What is daily volatility (σ) in a stock forecast?
Daily volatility (σ) is the typical day-to-day price swing for a stock, in dollars: one standard deviation of daily price changes over a trailing window. It is the primary diffusion parameter fed into the Schrödinger-equation solver that drives the quantum forecast — higher σ widens the CI90 confidence band directly, because a stock that swings more day to day genuinely has a wider range of plausible future outcomes. Annualised volatility is roughly σdaily × √252, the standard trading-day scaling used across the industry.
Realized vs. implied volatility
Quantustik's σ is realized volatility, computed from actual historical price changes — not implied volatility (the volatility the options market is currently pricing in, backed out of option premiums). The two often diverge: implied volatility can spike ahead of a known event like earnings even when recent realized volatility has been calm, because the options market is pricing forward-looking uncertainty rather than reading the recent past. A large gap between the two is itself a signal worth watching, though Quantustik's forecast band is driven by the realized figure.
Live example: AAPL's current beta is 1.10 against the S&P 500 — one input the quantum model uses to calibrate its diffusion (the volatility term) for this ticker. See the full AAPL forecast for the current CI90 band this volatility estimate produces.
Why volatility matters for position sizing
Volatility feeds directly into risk-first position sizing: higher σ means a wider stop-loss is needed to avoid being shaken out by normal noise, which in turn shrinks the recommended position size for a given dollar-risk budget. A high-beta, high-σ name and a low-beta defensive name with the same expected return should never get the same position size.
Frequently asked questions
What is the difference between realized and implied volatility?
Realized volatility is computed from actual historical price moves; implied volatility is backed out of current options prices and reflects forward-looking market expectations. Quantustik's forecast band is driven by realized volatility.
Why does higher volatility widen the CI90 band?
The band width comes directly from the diffusion term in the quantum model's forecast equation — a stock with a larger daily standard deviation of price changes has a genuinely wider range of plausible outcomes at any future horizon.
How does volatility affect position sizing?
Higher volatility requires a wider stop-loss to avoid normal noise triggering an exit, which reduces the recommended position size for a fixed dollar-risk budget — see the Kelly position size page.
Educational research only — not investment advice.