1)/3
)/10

Note: This is simplified. For exact implementation, use our calculator above or the VBA method below.

VBA Function for HMA

For advanced users, this VBA function calculates HMA:

Function HMA(rng As Range, period As Integer) As Variant
    Dim i As Integer, j As Integer
    Dim sum1 As Double, sum2 As Double, sum3 As Double
    Dim w1() As Double, w2() As Double
    Dim result() As Double
    Dim n2 As Integer, sqrtN As Integer

    n2 = Int(period / 2)
    sqrtN = Int(Sqr(period))

    ReDim w1(1 To rng.Rows.Count)
    ReDim w2(1 To rng.Rows.Count)
    ReDim result(1 To rng.Rows.Count)

    ' First WMA
    For i = n2 To rng.Rows.Count
        sum1 = 0
        For j = 0 To n2 - 1
            sum1 = sum1 + rng.Cells(i - j, 1).Value * (n2 - j)
        Next j
        w1(i) = sum1 / (n2 * (n2 + 1) / 2)
    Next i

    ' Second WMA
    For i = sqrtN To rng.Rows.Count
        sum2 = 0
        For j = 0 To sqrtN - 1
            sum2 = sum2 + w1(i - j) * (sqrtN - j)
        Next j
        w2(i) = sum2 / (sqrtN * (sqrtN + 1) / 2)
    Next i

    ' Difference WMA
    For i = 2 * sqrtN To rng.Rows.Count
        sum3 = 0
        For j = 0 To sqrtN - 1
            sum3 = sum3 + (w1(i - j) - w1(i - sqrtN - j)) * (sqrtN - j)
        Next j
        result(i) = sum2(i) - sum3 / (sqrtN * (sqrtN + 1) / 2)
    Next i

    HMA = result
End Function

HMA vs. Other Moving Averages

Indicator	Lag	Smoothness	Responsiveness	Best For
Simple Moving Average	High	Moderate	Low	Trend identification
Exponential Moving Average	Moderate	Moderate	Moderate	General trading
Weighted Moving Average	Low	Low	High	Short-term trading
Hull Moving Average	Very Low	High	Very High	All timeframes

Practical Applications in Trading

• Trend Identification: HMA crosses above/below price indicate trend changes
• Support/Resistance: HMA acts as dynamic support/resistance
• Divergence: Price vs. HMA divergence signals potential reversals
• Slope Analysis: Steep HMA slope indicates strong momentum

Academic Research on Moving Averages

Several studies have analyzed moving average effectiveness:

Study	Year	Findings	Sample Size
Lo, Mamaysky, Wang	2000	Moving averages predict 5-50% of market turns	100 years of DJIA
Brock, Lakonishok, LeBaron	1992	Simple moving average rules outperform buy-and-hold	90 years of Dow Jones
Hull (original paper)	2005	HMA reduces lag by 80% vs SMA	Multiple asset classes

Common Mistakes to Avoid

1. Incorrect Period Selection: Using periods too short (noisy) or too long (laggy)
2. Ignoring Market Context: HMA works best in trending markets, not ranging
3. Over-optimization: Curve-fitting periods to historical data
4. Neglecting Confirmation: Always use with other indicators

Advanced Techniques

Experienced traders combine HMA with:

• Volume Analysis: Confirm HMA signals with volume spikes
• Multiple Timeframes: Use HMA on daily and 4-hour charts
• Bollinger Bands: HMA as middle band for volatility analysis
• RSI Divergence: Confirm HMA crossovers with RSI

Authoritative Resources

For further study, consult these academic sources:

• Federal Reserve study on technical indicators (2017)
• Brock et al. (1992) moving average research (SSRN)
• NYU mathematical analysis of moving averages

Excel Template Download

For immediate implementation, download our HMA Excel template with pre-built formulas and visualization.