The Distribution of Realized Stock Return Volatility

Source: Andersen, Bollerslev, Diebold & Ebens (2001) · Journal of Financial Economics 61(1), 43–76 · doi:10.1016/S0304-405X(01)00055-1

TL;DR

Applies the realized-volatility approach (summing high-frequency intraday squared returns) to the 30 Dow Jones stocks and documents the unconditional distributional "stylized facts": realized variances/covariances are highly right-skewed, but logarithmic realized standard deviations and realized correlations are approximately Gaussian, daily returns standardized by realized volatility are nearly normal, and realized volatilities/correlations exhibit long memory with a common factor structure. The single-stock companion to Andersen-Bollerslev-Diebold-Labys (FX/indices).

What it models

Not a parametric return model but a characterization of the data-generating distribution of ex post realized volatility measured directly from intraday data — bypassing the distributional assumptions required by ARCH/stochastic-volatility or implied-volatility approaches.

Specification (the equation)

For each stock, daily realized variance is the sum of intraday squared returns sampled at a 5-minute horizon (used to mitigate microstructure frictions: price discreteness, infrequent trading, bid–ask bounce). By quadratic-variation theory, as sampling frequency rises this converges to integrated volatility ∫σ²(t)dt, so realized variance is a (theoretically error-free in the limit) model-free estimator. Realized covariances/correlations are built analogously from cross-products of intraday returns; realized volatility v = √(realized variance).

Estimation

Transaction prices for the 30 DJIA stocks from the NYSE TAQ data, sample January 2, 1993 – May 29, 1998 (1,366 trading days).

5-minute returns aggregated into daily realized variances, covariances, and correlations, then treated as directly observable series.

Distributions of realized vol, log realized vol, and standardized returns are examined; long-memory degree of fractional integration estimated.

Results replicated on a randomly selected control sample of 30 other liquid stocks.

What it captures (stylized facts)

Right-skewed realized variances/covariances; log realized standard deviations ≈ Gaussian, and realized correlations ≈ Gaussian.

Standardized returns (returns ÷ realized vol) are close to standard normal — fat tails in unconditional returns arise from time-varying volatility, not non-Gaussian innovations.

Long memory: realized volatilities and correlations behave like mean-reverting fractionally integrated processes with degree of integration d ≈ 0.35.

Strong common-factor / comovement structure across the volatilities and correlations.

Use & extensions

Justifies modeling and forecasting volatility in logs, underpins realized-volatility risk models, and motivates the long-memory HAR framework (Corsi, 2009). Direct successor to French-Schwert-Stambaugh and Schwert's monthly realized-vol work; companion to ABDL on FX and indices.

Limitations

Microstructure noise biases naive realized variance at very fine sampling, motivating the 5-minute compromise and later noise-robust estimators.

Requires clean, actively traded high-frequency data; jumps and overnight gaps need separate treatment.

Key references

Andersen, Bollerslev, Diebold & Ebens (2001) — The Distribution of Realized Stock Return Volatility — Journal of Financial Economics

Andersen, Bollerslev, Diebold & Labys (2003) — Modeling and Forecasting Realized Volatility — Econometrica

Corsi (2009) — A Simple Approximate Long-Memory Model of Realized Volatility (HAR) — Journal of Financial Econometrics

Provenance: verified/generated from the paper's full text.