Volatility indicators — ATR, bands, returns and option measures

A volatility measure describes a chosen scale of variation, not a trading direction. Distances in price units, dispersion of returns and values derived from option prices answer different questions. Choose the question and units before adding another line to the chart.

Choose the measurement before choosing a strategy

ATR uses candle ranges and previous Closes in price units. Historical return volatility uses a specified return series and scaling convention. Bollinger Bands use price dispersion around an average; one Keltner variant uses an average plus an ATR multiple. Implied volatility is derived from option prices under a pricing model, with a specified instrument and expiry.

Record symbol, source, timeframe, observation time and calculation settings. ATR(14) on H1 and D1 uses different bars; fourteen bars do not automatically mean two weeks. A measure may be a feature in a market-regime rule, but low or high values do not certify mean-reversion or breakout profitability.

Calculate True Range and a stated ATR version

True Range is max(High − Low, |High − previous Close|, |Low − previous Close|). For the Wilder version in this exercise, seed ATR with the mean of the first n supplied TRs; then ATR = ((n − 1) × prior ATR + current TR)/n. Check a platform’s actual smoothing and initialization before comparing outputs.

The fictional instrument below uses arbitrary price units, complete H/L/C records and a known preceding Close 100. Use n = 3 for readable arithmetic; these are not measured EUR/USD candles or optimised settings.

Bar 2 has High − Low = 2, yet its prior-Close gap gives TR 4. Seed is (3 + 4 + 3)/3 = 10/3. The next update is (2 × 10/3 + 5)/3 = 35/9, while a rolling three-TR mean is (4 + 3 + 5)/3 = 4. Different formulas need not agree.

An assigned fifth bar H 110, L 106, C 109 has prior Close 108, TR 4 and updated ATR (2 × 35/9 + 4)/3 = 106/27 ≈ 3.9259. Round only the displayed result. The ATR guide and True Range introduction expand these conventions. An ATR value is not a guaranteed next-bar distance or mandatory stop multiplier.

Bands describe different inputs and settings

Traditional Bollinger Bands surround an SMA with price-standard-deviation offsets. Price standard deviation is not the same variable as return standard deviation. BandWidth divides band width by the middle line. Touching a band alone does not define a buy or sell, and standard-deviation construction does not guarantee a future containment percentage.

One Keltner version uses EMA ± k × ATR. Other settings can select a different average or range calculation. There is no universal rule that one channel responds more slowly, or that a squeeze ends quickly with a profitable breakout.

For a separate assigned-value exercise, let SMA = 100, price standard deviation = 2 and Bollinger multiplier = 2: bands 96 and 104, BandWidth 8/100 = 8%. Let the Keltner basis be EMA 101, ATR 1.5 and multiplier 2: bands 98 and 104. The Bollinger lower band lies below 98, so the two Bollinger boundaries are not contained in that Keltner channel. These summary inputs are assigned, not calculated from an undisclosed common history.

If testing containment, state whether equality is allowed, which two boundaries must qualify and when their values are known. Record failed conditions rather than calling every narrow-looking pair a squeeze.

Return volatility and option values need their own conventions

Define log return as ln(current Close / prior Close). For four assigned daily log returns +0.01, −0.01, +0.01, −0.01, mean is zero and squared deviations sum to 0.0004. Using sample denominator N − 1 gives standard deviation √(0.0004/3) ≈ 1.1547%. Under a chosen 252-session convention, multiplying by √252 gives about 18.33%.

Four observations teach arithmetic, not a credible market estimate. Assigned log returns are not ordinary percentage returns, and 252 is a scaling convention. Equal one-period dispersion alone does not determine a longer horizon if changes are dependent.

Implied volatility comes from option prices and a model; it can differ by strike and expiry. It is not one universal thirty-day currency consensus or a guaranteed realized range. VIX refers to S&P 500 option prices, rather than measuring a selected FX pair. The linked intermarket discussion concerns a separate relationship to investigate; VIX crossing 25 does not by itself assign a currency direction.

Check the dependence hidden in time scaling

For two log returns with equal variance σ², variance of their sum is 2σ² + 2 Cov(r₁,r₂) = 2σ²(1 + ρ). Only zero covariance yields the √2 standard-deviation factor in this two-period model.

Construct each model with independent equally likely X,Y = ±1: r₁ = 0.01 X and r₂ = 0.01[ρX + √(1 − ρ²)Y]. All four equally probable combinations reproduce the stated variances. These are assumptions, not observed currency correlations or confidence limits for future prices.

The separate diagram normalizes assigned ATR 10 by price: 100 × 10/100 = 10%, versus 100 × 10/1000 = 1%. The quiz changes price 100→200, giving 10%→5%. This normalization does not turn ATR into return standard deviation or remove timeframe and smoothing requirements.

Turn a measurement into a separately tested rule

Choose one purpose, such as comparing actual execution costs between predefined ATR ranges. Determine boundaries using information available then, without future observations. Specify the complete sample, timestamps and units; retain cases with no expected follow-through.

A chosen ATR stop multiplier or monetary budget is a rule to assess, not an indicator requirement or loss guarantee. Different price distances do not establish net profits. Compare fills, fees, spread, slippage and funding where relevant, test a simpler alternative and reserve data not used to select settings.