Volatility Analysis for the CMT Exam: ATR, Bands, and Implied Risk

Volatility describes scale, not direction

An asset can rise with high volatility or decline quietly. Volatility measures help size positions, compare regimes, and interpret option prices. The 2026 CMT Program Guide includes historical and implied volatility at Level I, VIX range calculations and volatility risk premium at Level II, and advanced indexes at Level III. First identify which measure answers the question.

Compute True Range before ATR

For high H, low L, and previous close C, True Range = max(H - L, |H - C|, |L - C|). If yesterday closed at 100 and today traded from 97 to 103, True Range is max(6,3,3) = 6. If yesterday closed at 100 and the next bar spans 108 to 110, True Range is max(2,10,8) = 10. The gap matters even though intraday range was only 2.

ATR smooths a sequence of True Ranges. Software can use a simple mean or Wilder-style smoothing, so state the convention when matching calculations. ATR of 2.5 at a price of 50 is 5% of price; at 250 it is 1%. Normalized ATR aids cross-security comparisons.

A stop 2 × ATR away is a chosen convention, not an inherently optimal rule. It may be too close to chart structure or too far for the loss budget. If ATR expands after entry, moving the stop farther away while holding size unchanged raises monetary risk.

Historical and implied volatility

Historical volatility commonly annualizes standard deviation of periodic returns. For daily returns, a common approximation is daily standard deviation × sqrt(252). This describes a past sample under a stated day-count convention. Implied volatility solves for the volatility input consistent with option prices under a pricing model. It includes demand for protection, event expectations, skew, and risk premiums. It is neither a pure forecast nor a measure of past price movement.

The volatility risk premium is often described as implied volatility minus subsequently realized volatility over a matched horizon. Definitions vary. A positive historical average does not make short-volatility strategies safe; rare jumps can dominate many small premiums. Compare like maturities and instruments.

Worked VIX range

Suppose an index is at 4,000 and VIX reads 20. Treat 20% as an annualized option-implied volatility. A rough one-standard-deviation 30-calendar-day move is 20% × sqrt(30/365) = about 5.73%. In points, 4,000 × 5.73% = about 229. A symmetric illustration spans roughly 3,771 to 4,229.

This is a scale estimate under simplifying assumptions, not a promise that price stays inside the interval. Options-implied distributions can be skewed; jumps and changing volatility matter. If a question specifies trading days, use that convention consistently. Suppose 20-day ATR is 80 points. ATR describes recent daily true range, while 229 points is an approximate 30-day terminal-move scale. The horizon and statistic differ, so they are not interchangeable limits.

Bollinger Bands and a decision rule

A common band uses a 20-period average plus or minus two standard deviations of prices. If the average is 100 and the standard deviation is 4, bands sit at 92 and 108. Price touching 108 does not automatically mean sell. In a strong trend it can remain near the upper band. A squeeze indicates historically narrow dispersion for the chosen settings; it does not predict breakout direction.

One possible plan: after a squeeze, enter only on a close beyond a predefined range with improving breadth; size against a chart invalidation level; exit if price returns inside the range and the expansion fails. Set thresholds before looking at the outcome. ATR, band width, and historical volatility all reuse price movement, so three simultaneous signals may offer less independent evidence than they seem.

Regime change versus a temporary spike

A single large bar can raise ATR and historical volatility at once. That does not tell you whether volatility has entered a lasting new regime. Compare the current estimate with several horizons, inspect whether wider ranges continue, and identify whether the move was a scheduled event, a market-wide shock, or an instrument-specific gap. Implied volatility can rise before a known event and fall afterward even if price moves substantially; that pattern should not be described as an inaccurate forecast without comparing the priced distribution and realized move carefully.

Suppose a risk model targets 500 of planned loss and a stop distance grows from 2 to 4 as volatility expands. With no other constraints, risk-based size falls from 250 to 125 units. If the trader keeps 250 units while moving the stop to 4, planned loss doubles to 1,000. That is a sizing decision, not merely a changed indicator reading.

A prudent plan states when volatility estimates are updated and how rapidly weights can change. Re-estimating every bar may cause excessive turnover; never updating can leave risk stale. The right frequency depends on holding period, transaction costs, and mandate. Study the measurement and the decision separately.

Common traps and self-check

Do not read VIX as a guaranteed return, assume high volatility means bearish, mix calendar and trading-day conversions, or claim a two-standard-deviation price band contains 95% of observations. Price levels are serially dependent and often non-normal.

Self-check: Yesterday closed at 40; today traded from 42 to 44. True Range? Answer: max(44 - 42, |44 - 40|, |42 - 40|) = max(2,4,2) = 4. The gap increases total movement beyond the intraday range.

Next, calculate True Range for five bars and explain how a changed ATR would affect a fixed money-risk position. Compare with the official objectives and the volatility practice topic.