8.1 Moving Averages

Moving averages are the workhorse smoother of classical technical analysis. On CMT Level I they sit in Classical Techniques (33% of the 132-question exam) under Internal and External Technical Indicators. A typical item will not ask you to invent an exotic kernel. It will ask whether you know what is being averaged, how weights are applied, how long the window is, and what decision the line is being used for. This OpenExamPrep chapter is independent study material for those CMT Level I topics.

What a moving average is

A moving average (MA) is a calculated series that replaces each bar’s raw price with a summary of recent prices. You choose an input (almost always the close in introductory work), a length n in bars, and a weighting rule. As time advances, the window moves: new data enter and old data leave or fade. The result is a line that is smoother than price and lags turning points because it is built from the past.

Three properties show up again and again:

• Smoothing. One-bar noise is reduced, so the path of the last n bars is easier to see than on the raw print.
• Lag. The average turns after price turns. Longer n means more lag. Lag is acceptable in a trend filter and costly if you expected a precise top ticker.
• Reference. A rising MA is a dynamic mean of the chosen window. Price above a rising average is the usual language of an uptrend in that timeframe; price below a falling average is the usual language of a downtrend.

An MA is a filter, not a forecast engine. It describes the path of the input series. Change the interval (daily versus weekly versus 60-minute) and the same n covers a different amount of calendar time. Most equity and index teaching uses the close. Futures work sometimes averages typical price (high + low + close) / 3. The Level I idea does not change: you are filtering a series.

Simple versus linearly weighted moving averages

A simple moving average (SMA) gives every bar in a finite window the same weight 1/n. For closes C₁ … Cₙ, oldest to newest:

SMA = (C₁ + C₂ + … + Cₙ) / n

When a new close arrives, drop the oldest close and add the newest. Because the dropped bar still had full weight until it left, a large old print falling out of the window can shove the SMA even if today’s change is tiny. That “boxcar” effect is a favorite multiple-choice trap.

A linearly weighted moving average (LWMA), also called a weighted moving average (WMA) on many platforms, still uses a hard window of n bars, but it tilts toward the present. The newest close gets weight n, the prior close n−1, down to weight 1 on the oldest close. Divide by the sum of weights, n(n+1)/2. The LWMA is more responsive than an SMA of the same n because yesterday outranks the oldest bar. Once a bar ages beyond n, its weight goes to zero—the cutoff is still abrupt, just less violent than the SMA’s equal-weight drop.

Tiny SMA worked example

Five daily closes, oldest to newest: 10, 12, 11, 13, 14.

Five-day SMA = (10 + 12 + 11 + 13 + 14) / 5 = 12.

A sixth day closes at 15. Drop 10 and add 15:

New SMA = (12 + 11 + 13 + 14 + 15) / 5 = 13.

The close rose by 1, and the SMA also rose by 1, because the bar that left (10) was far below the new close (15). If the bar that left had been 14, the SMA would have barely moved. An SMA’s change depends on both the incoming price and the outgoing price.

The same original five closes as a five-period LWMA:

(14×5 + 13×4 + 11×3 + 12×2 + 10×1) / 15 = 189 / 15 = 12.6.

The LWMA (12.6) sits above the SMA (12) because the latest prints were the higher ones. That is linear weighting doing its job: recency bias inside a fixed window.

Wilder smoothing and the exponential moving average

J. Welles Wilder Jr. built the Relative Strength Index (RSI), Average True Range (ATR), and the directional movement system with a recursive smoother. Today’s value is yesterday’s smoothed value plus a fraction of the surprise:

Wilder_t = Wilder_{t−1} + (Input_t − Wilder_{t−1}) / n

That is an exponential moving average whose smoothing constant α = 1/n. Many chart platforms label a separate exponential moving average (EMA) with α = 2/(n+1). For n = 14, Wilder uses 1/14 ≈ 0.071, while a common EMA-14 uses 2/15 ≈ 0.133—nearly twice as much weight on the new bar. Wilder-14 is not the same object as EMA-14 unless the platform documents α.

Recursive averages have no hard window. Influence of an old shock fades geometrically and never quite hits zero. An SMA of similar length will “forget” a crash the day it drops out of the box; an EMA or Wilder line can still lean on that memory.

Wilder’s 14-period convention is the default lookback on several of his studies (RSI, ATR, ADX/DMI). Treat 14 as an indicator default, not as a fourth official “trend of the market.” Mixing “the 14-day RSI” with “the 20-day SMA as a short-trend map” is fine; treating them as interchangeable lengths is how items get missed.

Length of the three most common trends

Technicians talk about short, intermediate, and long trends as nested swings. A classic daily-bar teaching map is 20 / 50 / 200:

These numbers are a teaching map, not a required platform setting and not a claim that markets must respect them. On weekly bars, a 40-week average covers a similar long calendar idea with a smaller n. On a 15-minute chart, “200” is a few days, not a year. Always state the interval.

Relative lag: in a simple step-change thought experiment, an SMA’s lag is on the order of half the window. A 20-day SMA is usable for swing timing. A 200-day SMA is a regime filter. A 14-period Wilder study on the same daily chart is shorter than the 20-day short-trend map and exists to stabilize RSI, ATR, and DMI—not to relabel the long-term trend.

Strategies for using moving averages

Level I uses cluster into three families.

Trend filter (one-MA method). Permit longs only while price—or a faster average—holds above a chosen MA (often the 50-day or 200-day on daily charts); permit shorts or stand aside when it does not. The average is a permission layer. Entries can still come from breakouts, patterns, or a second indicator. This is the same “one-MA method” idea you meet in trend identification: the line answers are we treating this as an up-regime or a down-regime? rather than where is the exact entry tick?

Crossovers (two-MA method). The shorter average crossing above the longer one is the bullish cross (popular commentary: “golden cross” for a 50-day SMA moving above a 200-day SMA). The opposite cross is bearish (“death cross” in the same slang). Teaching pairs include 20/50 and 50/200. Crossovers confirm that the fast mean has overtaken the slow mean; they are late on purpose. They pay in persistent trends and whipsaw when price chops and the two lines weave. A third filter (slope, ADX, or a still-longer MA) is how practitioners reduce fake crosses—the exam first wants the raw definition.

Dynamic support and resistance. In an advance, pullbacks toward a rising SMA or EMA often attract buyers; in a decline, rallies toward a falling MA often attract sellers. A decisive close through a widely watched average (especially the 50-day or 200-day on liquid indexes) is read as a change in the crowd’s reference. Failed breaks—a spike through the average that then closes back—are part of the same vocabulary. None of this is a physical law; it is observed dealing around a public number.

Always pair the rule with the bar size. A 50-period MA on a 60-minute chart is not the 50-day SMA.

Moving-average bands and envelopes

A moving-average envelope (MA band in older wording) plots the same average shifted up and down by a fixed percentage (or a fixed point amount). Example: 20-day SMA ± 2.5%. Width does not automatically expand when volatility rises. Price riding the upper envelope can describe a strong trend; rapid tags of both envelopes often describe a range.

Envelopes ask: how far is price from its recent mean, in percent? They do not ask: is that distance large relative to recent volatility? Variable-width volatility bands (Bollinger Bands in the next section, and Keltner-type channels later) answer the second question. Keep the Level I contrast: percent envelopes are constant in percent; standard-deviation bands are not.

Exam traps

Equal-weight SMA versus recency-weighted LWMA versus recursive EMA/Wilder. Daily 20/50/200 as nested trend labels versus Wilder 14 as an indicator default. Crossovers confirm with lag; they do not remove lag. Envelopes are not Bollinger Bands. “n periods” is meaningless until you name the bar size.

The bar chart is a length map, not a ranking of “importance.” A 200-day filter and a 20-day swing overlay answer different questions on the same daily chart. Wilder’s 14-period default does not appear on this map because it is an indicator smoothing convention, not a third-plus “market trend” label.