16.2 Measuring Historical Volatility

Measuring what already happened

Once you can define volatility, CMT Level I asks how technicians quantify historical fluctuation on a price bar. Three named tools dominate this objective: Wilder’s True Range, Bollinger Bands (here as a volatility envelope, not a full indicator monograph), and Keltner Channels, including Chester Keltner’s original arithmetic. The Program Guide also wants volatility cycles: contraction and expansion as a repeating market behavior, not a rigid 20-day sine wave.

Wilder’s three True Range measurements

J. Welles Wilder Jr. introduced True Range (TR) in New Concepts in Technical Trading Systems (1978). A simple high minus low understates movement whenever price gaps beyond the prior close. True Range repairs that by taking the greatest of three quantities:

1. Current High − Current Low (today’s printed range).
2. |Current High − Previous Close| (how far the high is from where the last session ended, capturing an upside gap).
3. |Current Low − Previous Close| (how far the low is from the prior close, capturing a downside gap).

Those three are the list to memorize. TR is always non-negative. Average True Range (ATR) is then a smoothed average of TR; Wilder’s original popular default is 14 periods with his smoothing method. Level I items may stop at the three TR building blocks. Later applications (chandelier stops, position sizing, modern Keltner width) all inherit this gap-aware range.

Worked example A (no gap). Prior close 100. Today high 102, low 97.
High − low = 5.
|102 − 100| = 2.
|97 − 100| = 3.
TR = 5. The session’s own range already contains the close-to-extreme distances.

Worked example B (gap down). Prior close 100. Today opens and trades 96–92, never tagging 100.
High − low = 4.
|96 − 100| = 4.
|92 − 100| = 8.
TR = 8. A naive high-low range of 4 would have missed four points of overnight risk. That is why Wilder replaced raw range with True Range for volatility and stop work.

Worked example C (gap up, then fade). Prior close 50. Today high 56, low 51.
High − low = 5.
|56 − 50| = 6.
|51 − 50| = 1.
TR = 6, the gap-inclusive high versus prior close.

Exam trap: TR is not “close minus close,” not the 14-day ATR itself, and not standard deviation. ATR is the average of TR; TR is the one-bar input.

Bollinger Bands as a volatility recap

John Bollinger popularized bands that sit a multiple of the standard deviation of closing prices around a moving average, typically a 20-period simple moving average (SMA) with two standard deviations. Upper band = SMA + kσ. Lower band = SMA − kσ. Default k = 2. Because standard deviation is a historical-volatility statistic, the distance between the bands is a direct volatility envelope. When realized fluctuation shrinks, the bands narrow; when it expands, they widen.

Two derived readings matter for this chapter without rebuilding an entire Bollinger lesson:

• Bandwidth = (Upper − Lower) / Middle. Low bandwidth is a squeeze: historically compressed volatility.
• %B locates the close inside the envelope. It is a position reading, not a second volatility formula.

For volatility analysis, the exam point is that Bollinger width is a standard-deviation measure of historical volatility around a typical SMA midline. Price can walk the band in a strong trend, so a touch of the upper band is not automatically “overbought” in the mean-reversion sense. A squeeze is a volatility statement: ranges have been small. What comes next is often larger ranges, but the direction of the break is not given by bandwidth alone.

Do not confuse the 20,2 defaults with a law of nature. Bollinger published them as starting parameters. Other windows and multipliers exist. Level I still expects you to recognize the standard-deviation construction and the squeeze-to-expansion story.

How volatility cycles

Historical volatility is not a random walk around a single mean in the way a drifting price series can be. Two empirical facts sit side by side:

• Clustering (short horizon): large-range days tend to follow large-range days. Panic and celebration both persist for a while.
• Cycling / mean reversion (intermediate horizon): long stretches of contraction tend to be followed by expansion, and extreme expansion tends to cool. This is the cycle the Program Guide wants you to recall.

The cycle is not a fixed-length oscillator you can mark with a protractor. A squeeze can last a handful of bars or many weeks. Expansion can be a one-day news spike or a multi-week trend. The practical technician response is regime-aware:

• After a long squeeze, expect the next meaningful move to travel farther than the compressed bars suggested. Breakout methods have a statistical context; fading the first expansion as if the coil were immortal is a common error.
• After a volatility spike, expect ranges to moderate eventually, but do not assume the first down-tick in ATR is a trend reversal in price. Volatility can fall while price keeps drifting in the panic direction, or while a recovery grind begins.
• Position size should follow the cycle. The same 100-share habit in a 0.8 percent ATR name becomes reckless when ATR is 3 percent.

Think of the cycle as energy storage and release. Compression stores. Expansion spends. Indicators that use a fixed lookback (including Bollinger σ and ATR) are how you see that energy on the chart.

Keltner’s original channel calculation

Chester W. Keltner, in How to Make Money in Commodities (1960), built an envelope from range, not from standard deviation and not from Wilder’s later ATR.

Original construction:

• Typical price for each day = (High + Low + Close) / 3.
• Midline = 10-day simple moving average of typical price.
• Range each day = High − Low (the raw daily range, not True Range).
• Band offset = 10-day simple moving average of that high-minus-low range.
• Upper channel = midline + that 10-day average range.
• Lower channel = midline − that 10-day average range.

So the original Keltner channel is a 10-day SMA of typical price ± 1× the 10-day SMA of the daily high-low range.

Worked numbers. Ten-day SMA of typical price = 50.00. Ten-day SMA of (H − L) = 1.20. Original bands sit at 51.20 and 48.80. A close through those rails, in Keltner’s framework, was a trend clue, not a mean-reversion fade by default.

Later popularizations, especially Linda Bradford Raschke’s widely used version, switched the midline to an exponential moving average (EMA) of the close (often 20 periods) and switched the width to a multiple of ATR (often 2 × ATR). That modern envelope is what many platforms label “Keltner Channels” today. The Program Guide asks for the original calculation. If an item says “Keltner’s original,” answer 10-day SMA of typical price and 10-day SMA of high − low, not 20-EMA ± 2 ATR.

How Keltner Channels differ from Bollinger Bands

Keep a hard contrast. Both are envelopes around a central tendency. They differ in how width is measured and, in typical use, what the midline is.

Width. Bollinger Bands use standard deviation of closes. Outliers get extra weight because deviations are squared. A single shock session balloons the bands. Keltner width uses range: originally the SMA of high − low, and in common modern use ATR (which is built from Wilder’s True Range). ATR already includes gaps, so modern Keltner width is gap-aware. Range averages react more linearly than σ; the envelope usually looks smoother and less elastic on a spike bar.

Midline. Bollinger’s default midline is an SMA of the close. Modern Keltner typically uses an EMA of the close (faster to recent prices). Original Keltner used an SMA of typical price, which already blends high, low, and close.

Interpretation flavor. A Bollinger squeeze is a σ-contraction signal. Walking a Bollinger band can be trend continuation. A close outside a Keltner channel is often treated, in channel methods, as a trend / breakout event because the rails are a typical-range budget. None of these rules is automatic on every timeframe. The exam wants the construction difference, not a vendor’s trade recipe.

Exam traps: (1) assigning standard deviation to Keltner; (2) assigning ATR to original 1960 Keltner; (3) saying both midlines must be SMAs; (4) treating a squeeze as a directional forecast. Measure first. Direct second. Size third.