Volatility

Volatility is the degree to which the price or return of an asset moves up and down over time. A share whose price lurches several percent a day is highly volatile; a short-term government bill whose value barely changes has low volatility. In finance the word usually refers to a specific number: the annualised standard deviation of returns, expressed as a percentage.

There are two main kinds. Historical, or realised, volatility is measured from past prices. Implied volatility is worked out from the prices of options and shows how much movement the market expects in future. Volatility is often treated as a stand-in for risk, but the two are not identical: volatility measures the size of swings in both directions, while most investors worry mainly about losses.

Think of two lakes. On one, the water is almost always flat; on the other, the surface is choppy and waves rise without warning. A small boat can cross either lake, but the trip across the choppy one is more nerve-racking and more likely to end with someone getting wet.

Volatility describes how choppy the water is for an investment. It does not say whether the investment will end up higher or lower, only how rough the ride is likely to be along the way. Historical volatility looks back at how big the waves were. Implied volatility is closer to a weather forecast, built from what people are willing to pay for protection against storms.

Historical volatility starts with the standard deviation of daily, weekly or monthly returns over a chosen window, such as 30 days or one year, and then scales it to a yearly figure:

• $\sigma_{\text{period}}$ is the standard deviation of returns for each period, such as each trading day.
• $n$ is the number of such periods in a year, about 252 for trading days, 52 for weeks or 12 for months.
• $\sigma_{\text{annual}}$ is the annualised volatility.

If a share's daily returns have a standard deviation of 1%, its annual volatility is about 1% × √252 ≈ 1% × 15.9 = 15.9%. If the daily figure doubles to 2%, annual volatility doubles to about 31.7%. Returns are usually measured as the logarithm of the price ratio from one day to the next, which makes them easier to add up across periods.

Volatility clusters: calm periods tend to follow calm periods and turbulent ones follow turbulent ones. Robert Engle's ARCH model (1982) and Tim Bollerslev's GARCH extension (1986) were built to capture this pattern, and Engle shared the 2003 Nobel memorial prize in economics for the work.

An option's price depends on how much the underlying asset is expected to move before the option expires. Pricing models such as the one published by Fischer Black and Myron Scholes in 1973, extended by Robert Merton, can be run in reverse: given the option's market price, they produce the volatility the market is implicitly assuming. That figure is implied volatility. When implied volatility differs across strike prices, traders speak of a volatility "smile" or "skew", a pattern that became pronounced in equity options after the October 1987 crash.

The best-known measure is the Cboe Volatility Index (VIX), often called the "fear gauge". Cboe introduced it in 1993, originally based on at-the-money options on the S&P 100. In September 2003 Cboe changed the method to use a wide range of options on the S&P 500, so that the VIX now estimates the market's expectation of S&P 500 volatility over the next 30 days. Futures on the VIX began trading in 2004 and options in 2006. The VIX tends to jump when shares fall sharply; its highest close on record was 82.69 on 16 March 2020, during the COVID-19 market crash.

Products linked to volatility carry their own risks. On 5 February 2018 the VIX more than doubled in a single day, and several exchange-traded products that had bet on volatility staying low lost most of their value, leading to the closure of at least one.

• Economic surprises. Unexpected changes in inflation, interest rates or growth figures, and fears of recession, move whole markets.
• Company news. Earnings reports, mergers and lawsuits cause large moves in single shares.
• Liquidity. Assets with thin trading volume or poor liquidity can move sharply on small orders.
• Leverage. Investors using borrowed money may be forced to sell when prices fall, through a margin call, which deepens declines.
• Crises and shocks. Events such as the 2008 financial crisis produce long spells of high volatility.

Asset classes differ widely. Cash and short-term Treasury bills are the least volatile; investment-grade bonds sit higher; broad equity indices higher again; and single shares, commodities and cryptocurrencies such as Bitcoin are typically the most volatile.

Volatility is built into many investment tools. It is the denominator of the Sharpe ratio, a key input in option pricing and in banks' value-at-risk models, and a factor in setting margin requirements. Some funds target a fixed level of volatility, cutting exposure when markets become choppy. Fund documents in the European Union rank funds on a risk scale that is driven in large part by volatility.

For long-term investors, volatility matters most when they might be forced to sell at a bad time. A volatile asset held for decades may be appropriate for one investor and unsuitable for another with a shorter time horizon or lower risk tolerance, which is why it sits at the centre of the risk–return trade-off. Volatility is also distinct from beta, which measures only how much of an asset's movement is tied to the market as a whole.

• Cboe Volatility Index (VIX)