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Volatility Cone: Comparing Realized Volatility Across Horizons

Build and interpret a volatility cone from matched rolling windows, annualized realized volatility, historical quantiles, and documented data choices.

Updated

For education only; this is not individualized investment, legal, or tax advice. Options and other investments can lose money.

Direct answer

A volatility cone is a set of historical quantiles for realized volatility, calculated separately for several lookback horizons. For 10, 20, 60, 120, or 250 trading-day windows, a common display uses the 10th, 25th, 50th, 75th, and 90th percentiles. Joining the same quantile across horizons creates the cone.

The comparison is within the same underlying and the same return convention: “Where is today’s estimate relative to this asset’s history at a comparable horizon?” A cone is descriptive. It does not forecast direction, establish mean reversion, or prove that an option is cheap or expensive. Compare a 20-day observation with the 20-day distribution, not with the 250-day median.

This article’s example is for daily adjusted closes of a U.S.-listed equity or index, observed through 2026-08-23, with a 252-trading-day annualization convention. A different product, market session, currency, data vendor, or ex-dividend policy can produce a different cone. Your broker account type, exercise and assignment process, margin rules, and tax and disclosure obligations depend on the product and the jurisdiction where the account is held; the OCC document applies to U.S. standardized options and is not a rulebook for every market.

Construction and statistical meaning

Use one documented price series and calculate daily log returns r_i = ln(P_i/P_(i−1)). A common close-to-close sample estimator for an n-return window is:

RV_n = sqrt(252) × sqrt[Σ(r_i − r̄)^2 / (n − 1)]

Roll the window one trading day at a time, then compute each horizon’s historical quantiles. Record the security identifier, market and timezone, vendor and data vintage, adjustment policy, sample dates, missing-value rule, return definition, annualization factor, whether the current day is included, and quantile algorithm. Splits, distributions, stale prices, halts, and bad ticks can create artificial volatility.

Short windows have wider sampling distributions because a few returns and one gap can dominate the estimate. Long windows dilute isolated shocks and look smoother; that statistical smoothing does not cap long-horizon economic or gap risk.

Rolling observations are dependent. Consecutive 60-day estimates share 59 returns, so a 90th-percentile line is an empirical rank, not a 90% probability from independent trials. Report the effective observation count, test non-overlapping samples or bootstrap sensitivity, and suppress tail quantiles when the history is too short.

Close-to-close volatility includes overnight gaps but not the intraday path. Range-based and high-frequency estimators use different inputs and answer different questions. Choose the estimator before viewing the result and keep it fixed across horizons.

Matched-horizon example

Suppose five years of adjusted daily data produce:

Window 10th Median 90th Current
20 days 16% 24% 43% 46%
60 days 19% 27% 38% 31%
250 days 22% 29% 34% 28%

The current 20-day estimate is above its historical 90th percentile, the 60-day estimate is moderately elevated, and the 250-day estimate is near its median. This describes a recent concentrated shock that has not yet dominated the long window; it does not establish that 20-day volatility must fall next.

An at-the-money U.S.-listed option with 21 trading days remaining has IV of 52%. Comparing 52% with the nearby 20-day distribution can be a screening input, but IV is forward-looking option pricing while the cone is backward-looking realized volatility. If an earnings release is scheduled in 8 days and the market implies an approximately 9% event move, part of IV may price a jump absent from ordinary historical windows. 52% − 43% = 9 points is neither an arbitrage nor an expected return.

Reliable workflow and controls

  • Freeze the security, market session, currency, data vintage, adjustment policy, and as-of date before calculating.
  • Use one return definition and annualization convention across every horizon; count returns, not prices.
  • Maintain recent-regime and full-history cones, and label earnings, halts, mergers, crises, and business changes.
  • Match option remaining maturity to a nearby realized window, and separate known event variance from ordinary history.
  • Compare absolute volatility and the asset’s own-history percentile separately; a 35% level can be ordinary for one asset and extreme for another.
  • Report sample size and overlapping-window dependence; add non-overlapping or bootstrap sensitivity for tail-based decisions.
  • Keep unrounded observations and report each window’s endpoints so the result can be reproduced.
  • Use high historical quantiles for scenario calibration, never as hard risk limits; future gaps can exceed the sample maximum.
  • Reproduce results from a frozen data version before publication or a risk-limit change.
  • Treat unavailable horizons as unavailable; do not extrapolate a 250-day cone from fewer than n valid returns.

Common misconceptions

  • “Above the 90th percentile means a 90% chance of decline.” It only locates the current estimate within a historical sample.
  • “The cone predicts mean reversion.” It supplies no timing, direction, or transition probability.
  • “IV above the upper cone is automatically expensive.” IV includes forward events, skew, risk premia, liquidity, and hedging costs.
  • “The historical maximum is the worst possible outcome.” It is only the largest observation in one sample.
  • “All rolling points are independent.” Adjacent windows share nearly all their returns.
  • “Any horizon can be compared with any expiry.” Mismatches confound sampling and term effects.
  • “A smoother long window means less tail risk.” Smoothing an estimator does not remove jumps or future regime change.
  • “One sample period is objective.” Crisis inclusion, constituent survival, and changing business structure can move every quantile.

Authoritative sources

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