What it means
Volatility is not the same thing as the risk of losing money, although the two words are often used interchangeably. A share that rises 5% every single week is extremely volatile and has made nobody poorer, so what volatility really captures is uncertainty about the size of the next move rather than its direction.
The standard measure is the standard deviation of returns, which asks how far a typical period's return sits from the average return over the same window. Because the answer depends on whether you used daily, weekly or monthly data, results are scaled to a common annual basis by multiplying by the square root of the number of periods in a year.
Two versions get quoted and they answer different questions. Historical, or realised, volatility looks backwards at what prices actually did over a chosen window.
Implied volatility is derived from option prices and reflects what traders are currently paying to insure against future movement, which is why it is often described as the market's fear gauge. Volatility clusters, which is one of the most reliable patterns in finance.
Quiet periods tend to be followed by quiet periods and violent ones by more violence, which is why risk teams shorten their measurement windows during a crisis and why a comfortable long-run average can badly understate what the coming month might bring. For an operating business, volatility feeds directly into hedging costs, the price of raising equity, the size of pension deficit swings and the fair value of any traded assets sitting on the balance sheet.
Finance teams rarely need to forecast volatility, but they should know exactly which of their numbers move when it rises.
In practice
Real-world examples.
Example
A corporate treasurer prices a currency option to cover a $4,000,000 supplier payment and finds the premium has doubled since the previous quarter. Nothing about the exchange rate has changed, but implied volatility has risen sharply, so the insurance costs more.
Example
A pension trustee board sees the scheme's funding level swing by 9 percentage points in a single quarter despite no change in membership. The volatility of both equity markets and long-dated bond yields is doing the work, and the trustees respond by increasing the hedged proportion of the portfolio.
Example
A private company planning a flotation postpones it when the main volatility index doubles in a fortnight. Its bankers advise that investors demand a larger discount to the intended price when volatility is elevated, which would have cost the founders more than waiting.
Think of it
“Market volatility is how much the market moves-overall market price swings.
Formula
Calculation
Volatility for a period = standard deviation of returns over that period. Annualised volatility = period standard deviation x the square root of the number of periods in a year, which is 12 for monthly data and 252 for daily trading data.
Take five monthly returns for a share: +4%, -2%, +3%, -1% and +1%. The mean is (4 - 2 + 3 - 1 + 1) / 5 = 5 / 5 = 1%. The deviations from that mean are +3, -3, +2, -2 and 0 percentage points, and squaring them gives 9, 9, 4, 4 and 0, which sum to 26.
Using the sample formula, the variance is 26 / (5 - 1) = 6.5, so the monthly standard deviation is the square root of 6.5, which is 2.55%. Annualised, that is 2.55% x the square root of 12, and since the square root of 12 is about 3.46, volatility works out at roughly 8.8% a year. A second share with a monthly standard deviation of 5.1% would annualise to about 17.7%, exactly twice as volatile.Case study
Seen in the real world.
Marrowfield Foods is a fictional snack manufacturer, described here as an illustrative example. It bought roughly $20,000,000 of edible oils each year and had always purchased on the spot market, on the reasonable-sounding basis that prices average out over time.
Over a three-year stretch, the annualised volatility of its main input roughly doubled, and the gap between the cheapest and most expensive quarter widened from about 8% to about 22% of annual spend. Averages still worked over a decade, but the fictional company reported quarterly, and its gross margin now swung by more than 3 percentage points for reasons entirely outside management's control.
The illustrative response was not to try to predict prices. Marrowfield began hedging half of its expected annual volume on a rolling twelve-month basis, accepting a modest ongoing cost in exchange for a far narrower range of outcomes, and its board stopped spending each quarterly meeting explaining commodity movements to shareholders.
Watch out
Common mistakes.
- Treating volatility as a measure of loss, when it describes the size of movements in both directions and says nothing about which way prices will go.
- Comparing a daily volatility figure with an annual one without scaling, which understates the annual number by a factor of roughly sixteen.
- Assuming a long calm period means volatility is permanently low, when volatility clusters and quiet markets can turn violent very quickly.
Questions
People also ask.
What is the difference between historical and implied volatility?
Historical volatility measures what prices actually did in the past, while implied volatility is backed out of current option prices and reflects what traders expect ahead.
Does high volatility mean I should sell?
Not automatically, because volatility affects the range of outcomes rather than their average, though it does mean position sizes and hedging arrangements deserve a fresh look.
Why is volatility annualised?
So that measures taken from daily, weekly or monthly data can be compared on the same basis, using the square root of the number of periods in a year.
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