SV · Statistical indicators
Probability cone
Also called: volatility cone, price cone, expected range cone
A probability cone projects a range of future prices that widens with the square root of time, scaled by volatility and a chosen confidence level.
Definition
A probability cone is a chart overlay that draws upper and lower price bands forward in time from the current price. The bands mark where price would stay with a chosen probability, such as one or two standard deviations, under a model of returns, usually lognormal with constant volatility.
The bands widen as the horizon grows, so the overlay looks like a cone opening to the right.
Intuition
Uncertainty compounds with time. If daily returns are independent with the same volatility, the standard deviation of the cumulative return grows with the square root of the number of days. The cone makes that visible: it shows what a normal-sized move looks like at each future date given current volatility.
Traders use it to frame targets and stops against what volatility alone would produce, and to see when price has moved further than the assumed model considers usual.
How it's calculated
With current price S0, annualized volatility σ, horizon t in years, and z the number of standard deviations:
Upper(t) = S0 · exp(μt + zσ√t) Lower(t) = S0 · exp(μt − zσ√t)
Many cones set the drift μ to zero, or to −σ²/2 so the center tracks the median of a lognormal. For two-sided coverage, z = 1 corresponds to about 68% and z = 2 to about 95% under a normal distribution.
The volatility input can be realized (historical) volatility, a forecast such as GARCH, or implied volatility from options. Implied volatility gives a market-implied cone; realized volatility gives a backward-looking one.
Example: with price 100, annual volatility 20% and a three-month horizon (t = 0.25), the one-sigma cone with zero drift spans 100 × e±0.10, about 90.5 to 110.5, and the two-sigma cone spans about 81.9 to 122.1.
How to read it
Price touching an outer band means the move so far is large relative to the assumed volatility, not that it must reverse. Fat tails mean real prices leave a two-sigma band more often than the normal model suggests.
Compare cones built with implied and realized volatility: when the implied cone is much wider, options are pricing more movement than recent history shows.
Common mistakes
- Treating band edges as support and resistance.
- Assuming normal coverage probabilities hold exactly; real returns have fatter tails.
- Using annualized volatility with a horizon measured in calendar days without converting consistently (252 trading days versus 365 calendar days).
- Keeping a stale volatility input after a regime change.
In Saqrid
SV's 100 built-in proprietary formulas include probability-cone and expected-move tools, alongside Hurst, entropy and momentum formulas.
Open SV.
Go deeper
Saqrid Institute lesson: The Normal & Lognormal Return Model. Lesson text is open to read without an account.