Volatility

Volatility is the degree to which a measured quantity varies over time. Applied to investments it means the dispersion of returns around their average: a holding whose annual results cluster tightly around 6 percent has low volatility, and one that swings between 40 percent and negative 25 percent has high volatility, even if both average the same thing over a decade. The same idea applies outside markets. Someone whose self-employment income swings between a lean quarter and a busy one has volatile income, measured the same way.

The statistic almost always used is standard deviation, reported as an annual figure so that daily, monthly and yearly data can be compared. It is a description of past or expected movement, and by construction it is symmetric. A year in which a fund gains 30 percent contributes to its measured volatility exactly as much as a year in which it loses 30 percent.

That symmetry is the reason the page exists, because it is where the everyday use of the word and the statistic part company. Investors use "volatile" to mean "frightening", and the number does not distinguish frightening from delightful. FINRA's own framing of risk is much closer to what a household actually cares about: "risk is any uncertainty with respect to your investments that has the potential to negatively impact your financial welfare". That definition points at outcomes and at your circumstances. A standard deviation points at the width of a distribution and knows nothing about your goals, your time horizon or whether you would be forced to sell.

Two consequences follow, and they run in opposite directions. Volatility can overstate danger for someone who will not touch the money for thirty years, because the swings resolve into a long-run result and nothing forces a sale at the bottom. And it can badly understate danger where the real exposure is not captured by ordinary price movement at all: an illiquid asset that is infrequently priced can show low measured volatility while carrying a real chance of permanent loss, and a portfolio can look calm right up to the point at which something breaks. Low measured volatility is a statement about how the price has behaved, not a promise about what can happen.

There are two families of measure and confusing them is common. Realized or historical volatility is computed from prices that have already happened, so it is a fact about the past. Implied volatility is extracted from the prices of options, so it is a reading of what market participants are collectively paying to hedge, and it describes an expectation about the future. The best known implied measure is the VIX, which Cboe describes as "a leading measure of market expectations of near-term volatility conveyed by S&P 500 Index (SPX) option prices", introduced in 1993 and characterized by Cboe as a barometer of investor sentiment and market volatility. A high VIX is a statement that options are expensive, which is another way of saying market participants expect a wide range of outcomes. It is not a forecast of direction.

A separate and frequently confused point is that volatility drags on the compounded result: a sequence of returns with more variation ends up behind an equally averaged but smoother sequence. That is a property of compounding rather than of the volatility statistic itself, and it belongs to the page on annualized return, which sets it out with a worked illustration. Related but distinct again is sequence of returns risk, which is about the order in which results arrive rather than their spread, and which matters specifically to a portfolio being drawn on.

One property of standard deviation is worth knowing precisely because it is a limitation: it ignores order entirely. Reshuffle a decade of annual returns into any sequence you like and the standard deviation is unchanged, even though a retiree drawing income would experience the shuffles very differently. Any measure that treats a set of returns as a bag of numbers cannot say anything about that, which is one more reason to keep it as one input rather than as a summary of risk.

Standard deviation is computed by taking each period's return, measuring how far it sits from the average return, squaring those distances, averaging the squares, and taking the square root. Squaring is what makes the measure symmetric: a shortfall and an overshoot of the same size contribute equally. The result is expressed in the same units as the returns, so a portfolio with an average annual return of 7 percent and a standard deviation of 12 percentage points is being described as having produced results that commonly landed somewhere either side of 7 by roughly that much.

A hypothetical illustration, using numbers chosen so the arithmetic is visible. Suppose a fund's four annual returns are plus 15 percent, minus 5 percent, plus 15 percent and minus 5 percent, and treat those four years as the whole record rather than as a sample. The average is 5 percent. Every year sits exactly 10 percentage points away from that average, so every squared distance is 100, the average of the squares is 100, and the standard deviation is the square root of 100, which is 10 percentage points. A second fund that returned exactly 5 percent in each of those four years has the same average and a standard deviation of zero. The two funds ended in almost the same place and one of them was a great deal harder to hold.

In practice the figure is usually computed from monthly or daily returns and then annualized, which is why the same fund can be quoted with different volatility numbers by different sources. Comparing two figures is only meaningful if the measurement period and the data frequency match. A fund with a lower reported standard deviation measured over three years may simply have been measured across a calmer stretch of market history than its competitor.

What the measure is good for

• It compresses a long, noisy return history into a single comparable number.
• It is standardized enough that two funds measured the same way over the same period can be sensibly compared.
• Implied measures such as the VIX give a live reading of what market participants expect rather than only what has already happened.
• It is a reasonable proxy for how uncomfortable a holding is likely to be, which matters because discomfort is what drives people to sell at the wrong time.

Where it misleads

• It is symmetric, so an unusually good year raises it exactly as much as an unusually bad one.
• It ignores the order of returns entirely, which is precisely what matters to someone drawing income from a portfolio.
• Infrequently priced assets can report low volatility while carrying a real chance of permanent loss, so a low number is not evidence of safety.
• It says nothing about your horizon, your income stability or whether you could be forced to sell, all of which determine what a given swing actually costs you.
• Figures computed over different periods or from different data frequencies are not comparable, and it is rarely obvious from a fact sheet which was used.