Beta and Volatility
Two different measures of movement. Historical volatility says how much a security moves; beta says how much of that movement is shared with the market.
MadStockAlerts Research · Updated August 28, 2026
What to take away
- Historical volatility is the dispersion of a security's own returns.
- Beta is the sensitivity of those returns to the market's.
- A high-volatility stock can have a low beta if its movement is idiosyncratic.
- Both are estimated from a chosen window, and the estimate changes with the window.
- Diversification reduces idiosyncratic risk and does nothing to beta.
- Every published beta depends on an unstated window, frequency and benchmark, so two providers can differ by a third.
MAD Academy Training Video · 0:45
Beta Is a Backward-Looking Average
Beta describes how a stock moved with the market over a past window, and it goes missing in exactly the conditions you would want it for.
This lesson is part of a Stock Alerts + Tools plan.
Volatility
Historical volatility is the standard deviation of returns, usually annualised. It is directionless: a security that rose thirty percent and one that fell thirty percent in equally jagged fashion have similar volatility.
annualised volatility = standard deviation of daily returns x sqrt(252)
- 252 is the conventional count of US trading days in a year
It is distinct from implied volatility, which is derived from option prices and describes what the market expects rather than what has happened. The two frequently disagree, and the gap between them is itself a traded quantity.
Beta
beta = covariance(security, market) / variance(market)
| Beta | Interpretation |
|---|---|
| Above 1 | Historically moved more than the market, in the same direction |
| About 1 | Moved roughly with the market |
| Between 0 and 1 | Moved with the market but less |
| Below 0 | Moved against the market; rare and usually unstable |
Beta is a historical regression coefficient, not a property of the company. It describes how the two return series happened to co-move over the window measured, and it changes when either the window or the benchmark changes.
The distinction that matters
A biotech awaiting a trial result can be enormously volatile and have a beta near zero, because its movement is driven by an event that has nothing to do with the index. High volatility with low beta is idiosyncratic risk; high beta is amplified market risk. Diversification reduces the first and does nothing to the second.
This is why a portfolio of thirty high-volatility, low-beta names can be less exposed to a market decline than a portfolio of five high-beta ones, despite every individual holding in the first looking more dangerous.
Both are estimates
Beta computed on two years of weekly returns and beta computed on five years of monthly returns give different answers for the same stock, and neither is wrong. Providers use different windows and different benchmarks, which is why quoted betas disagree between sources.
Both are also backward-looking. A company that has changed materially, through a large acquisition, a divestiture or a shift in its business mix, may have a historical beta that no longer describes it at all.
How beta is estimated, and why it moves
Beta is the slope of a regression of a security's returns against a benchmark's, and every published beta therefore depends on three choices that are rarely stated alongside the number.
- The window: two years of weekly returns and five years of monthly returns produce different numbers for the same security.
- The frequency: daily returns pick up short-term noise and microstructure effects that monthly returns average out.
- The benchmark: beta against a broad index and against a sector index are different quantities.
- Adjustment: many providers shrink the raw estimate toward 1, on the empirical finding that betas revert over time.
The consequence is that two data services can publish betas for the same company that differ by a third, with neither being wrong. It also means beta is a backward-looking estimate carrying real standard error, not a property of the security.
Beta also assumes the relationship is linear and stable, and it is neither during a crisis. Securities that behaved independently for years can move together in a stress period, which is exactly when a beta estimate is being relied upon.
Realised and implied volatility
Volatility comes in two forms measuring different things, and conflating them is one of the more consequential errors in reading a security's risk.
| Realised | Implied | |
|---|---|---|
| What it measures | How much price actually moved | How much the option market expects it to move |
| Computed from | Historical returns | Option prices, solved backwards |
| Direction in time | Backward-looking | Forward-looking, over the option's life |
| Behaviour around events | Rises after | Rises before, and collapses after |
The last row is the practically important one. Implied volatility rises ahead of a scheduled event because the range of outcomes widens, and it collapses immediately afterwards once the outcome is known. Realised volatility does the opposite: it is low before and spikes after.
Implied volatility also encodes a market-implied expected move, which is a direct statement of how large a reaction is already priced. That makes it useful even to someone who never trades an option, as a measure of what a result would have to beat to be a surprise.