Glossary term
Volatility
Definition
How much a path wiggles. Not the same as ruin, and not the same as drawdown.
How it works
Volatility is the standard deviation of returns: how widely a series of periodic changes is spread around its average. It is usually quoted annualized. Daily volatility is scaled by the square root of the number of trading periods in a year, commonly √252 for daily data, because variances of independent periods add while standard deviations do not.
It is order-blind. The calculation uses the set of returns and ignores the sequence in which they arrived. That makes it stable and easy to estimate, which is why most risk machinery is built on it, and it also means volatility cannot see the thing many people worry about, which is how deep a fall gets and how long it lasts.
Worked example
Suppose a series has a daily standard deviation of 1.0%. Annualized volatility is 1.0% × √252 = 1.0% × 15.87 = about 15.9%.
Volatility also subtracts from compounded growth. Geometric growth is roughly the arithmetic average minus σ²/2. At 20% volatility the drag is 0.20² / 2 = 0.02, about two percentage points a year, so a quoted 7% average compounds at about 5%. And the course's reshuffling demonstration: thirty identical daily returns, ordered two ways, share the same 1.90% volatility yet one path has a worst drawdown of −7.2% and the other −23.1%.
Hypothetical, for education only. Not a recommendation and not a prediction.
Common mistake
The mistake is using volatility as a stand-in for the chance of a large loss, or treating a low figure as safety. A calm series can still carry a deep hole, and a lively one can have a shallow one. Volatility answers how much a path typically wiggles. Ask a different question, how bad did it get from the peak, and a different number answers it.