Volatility Cone

Ask a local "is it cold today?" and the honest answer needs context: cold for July, or cold for January? A meteorologist answers by showing you the historical range of temperatures recorded on that calendar date over many years — today's reading only means something next to that range. A volatility cone does the same job for options. It doesn't tell a trader whether volatility will rise or fall; it tells them where today's volatility sits relative to history, at a given time horizon, so "18% implied vol" stops being a bare number and becomes cheap, rich, or ordinary.

Building the cone

For each maturity — say 1 month, 3 months, 6 months, 1 year — take every historical window of that length in the price history and compute the realized volatility over each one:

$$\sigma_{\text{realized}} = \sqrt{\frac{252}{n-1}\sum_{i=1}^{n} (r_i - \bar r)^2}.$$

In words: $r_i$ is the daily log return on day $i$, $\bar r$ is the average daily return over the window, $n$ is the number of trading days in the window, and $252$ annualizes a daily variance into a yearly one by scaling up for the roughly 252 trading days in a year. Do this for every rolling window of a given length and you get a distribution of realized vols for that maturity. Plot the minimum, some low percentile (say 10th), the median, a high percentile (90th), and the maximum, at each maturity — the resulting shape, wide at short maturities and narrowing as they stretch out (because averaging over longer windows smooths out noise), is the cone.

Worked example 1 — reading the cone

Suppose a stock's 3-month realized vol, computed over every rolling 3-month window in the last five years, has ranged from a low of 14% to a high of 42%, with a median of 22%. Today's 3-month implied volatility, quoted by the options market, is 19%. That sits below the median and closer to the low end of the historical range — a trader reads this as implied vol being cheap relative to the stock's own history, a candidate for buying volatility (e.g., a long straddle) rather than selling it, all else equal.

Worked example 2 — computing one point on the cone

Take five overlapping weekly windows of daily log returns and suppose their annualized realized vols come out to 18%, 21%, 25%, 19%, 30%. Sorted: 18, 19, 21, 25, 30. The median (middle value) is 21%; the range is 18% to 30%. That single 1-week maturity point on the cone would be plotted as a bar from 18% to 30% with a mark at 21%. A real cone uses hundreds of overlapping windows per maturity, not five, but the arithmetic — sort the realized-vol samples, read off percentiles — is identical.

The bell curve above stands in for the distribution of realized-vol samples that feed one point on the cone — drag the mean and spread and watch how a wider historical range produces a taller, flatter cone band at that maturity, exactly the effect a stock going through a volatile stretch has on its own cone.

What this means in practice

Volatility cones are a cheap first screen before a vol trade: is implied rich or cheap versus this name's own history, at this maturity? Vol desks use them alongside the implied volatility surface — the cone adds the historical dimension the surface alone doesn't show. They're most useful for relative judgments across maturities on the same underlying, not for comparing across different stocks, since every name has its own typical vol regime.