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Key Takeaways
- Each average weights price differently, and the weights decide how fast the line turns: the example’s six values run from $103.50 to $107.48 on the same five closes.
- SMA and WMA forget everything outside their window; EMA and Wilder smoothing keep a fading memory of every past price.
- A standard EMA weights the newest price more than an SMA of the same period but carries the same average lag, (n - 1) / 2 bars, so the price path decides which one turns first.
- Wilder smoothing moves 1 / n of the way to each new price, so its average lag at the same period is n − 1 bars, double the EMA’s (n − 1) / 2, and its early values lean on the starting seed.
- Hull combines three WMAs to reduce delay on a price ramp. Its negative coefficients allow the line to extend beyond the prices in its input window.
- VWMA weights each close by its volume, so it sits above the SMA when the heavy volume traded at higher prices: $105.20 against $104.00 in the example.
What are the types of moving averages?
The types of moving averages are different weighting schemes that turn a price sequence into a changing baseline. Six common types are the simple (SMA), weighted (WMA), exponential (EMA), Wilder smoothed, volume-weighted (VWMA) and Hull (HMA) moving averages. They differ in how much weight the newest price receives, how much history they retain and whether volume enters the weights.
SMA gives equal weight to a fixed window. WMA increases weight linearly toward the newest observation. EMA and Wilder smoothing carry the previous value forward. VWMA uses volume weights within a rolling window. HMA combines three WMAs to reduce delay on a sustained price ramp.
Six moving averages calculated on the same prices
The closes are $100, $102, $101, $105 and $108. At period 4, the final SMA is $104.00 and the WMA is $105.10.
Seed EMA and Wilder smoothing with the first four-close mean of $102. EMA applies alpha = 0.40 and reaches $104.40. Wilder smoothing applies alpha = 0.25 and reaches $103.50.
The last four volumes are 1.0, 1.2, 0.8 and 3.0 million shares. Their VWMA is $105.20. The $108 close carries half of the six million shares in that window.
For HMA(4), form twice WMA(2) minus WMA(4), then apply WMA(2) to that intermediate series. The result is $107.48, the highest of the six, because Hull’s extrapolation leans hardest on the latest closes.
Formula
MA(n) = sum(w_i × P_i) / sum(w_i). SMA: w_i = 1. WMA: w_i = n − i. VWMA: w_i = V_i. EMA: recursive with alpha = 2 / (n + 1). SMMA: recursive with alpha = 1 / n. HMA(n) = WMA( 2 × WMA(price, n/2) − WMA(price, n), √(n) ).- P_i is the price i bars back, with i = 0 the most recent bar.
- w_i is the weight the average assigns to that bar, and the weights are normalized by their own sum.
- alpha is the exponential smoothing factor applied to the newest price in a recursive average: new = old + alpha × (price − old).
- V_i is the volume traded during bar i.
- Average lag in bars, the mean observation age: (n − 1) / 2 for SMA and standard EMA, (n − 1) / 3 for WMA, and (1 − alpha) / alpha for any exponential average. For HMA with half-length m and final length q, the delay on a steady trend is (2m − n + q − 2) / 3.
- For a standard EMA, alpha = 2 / (n + 1); for Wilder smoothing, alpha = 1 / n. A VWMA’s lag moves with the volume: heavy recent volume pulls it toward the latest prices.
Worked Example
Evaluate six period-4 averages on closes of $100, $102, $101, $105 and $108. The last four volumes are 1.0, 1.2, 0.8 and 3.0 million shares. Seed EMA and Wilder smoothing at $102, the mean of the first four closes, then update on $108. HMA uses all five closes; the fixed four-bar windows use the final four.
- SMA(4) = ($102 + $101 + $105 + $108) / 4 = $104.00
- WMA(4) = (1 × $102 + 2 × $101 + 3 × $105 + 4 × $108) / 10 = $105.10
- EMA(4), alpha = 2 / (4 + 1) = 0.40, from the $102.00 seed: $102.00 + 0.40 × ($108 − $102.00) = $104.40
- SMMA(4), alpha = 1 / 4 = 0.25, from the same $102.00 seed: $102.00 + 0.25 × ($108 − $102.00) = $103.50
- VWMA(4) = ($102 × 1.0 + $101 × 1.2 + $105 × 0.8 + $108 × 3.0) / 6.0 = $631.20 / 6.0 = $105.20
- HMA(4) = (104.63 + 2 × 108.90) / 3 = $107.48
The same five closes produce values from $103.50 to $107.48. The weight profile explains the difference: EMA applies 40% of the gap to its $102 seed, Wilder smoothing applies 25%, and the VWMA gives the $108 close half of the current window’s volume weight.
Moving average lag and responsiveness
The newest input receives weight 1 / n in an SMA and 2 / (n + 1) in a standard EMA. At period 4, those weights are 25% and 40%.
Lag is a different question: the average age of the prices in the line. An SMA lags (n − 1) / 2 bars and a WMA (n − 1) / 3. An exponential average lags (1 − alpha) / alpha, which gives (n − 1) / 2 for a standard EMA and n − 1 for Wilder smoothing.
On a straight price ramp, each line trails price by that many bars once it is established. An EMA seeded with its SMA keeps that lag from the seed onward; a Wilder average starts from its seed and settles into its full n − 1 bar lag over the following updates.
Hull cuts that lag sharply. With whole-bar half-length m and final smoothing length q, its delay on a ramp is (2m − n + q − 2) / 3: two thirds of a bar at n = 16, m = 8 and q = 4, and zero at n = 4.
Which moving average fits each charting task?
Use SMA for an equal-weight reference. Match the price input, interval, sessions and adjustments to reproduce the same line across platforms.
Use EMA for a recursive baseline with a defined newest-price weight. Standard MACD uses EMA smoothing at each stage.
Use Wilder smoothing where the indicator calls for it, including standard RSI and ATR. Wilder(14) and EMA(27) share alpha = 1/14 and give identical results with identical seeds and inputs.
Use VWMA to see where the volume traded: a VWMA above the SMA says the heavy volume came at higher prices, as in the example’s $105.20 against $104.00, and below says it came lower.
Use HMA to catch slope changes early. Its negative coefficients let the line run beyond the highest or lowest input price. Fix the whole-bar lengths for n/2 and sqrt(n) before you compare two charts.
Choose the type, period and decision bar as part of one trading rule. Match the expiration to the average you trade: a slow SMA crossover and a fast HMA turn imply different holding periods, and the Options Profit Calculator shows each structure’s payoff at the target across those dates.
Limitations of moving averages
- Judge each line by its lag. A standard EMA weights the newest price more yet lags as far as an SMA of the same period, and HMA’s low delay holds on a straight price ramp.
- Test the type on the market you trade: which line turns or crosses first comes from the price path.
- Fix the period, price input, session, adjustments and seed before you compare lines. Recursive averages remember prices beyond their nominal period, so give them a warm-up stretch before you trade their early values.
- Read HMA overshoots and VWMA tilts as the math at work. Negative coefficients let HMA run beyond the input prices, and a VWMA leans toward heavy-volume bars, as the $108 close with half the window’s volume shows.
Bottom line
Moving average types differ in how they weight recent prices, past values and volume, and those weights set each line’s lag and shape. Choose the type for the task, state the period, seed and price input, and compare averages by their weight profiles rather than by their names.
Clear answers
Frequently Asked Questions
Sources and Further Reading
- NIST/SEMATECH e-Handbook of Statistical Methods: EWMA Control Charts
- NIST/SEMATECH e-Handbook of Statistical Methods 6.4.3.1: Single Exponential Smoothing
- Alan Hull: Hull Moving Average
- Schwab thinkorswim Learning Center: Weighted Moving Average study
- Fidelity Technical Indicator Guide: Average True Range (Wilder smoothing)
- Fidelity Viewpoints: What Moving Averages Say About Stocks
How entries are sourced, calculated and updated: editorial methodology.