Volatility and uncertainty

EN source master · P05-L07 · 30 minutes estimated · needs_review

Offline formative study. No wallet connection, real funds, private keys, signatures, live trade or personal portfolio inputs. Visuals are specifications. This source master remains needs_review; completing the formative exercise does not issue certification.

Two volatility measures can disagree because they summarize different inputs, not because one discovers future direction.

True range includes gaps

True range is max(high−low, abs(high−previous close), abs(low−previous close)) [ATR]. The previous close matters when today's entire range lies above or below it. Our three-bar exercise averages true ranges arithmetically; this is a declared simple moving average of true range (SMA-TR), not TradingView's default average true range (ATR) with Wilder/relative moving average (RMA) smoothing.

Dispersion has another denominator

For sampled returns, sample variance=sum squared deviations from the sample mean divided by n−1; sample standard deviation is its square root. Sample-mean uncertainty depends on dispersion, size and assumptions [NIST]. Do not interchange a price-unit range with return percentage points.

Sampling and smoothing change the result

An hourly range, daily range and close-to-close return lose different information. A longer smoother can lag a sudden regime change. Missing extreme prices can understate range; sampled closes can conceal large intrabar paths. Annualization would require an explicit sampling calendar and dependence assumptions; none is used here.

Volatility is not direction

High true range can arise in either direction. A large average is neither a target nor a safe stop distance. Extrapolating historical dispersion into a stable future regime can create false confidence. Recompute if previous close, high/low or sample membership changes. Preserve the measurement choice, lookback and limitations rather than inventing a predictive interval.

• True range: largest declared range/gap distance.
• Sample standard deviation: dispersion around the sample mean with n−1 denominator.
• Price-unit range: absolute units, unlike percentage returns.
• Regime dependence: measurement may change when conditions change.

ILLUSTRATIVE bars A/B/C: previous close for A=100; A high105 low103 close104; B high106 low102 close103; C high104 low100 close101. Separate return sample R=[−2%,0%,+2%]. These are independent fixtures; R is not derived from the A/B/C closes.

High/low range marks, previous-close markers and TR labels 5/4/4; separate percentage-return dispersion panel. Identify incomplete OHLC (opens absent), no invented candles.

The two declared fixture measurements with their separate units and datasets.

A direction, a future confidence band, an annualized forecast or market safety.

• OBSERVED: FIX-P05-L07 stipulates A low=103 and previous close=100.
• INFERRED: A true range=5 includes the gap.
• UNKNOWN: future regime and within-bar ordering.
• INSUFFICIENT EVIDENCE: measured volatility guarantees a future loss bound.

• Using high−low only despite a gap.
• Calling SMA-TR default ATR.
• Mixing price units and percentage points.

Calculate each true range and the three-bar SMA-TR. For R, compute mean, sample standard deviation and population-denominator alternative. Explain why neither yields direction.

Deliver calculations or annotations, claim/source table and limitations. Suggested allocation: study 12 minutes, exercise 8, correction/quiz 10; estimate subject to calibration.

• Preserve previous close and extremes.
• Name smoothing and estimator.
• Keep units separate.
• Avoid unstated annualization.

Volatility comparisons require named inputs, units, estimators and smoothing; neither range nor dispersion predicts price.

• Compare range-based and return-dispersion measures.
• Keep estimator, units and gap coverage visible.

P05-L08 after correction review.

NONE in the authoritative catalog. The supplied offline fixture/package is sufficient; no paid feature or unverified Production capability is required. Lab/certification metadata denotes downstream associations, not access gates or live awards.

• [ATR] TradingView — ATR — True-range construction and smoothing choice. Checked 2026-10-01; locator turn10view3.
• [NIST] NIST — Confidence limits for mean — Sample-mean uncertainty depends on dispersion, size and assumptions. Checked 2026-10-01; locator turn11view4.