What is Realized Volatility? Definition, Formula, and Example
Realized volatility (RV) is the actual historical standard deviation of an asset's log returns, annualized — a backward-looking measure of how volatile an asset has been, in contrast to implied volatility, which prices the market's forward expectation.
Plain-English Definition
Realized volatility (RV) is the actual, historical standard deviation of an asset's log returns, annualized — what volatility *was*, in contrast to implied volatility (IV), which prices what the options market expects volatility *to be*. RV is the most-used input in quantitative position sizing, vol-targeting strategies, and the denominator in the IV/RV ratio that vol traders use to grade options as rich or cheap.
How Realized Volatility is Calculated
The standard close-to-close estimator over an n-day window:
RV = √252 × stdev( ln(P_t / P_{t-1}) ) for t = 1...n
The √252 factor annualizes the daily standard deviation (252 US trading days per year). Common windows are 10-day, 20-day, 30-day, 60-day, and 252-day. Practitioners report RV in the same units as IV — percent per annum — so a 20-day RV of 14% on SPY is directly comparable to a 14% at-the-money implied vol.
Higher-precision estimators used on quant desks:
| Estimator | Inputs | Efficiency gain vs. close-to-close |
|---|---|---|
| Parkinson | High, low | ~5× |
| Garman-Klass | Open, high, low, close | ~7× |
| Yang-Zhang | OHLC + overnight | ~8×, handles gaps |
| Realized variance (5-min) | Intraday returns | Theoretically unbiased |
"Efficiency" here means lower estimator variance for the same window length — a Garman-Klass 10-day RV is roughly as stable as a close-to-close 70-day RV.
Worked Example
From April 21 to May 20, 2026 (20 trading days), SPY daily log returns had a standard deviation of 0.83%. Annualized: 0.83% × √252 ≈ 13.2%. Over the same window, the VIX averaged 16.4 — implied vol traded at a ~3.2-point premium to realized, which is the variance risk premium that vol sellers harvest in normal regimes.
By comparison, the same 20-day calculation for TSLA produced an RV of 42%, with 30-day ATM IV at 48% — a similar 6-point premium but at four times the dollar magnitude per Vega.
When Traders Use Realized Volatility
- IV/RV ratio: a vol-richness signal. IV/RV > 1.2 historically favors net options sellers; IV/RV < 0.95 favors buyers.
- Position sizing / vol targeting: scale exposure inversely to recent RV to keep portfolio risk constant. AQR, Bridgewater, and most CTAs use this directly.
- GARCH and stochastic-vol model calibration: RV is the dependent variable.
- Regime detection: a sharp divergence between 20-day and 60-day RV (>1.5×) signals a volatility regime shift and is a common input to risk-parity rebalancing rules.
Limitations and Misconceptions
RV is purely backward-looking. A single 5-sigma day dominates the 20-day window for nearly a month — the August 5, 2024 yen-carry unwind pushed SPY 20-day RV from 9% to 18% on a single print. Close-to-close estimators ignore intraday range and overnight gaps, understating true volatility by 25–40% in trending or gap-prone names. And RV does not predict next-period RV well — daily return autocorrelation is near zero, although the *volatility process itself* clusters strongly, which is why GARCH and HAR-RV models exist. RV ≠ risk: a low-RV grind into a binary event (earnings, FDA decision, FOMC) can mask the true distribution of next-day outcomes.