Hull Moving Average Calculation: A Comprehensive Guide

The Hull Moving Average (HMA) is a unique and effective tool used in technical analysis to smooth price data and help traders identify trends more accurately. Developed by Alan Hull, the HMA aims to reduce lag and enhance responsiveness to price changes. In this article, we will delve into the intricacies of calculating the HMA, its advantages over traditional moving averages, and practical applications in trading strategies. By the end of this guide, you'll have a clear understanding of how to leverage the HMA for improved trading outcomes.

To begin, the HMA formula is as follows:

HMA(n) = WMA(2*WMA(n/2) - WMA(n))

Where:

• WMA = Weighted Moving Average
• n = the period for the moving average

Understanding the Components

1. Weighted Moving Average (WMA): The WMA gives more weight to recent prices, making it more responsive to price changes compared to a simple moving average (SMA). The formula for WMA is:

WMA = (P1 * W1 + P2 * W2 + ... + Pn * Wn) / (W1 + W2 + ... + Wn)

Where:

• P = price at each period
• W = weight for each period, usually increasing for more recent periods.

2. Applying the HMA Calculation:

• Step 1: Determine the period (n) for your HMA.
• Step 2: Calculate the WMA of the first half (n/2) of the data.
• Step 3: Calculate the WMA of the full period (n).
• Step 4: Use the HMA formula to compute the final value.

Example Calculation

Let’s illustrate with a practical example. Suppose you want to calculate the HMA for a period of 14 days (n = 14) using the following hypothetical closing prices:

Day	Closing Price
1	10
2	12
3	11
4	13
5	12
6	15
7	14
8	16
9	18
10	17
11	19
12	20
13	22
14	21

1. Calculate WMA(n/2) for 7 days (Day 8 to Day 14):

   • Assign weights: 1 through 7, where 7 is for Day 8.
   • Compute WMA for Days 8 to 14:

   WMA(7) = (167 + 186 + 195 + 204 + 223 + 212) / (7 + 6 + 5 + 4 + 3 + 2)

   WMA(7) = (112 + 108 + 95 + 80 + 66 + 42) / 27 = 503 / 27 ≈ 18.62

2. Calculate WMA(n) for 14 days:

   • Assign weights: 1 through 14.
   • Compute WMA for Days 1 to 14:

   WMA(14) = (101 + 122 + ... + 21*14) / (1 + 2 + ... + 14)

   Calculate the numerator and denominator:

   • Numerator = 10 + 24 + 33 + 52 + 60 + 90 + 98 + 128 + 162 + 170 + 209 + 240 + 286 + 294 = 1740
   • Denominator = 105

   WMA(14) = 1740 / 105 ≈ 16.57

3. Calculate the HMA: HMA(14) = WMA(2 * WMA(7) - WMA(14)) = WMA(2 * 18.62 - 16.57)

   • Substitute: HMA(14) = WMA(20.67 - 16.57) = WMA(4.1) (Calculate this using the corresponding weights for the latest data).

Advantages of HMA

• Reduced Lag: Compared to SMA and EMA, the HMA provides quicker signals.
• Enhanced Trend Detection: It helps in identifying the direction of price movements more accurately.

Conclusion

Incorporating the Hull Moving Average into your trading strategy can provide you with a significant edge. Its unique calculation method makes it ideal for traders seeking to reduce lag while remaining responsive to market changes. By understanding how to calculate and apply the HMA effectively, you can enhance your analytical capabilities and improve your trading performance.