Volatility

A measure of dispersion, not of direction. It comes in two families that are frequently confused. Realised or historical volatility is computed from returns that have already happened. Implied volatility is backed out of option prices and describes what the market is currently paying for movement between now and an expiry. One looks backwards at a record, the other forwards at a price, and they routinely disagree.

The standard calculation takes the returns over a chosen interval, computes their standard deviation, and scales that figure to a year by multiplying by the square root of the number of such intervals in a year. The window is part of the answer rather than a detail of it, since a measure over twenty days and a measure over a year describe different things about the same market. Range based measures such as the average true range answer a related question in price units rather than in percentages, and they are not interchangeable with a standard deviation.

The scaling is where the honest caveat sits. Multiplying by the square root of time assumes returns are independent of one another and drawn from the same distribution, and market returns are neither: quiet periods and violent periods cluster, and large moves occur more often than a normal distribution allows for. Statisticians and practitioners have argued for decades about which estimator handles that best, and the argument is unresolved. The related trap is treating a low reading as low risk. A rate held inside a narrow band by policy, as under a currency peg, records very low volatility for as long as the arrangement holds and describes the arrangement rather than the currency.