Stock Return Volatilityintermediate

Measuring Realized Volatility

Realized volatility can be proxied in more than one way. The return standard deviation uses closing prices: it is the spread of periodic returns around their mean. The High-Low range estimator instead uses each period's intraday high and low, on the logic that the trading range itself reveals how far the price travelled even when it closes near where it opened. Range-based estimators are often more efficient with limited data. A common pitfall is to call CAPM beta a volatility measure: it is not. Beta is systematic risk, the stock's sensitivity to the market, and belongs to a different family entirely.

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

Closing prices alone can hide a stormy day that ends calmly, so the High-Low range listens to the whole session, not just the bell. Both the standard deviation and the range are trying to answer one question, how violently did the price move, which makes them genuine volatility proxies. Beta answers a different question, how much does this stock dance with the market, so bolting it onto the volatility list confuses total movement with market-driven movement. The slide that lists beta as an SRV proxy gets this wrong.

Formulas

Return standard deviation

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

The close-to-close proxy: dispersion of the

n

returns

R_i

around their mean. Simple, but it ignores everything that happens inside each period.

High-Low (Parkinson) range volatility

\sigma_{HL} = \sqrt{\tfrac{1}{4\ln 2}\,\overline{\left(\ln \tfrac{H_t}{L_t}\right)^2}}

Uses the intraday high

H_t

and low

L_t

. The constant

c = 1/(4\ln 2)

scales the squared log-range to an unbiased variance under a continuous random walk. More efficient than close-to-close when intraday data are available.

CAPM beta — systematic risk, NOT volatility

\beta_i = \frac{\mathrm{Cov}(R_i, R_m)}{\mathrm{Var}(R_m)}

Beta is the sensitivity of stock

i

to the market

R_m

. It captures only the market-driven part of risk, not total dispersion, so it is a measure of systematic risk and not a volatility proxy.

Worked examples

Scenario

A VNIndex stock opens and closes a session almost unchanged, so its daily return is near zero, yet during the day it spiked up 5% and dropped 4%. Which proxy captures that turbulence?

Solution

The return standard deviation sees a near-zero return that day and registers little volatility, badly understating the action. The High-Low range estimator reads the 5% high and the 4% low, so $\ln(H_t/L_t)$ is large and it records substantial volatility. This is exactly why range-based proxies often outperform close-to-close measures: they capture intraday travel the closing price hides.

Scenario

A risk report lists three "volatility" measures for a stock: return standard deviation, the High-Low range, and CAPM beta. Which one does not belong, and why?

Solution

CAPM beta does not belong. The standard deviation and the High-Low range both measure total realized dispersion, the actual size of price moves. Beta instead measures systematic risk, how the stock co-moves with the market. A low-beta stock can be extremely volatile if its swings are firm-specific, so beta and volatility are distinct. The correct framing keeps beta in the systematic-risk family, bridging to the Investment material.

Common mistakes

✗CAPM beta is a measure of volatility. Beta measures systematic risk, the sensitivity to the market, not total dispersion; a stock can have a low beta yet high volatility. Listing beta as an SRV proxy is incorrect.
✗The High-Low range and the standard deviation always give the same number. They use different information (intraday range versus closing returns) and rest on different assumptions, so they can diverge, especially when prices close near where they opened after a turbulent session.
✗Range-based estimators are always inferior to close-to-close. With limited observations the High-Low estimator is often more efficient, because each day's range carries more information than a single close-to-close return.
✗Volatility and systematic risk are interchangeable. Total volatility includes both market-driven and firm-specific movement; systematic risk (beta) is only the market-driven component, so the two are conceptually separate.

Revision bullets

•Return standard deviation: dispersion of close-to-close returns
•High-Low range: uses intraday high/low, often more data-efficient
•Both proxy total realized volatility (the size of price moves)
•CAPM beta = systematic risk (market sensitivity), NOT volatility
•A low-beta stock can still have high total volatility

Quick check

A stock closes a day almost flat but swung sharply up and down during the session. Which volatility proxy best captures that intraday turbulence?

Why is CAPM beta not a measure of stock return volatility?

Connected topics

Return Volatility SRV → Distress Managing SRV Systemic vs Systematic

Sources

Schwert (1989), JF
Schwert, G. W. "Why Does Stock Market Volatility Change Over Time?" Journal of Finance, 44(5), 1115-1153, 1989.
Classic treatment of realized return-based volatility measures and their time variation.
Parkinson (1980), J. Business
Parkinson, M. "The Extreme Value Method for Estimating the Variance of the Rate of Return." Journal of Business, 53(1), 61-65, 1980.
Introduces the High-Low range volatility estimator and its scaling constant $c = 1/(4\ln 2)$ .
Bekaert & Harvey (1997), JFE
Bekaert, G., & Harvey, C. R. "Emerging Equity Market Volatility." Journal of Financial Economics, 43(1), 29-77, 1997.
Uses return standard deviation as the volatility measure in emerging markets, the context for VNIndex firms.

How to cite this page

Dr. Phil's Quant Lab. (2026). Measuring Realized Volatility. Derivatives Atlas. https://phucnguyenvan.com/concept/frm-srv-measures

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