Historical Volatility

Historical volatility is the realised dispersion of returns over a chosen window, scaled to a year so that a daily number can be compared with an option's implied volatility. A stock with 20 percent historical volatility has had daily moves whose annualised spread is about that. It is not a forecast. It is a description of the window you chose. Change the window and the number changes, sometimes a lot, after a crash enters or leaves it.

Traders compare historical volatility with implied volatility. If options price a much higher move than the stock has recently realised, option buyers are paying up for future uncertainty, which may be earnings or may be expensive premium. If implied sits below realised, options may be cheap relative to what the stock has actually been doing. Neither comparison is a trade by itself. The event calendar matters.

Use historical volatility to scale expectations. A 1 percent day is ordinary for a 30 percent name and a shock for a 10 percent name. Use it to compare the option market's price of movement with the movement that already happened. Use a sudden rise in the number as a regime flag: stops, size, and the meaning of a "small" pullback have all changed.

Treating the annualised number as the expected move for tomorrow. A 16 percent annual figure is not a 16 percent day. The daily scale is roughly the annual number divided by the square root of 252, and even that is a dispersion, not a prediction. Also using a window that quietly includes or excludes one crash.

Log-return standard deviation assumes the window is one regime. Markets change regime inside the window. The number will look calm the day before the break and will look high after, which is when you already know. It also ignores the direction of the moves.