Defining Volatility
In everyday language, a "volatile" investment is one whose price jumps around unpredictably. In finance, volatility has a precise definition: it is the standard deviation of an investment's returns over a given period, usually expressed on an annualised basis as a percentage.
Standard deviation measures how widely the actual returns are dispersed around the average return. If a fund has an average annual return of 10% and a standard deviation of 5%, then in roughly two-thirds of years (one standard deviation either side of the mean, assuming returns are approximately normally distributed) it will return somewhere between 5% and 15%. In about 95% of years it will return between 0% and 20%.
A fund with the same 10% average return but a standard deviation of 20% will return between -10% and +30% in about two-thirds of years — a far wider range of outcomes. Both funds have the same expected return; the more volatile one is simply far less predictable.
Annualised Volatility
Volatility is typically calculated from daily or monthly return data and then annualised. The standard approach for converting monthly volatility to annual volatility is to multiply by the square root of 12 (since there are 12 months in a year). Daily volatility is multiplied by the square root of 252 (the approximate number of trading days in a year). This square-root-of-time relationship holds under the assumption that returns are independent from day to day.
Annualised volatility figures allow meaningful comparison across funds. A fund reporting 15% annualised volatility is more stable than one reporting 25%, regardless of the frequency of underlying data used in the calculation.
What Standard Deviation Does Not Capture
Standard deviation is a useful and tractable measure of risk, but it has a significant limitation: it treats upside and downside deviations from the average symmetrically. A year in which the fund returned 30% above its average counts as equally "risky" as a year in which it returned 30% below its average.
This does not match how investors experience risk. As Daniel Kahneman and Amos Tversky demonstrated in their 1979 paper on prospect theory, losses are psychologically approximately twice as painful as equivalent gains are pleasurable. Investors are not symmetric in their responses to good and bad outcomes — they are loss-averse.
This means standard deviation systematically understates what investors find most uncomfortable about volatility: the downside. It also means that two funds with identical standard deviations but very different skewness (one with frequent small gains and occasional catastrophic losses; one with more symmetric outcomes) will be experienced very differently by investors.
When Volatility Is a Reasonable Proxy for Risk
Despite its limitations, standard deviation remains the most widely used risk measure in portfolio construction because of its mathematical tractability and its central role in the portfolio theory framework built by Harry Markowitz. When comparing funds with reasonably symmetric return distributions over the same time horizon, it is a useful first approximation.
The practical takeaway is to use standard deviation as a starting point and supplement it with drawdown measures and skewness analysis for a more complete picture of the risks an investment carries.