Not an implementation claim. This is measurement mechanics — the layer under every volatility-forecasting result and high-frequency backtest, and a classic place where naive pipelines silently produce garbage inputs.
Definition. Realized volatility (RV) estimates variance by summing squared high-frequency returns: RV = Σ r²ᵢ over a day’s intervals. In theory, finer sampling → better estimates. In practice, observed prices = efficient price + microstructure noise — bid-ask bounce (trades alternate between bid and ask, manufacturing back-and-forth “returns”), price discreteness, and asynchronous updates — and squared returns sum the noise along with the signal. Sample every second and noise dominates: RV diverges as sampling accelerates, the opposite of what statistics promises.
The worked example: the signature plot
The diagnostic every practitioner should run once: compute RV for the same day at many sampling frequencies (1s, 5s, 30s, 1m, 5m, 15m, 30m) and plot RV against frequency. Clean theory predicts a flat line; reality shows RV exploding at high frequencies — a liquid stock might show annualized vol of 15% at 15-minute sampling and 45% at 1-second sampling, the excess being pure bounce. The plot’s flattening point is your instrument’s noise horizon, and it varies enormously: seconds for ES futures, minutes for liquid stocks, tens of minutes for small caps and long-tail crypto. One plot per instrument class replaces a semester of theory — the same cross-validate-against-finer-data instinct applied to your own estimator.
The estimator toolkit, in practice order
- Sparse sampling (5-minute RV): the industry default — sample slow enough that noise is negligible relative to signal. Throws away data; robust; the HAR-RV baseline that’s so hard to beat is built on it.
- Subsampled/averaged RV: average multiple 5-minute grids at different offsets — recovers some discarded efficiency for free; the sensible default upgrade.
- Realized kernels / two-scale estimators: the econometrically serious tools — noise-robust by construction, usable at high frequency, with tuning parameters that need their own validation.
- Mid-quote construction: computing returns from mid-quotes rather than trade prices removes bounce at the source (not discreteness or quote noise) — often the cheapest large improvement, data permitting.
- Pre-averaging and cleaning: outlier/bounce-back filters on ticks before anything else; the unglamorous step that prevents one bad print from owning your day’s estimate.
Why it matters beyond estimation
Downstream contamination is the real stakes: volatility forecasting benchmarks are only comparable when noise handling matches — a “superior” forecaster fed cleaner RV inputs is an unfair race; volatility targeting and risk models inherit estimator bias directly into position sizes; high-frequency Sharpe ratios computed on noisy returns overstate both risk and opportunity (bounce looks like tradeable mean reversion — the classic fake signal, and the null every tick-level reversion claim must beat); and variance-based option strategies settle against realized measures whose construction is contractually specified — mismatch your estimator and hedge the wrong quantity.
Common ways this fails in production
- The fake reversion strategy: backtest on trade prices “discovers” tick-level mean reversion that is bid-ask bounce; live trading pays the spread to harvest a signal that is the spread.
- Estimator regime breaks: tick-size changes, decimalization-era differences, and venue migrations shift noise properties mid-sample — era-tagging applies.
- Crypto’s dirty ticks: wash trading and venue-quality variance make exchange choice part of the estimator; RV from a manipulated venue is a manipulated input.
- Silent frequency upgrades: a pipeline moved from 5-minute to 1-minute bars “for more data” quietly doubles measured vol and halves every vol-scaled position.
Questions to ask a paper using realized measures
- What sampling frequency and estimator — and is a signature plot (or noise-robustness check) shown?
- Trade prices or mid-quotes?
- Are competing forecasts fed the same realized input?
- For tick-level trading claims: does the effect survive on mid-quote returns?
What our scoring captures
Estimator hygiene is quietly one of the rigor axis’s sharpest discriminators in the volatility hub: papers specifying sampling scheme, estimator, and cleaning rules cluster at the top; papers computing “volatility” from raw ticks without comment populate the bottom. The map’s realized-vol branch is effectively ranked by this hygiene.
Downstream: volatility targeting → · vol forecasting map → · The noise’s source: market-making mechanics →