Stock Return Volatilitybeginner

Stock Return Volatility

Stock return volatility (SRV) measures how widely a stock's returns scatter around their own average over a window of time. The standard proxy is the standard deviation of returns, the square root of their variance. A higher SRV means returns swing more violently in both directions, so the equity is harder to value, riskier to hold, and more expensive to hedge. Crucially, SRV is total dispersion, not the portion explained by the market, which keeps it distinct from systematic risk.

Try it yourself

Volatility vs systematic risk

Three numbers, two different ideas. Standard deviation and the High-Low range both measure volatility — total risk. CAPM beta measures systematic risk — sensitivity to the market. Beta is not a volatility measure. Push the volatility slider and watch σ move while beta barely flinches.

Annualised volatility σ (close-to-close)0.3%

Volatility · total risk

σ, std dev (ann.)0.3%

σ, High-Low (ann.)0.4%

Both proxy the size of the swings (close-to-close σ and the Parkinson 1/(4 ln 2) range). Driven by the volatility slider.

Systematic risk · market sensitivity

CAPM beta β0.87

Slope of stock-vs-market excess returns. β = Cov(R_i,R_m)/Var(R_m). Systematic share R² = 13%. Driven by the beta slider.

Daily σ 2.0%High-Low daily σ 2.3%Stock–market corr 0.36

Firm-specific volatility (σ target, ann.)25%

Market beta β (true loading)1.1

σ (std dev) and the High-Low range track the size of the swings; beta tracks co-movement with the market. Move the volatility slider and σ changes while beta stays put. That is why listing CAPM beta as a volatility proxy is a category error.

Try this: load the meme-stock preset. Total σ rockets but beta sits near zero, the GameStop lesson: extreme volatility, almost no systematic risk.

Why it matters

Picture two stocks that both averaged a 1% daily return last quarter. One drifted quietly between 0% and 2% each day; the other lurched from minus 6% to plus 8%. Same mean, wildly different volatility. Volatility is the width of that daily swing, not its direction. A wide swing tells you the future is fuzzy, which is exactly why volatile firms pay more to borrow, face more distress risk, and demand a fatter risk premium from investors.

Formulas

Return standard deviation (the SRV proxy)

\mathrm{SRV} = \sqrt{\tfrac{1}{n-1}\sum_{i=1}^{n} (R_i - \bar R)^2}

The sample standard deviation of the

n

periodic returns

R_i

around their mean

\bar R

. Dividing by

n-1

rather than

n

corrects the downward bias of the sample variance.

Annualizing daily volatility

\sigma_{\text{ann}} = \sigma_{\text{daily}} \times \sqrt{252}

Under the i.i.d. assumption (independent returns, constant variance), volatility scales with the square root of the horizon. Roughly 252 trading days fill a year. The scaling breaks under volatility clustering or serial correlation.

Worked examples

Scenario

A VNIndex-listed firm posts daily returns over a month with a mean of 0.10% and a sample standard deviation of 1.80% per day. Express this as an annualized volatility.

Solution

The daily SRV is already 1.80%. Annualize it as $\sigma_{\text{ann}} = 1.80\% \times \sqrt{252} \approx 1.80\% \times 15.87 \approx 28.6\%$ . That figure is the stock's total return volatility for the year, the raw dispersion an investor or a distress model would feed in, with no attempt yet to split market-driven from firm-specific movement.

Scenario

GameStop (GME), January 2021. Driven by a retail short squeeze, the stock rose from about 17 dollars at the start of the month to an intraday high near 483 dollars late in January, with double-digit daily moves in both directions and several trading halts. What does this show about realized volatility?

Solution

GameStop is an extreme illustration of high realized volatility: returns scattered enormously around their mean, so the standard deviation of its daily returns spiked far above its normal level. Two lessons stand out. First, volatility captures the *size* of the swings, not their direction, the stock soared and then crashed, and both legs are volatility. Second, this was overwhelmingly firm-specific (a squeeze in one name), so it is total volatility, not systematic risk: GameStop's market beta did not explain the move. A distress or risk model fed this raw dispersion would flag the stock as extraordinarily risky to hold or hedge.

Common mistakes

✗Volatility measures the direction of returns. It measures the dispersion of returns around their mean, so a stock can have high volatility while trending up, down, or sideways.
✗CAPM beta is a measure of volatility. Beta measures systematic risk, the sensitivity of a stock to market moves, not total dispersion. A low-beta stock can still be highly volatile if most of its swings are firm-specific. Treating beta as an SRV proxy is a category error.
✗A stock with a higher average return must be more volatile. The mean and the standard deviation are separate moments; a high-return stock can be calm and a low-return stock can be wild.
✗Volatility is constant through time. Realized volatility clusters: quiet stretches and turbulent stretches arrive in runs, which is why a single historical number can mislead in a crisis.

Revision bullets

•SRV = how widely returns scatter around their own mean
•Standard proxy is the standard deviation of returns (use $n-1$ )
•Volatility is total dispersion, not market sensitivity
•Annualize daily volatility by $\sqrt{252}$ under i.i.d. returns
•Beta is systematic risk, a different concept from volatility

Quick check

Two stocks have the same average return last quarter, but stock A's daily returns ranged from minus 1% to plus 3% and stock B's from minus 7% to plus 9%. Which has higher stock return volatility?

Why is dividing by $n-1$ rather than $n$ used in the sample standard deviation of returns?

Connected topics

SRV → Distress Volatility Measures Managing SRV Systemic vs Systematic

Sources

Bekaert & Harvey (1997), JFE
Bekaert, G., & Harvey, C. R. "Emerging Equity Market Volatility." Journal of Financial Economics, 43(1), 29-77, 1997.
Models the standard deviation of equity returns as the central measure of stock-market volatility, with emerging-market evidence relevant to Vietnam.
Schwert (1989), JF
Schwert, G. W. "Why Does Stock Market Volatility Change Over Time?" Journal of Finance, 44(5), 1115-1153, 1989.
Foundational study of time-varying realized volatility and its links to leverage and economic activity.
SEC Staff Report (2021)
U.S. Securities and Exchange Commission. "Staff Report on Equity and Options Market Structure Conditions in Early 2021." October 2021.
Official account of the January 2021 GameStop episode, the extreme realized volatility, short interest, and trading halts.

How to cite this page

Dr. Phil's Quant Lab. (2026). Stock Return Volatility. Derivatives Atlas. https://phucnguyenvan.com/concept/frm-stock-return-volatility

← Back to the atlas See in the network →