Volatility
Volatility measures the spread of returns. It's a useful but incomplete risk measure, since it treats upward and downward moves the same.
Volatility says how much a price swings around its average. High volatility means large moves in both directions.
It's often equated with risk, and that's only partly right. A price that swings sharply upward has high volatility, but nobody experiences that as risk.
What volatility also fails to capture is the danger of a permanent loss. A company reliably, slowly going bankrupt has low volatility and maximum risk.
It's still useful, since it's measurable and comparable. Just read it alongside other measures, especially maximum drawdown, which describes what you actually had to live through.
Volatility is usually stated as the annualized standard deviation of log returns. Annualizing multiplies by the square root of the number of periods, which assumes independent returns. With autocorrelation present, as it is for illiquid assets with smoothed valuations, this method substantially understates actual volatility.
Standard deviation assumes a symmetric treatment of deviations. Alternatives include semivariance, which only counts negative deviations, and quantile measures like value at risk and expected shortfall beyond that quantile. The latter is preferable to value at risk, since it actually accounts for the shape of the tail.
Financial-market returns empirically show volatility clustering: periods of high fluctuation get followed by more of the same. Models of this family describe that effect and explain why volatility is short-term forecastable while return direction isn't. It follows that managing risk is easier than forecasting return.
Summary
- Volatility treats upward and downward moves the same.
- It doesn't capture the danger of a permanent loss.
- Volatility is forecastable; direction isn't.
Did you get it?
Why is volatility an incomplete risk measure?
Because it measures symmetrically and doesn't capture permanent losses.
When does the usual calculation understate volatility?
For illiquid assets with smoothed valuation and the resulting autocorrelation.
What is volatility clustering?
Periods of high fluctuation get followed by more of the same, which makes volatility short-term forecastable.