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Volatility Cone: Comparing Realized Volatility Across Horizons

For educational purposes only; not investment advice.

Direct answer

Section titled “Direct answer”

A volatility cone shows the historical distribution of realized volatility separately for multiple measurement horizons. For each rolling window, such as 10, 20, 60, 120, or 250 trading days, it plots selected quantiles—often the 10th, 25th, 50th, 75th, and 90th percentiles. Connecting equal quantiles across horizons forms the cone.

Its valid question is: “Where does today’s volatility sit relative to this asset’s own history at a comparable horizon?” It does not predict the next move, prove mean reversion, or declare an option cheap or expensive. A 20-day observation belongs against the historical 20-day distribution, not the 250-day median.

Construction and statistical meaning

Section titled “Construction and statistical meaning”

Using adjusted closing prices, calculate consistent daily log returns r_i = ln(P_i/P_(i−1)). One common close-to-close estimator for an n-day 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. Save the price source, adjustment policy, timezone, sample dates, missing-value treatment, return definition, annualization factor, whether the current day is included, and quantile algorithm. Splits, special distributions, stale prices, and bad ticks can manufacture false volatility.

Short windows usually have wider distributions because a few returns and one gap dominate the estimate. Longer windows dilute isolated shocks and appear smoother. That sampling effect does not mean long-horizon economic risk is naturally bounded.

Rolling observations are strongly dependent. Consecutive 60-day estimates share 59 returns, so a 90th-percentile line is an empirical rank, not an independently estimated “90% probability.” Show observation counts, consider non-overlapping robustness samples, and avoid quantiles where history is too short.

Close-to-close volatility includes overnight gaps but not the intraday path. Range-based estimators use other information and can answer a different question. Pick the estimator before looking at the result and keep it constant across the comparison.

Matched-horizon example

Section titled “Matched-horizon example”

Suppose five years of adjusted data produce these realized-volatility quantiles:

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

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

An ATM option with 21 trading days remaining has IV of 52%. Comparing 52% with the nearby 20-day distribution can be a useful screen, but IV is forward-looking option pricing while the cone is backward-looking realized volatility. If earnings occur in 8 days and the market implies a roughly 9% event move, much of the IV may represent a future jump absent from ordinary historical windows. 52% − 43% = 9 points is not an arbitrage or expected return.

Reliable workflow and controls

Section titled “Reliable workflow and controls”
  • Use total-return or otherwise correctly adjusted data and document every transformation.
  • Calculate multiple horizons with one return definition and annualization convention.
  • Maintain both a recent-regime cone and a full-cycle cone; explain why they differ.
  • Mark earnings, halts, mergers, crises, and structural business changes instead of silently mixing regimes.
  • Match option remaining maturity to a nearby realized window and separate known event variance.
  • Compare absolute level and own-history percentile separately; a 35% stock can be ordinary while 25% is extreme for another asset.
  • Report sample size and overlapping-window dependence; add non-overlapping or bootstrap sensitivity where decisions rely on a tail quantile.
  • Use historical high quantiles for scenario calibration, never as hard risk limits. Future gaps can exceed every observation.
  • Reproduce results from frozen data versions before publishing or changing a risk limit.
  • Treat unavailable horizons as unavailable. Do not extrapolate a 250-day cone from fewer than 250 valid returns.

Common misconceptions

Section titled “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 premium, liquidity, and hedging costs.
  • “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.” Mismatched horizons 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 materially move every quantile.
Section titled “Related topics”

Authoritative sources

Section titled “Authoritative sources”