Realized Volatility

Complete definition

Realized volatility (RV) is the actual observed price movement of an underlying asset, measured statistically as the standard deviation of returns over a specified period and annualized. Unlike implied volatility (IV), which is forward-looking and derived from options prices, realized volatility is backward-looking and computed from actual historical price data. The standard calculation: - Compute daily log-returns: r_t = ln(P_t / P_{t-1}) - Calculate the standard deviation of these returns: σ_daily - Annualize: σ_annualized = σ_daily × √252 (using trading days) This produces realized volatility expressed in the same units as implied volatility (annualized standard deviation, expressed as a percentage). A stock with 20% realized vol moved within a one-standard-deviation range of ±20% annualized over the calculation period. Realized volatility windows: - **5-day RV**: ultra-short-term, captures last week's vol - **20-day RV**: monthly vol baseline, the most-cited "recent vol" - **63-day RV**: quarterly vol - **252-day RV**: annual vol - **Long-run RV** (multi-year): historical baseline for the underlying RV is critical for options trading because: **Volatility risk premium (VRP)**: implied vol typically exceeds realized vol on equity indices. This 2-5 percentage point premium is the structural edge of systematic premium-selling. Over multi-year periods, VRP averages around 3-5 vol points on SPX. **IV vs RV spread analysis**: comparing current IV to recent RV reveals mispricing: - IV >> RV: implied vol is rich → favor selling premium - IV << RV: implied vol is cheap → favor buying premium - IV ≈ RV: fair pricing, no edge **Volatility regime classification**: clustering of high-RV periods followed by low-RV periods is a feature of equity markets. Major vol spikes (March 2020, August 2024) precede regimes of elevated RV; calm periods (mid-2017, 2021 H1) have unusually low RV. **Gamma scalping economics**: profit drivers for gamma scalpers depend on RV exceeding IV. Pre-position vol surveys often compare expected near-term RV vs current IV to gauge edge. For retail options traders, the practical use of RV: - **Sizing iron condors**: high RV in the underlying signals widening expected moves; tighten short strikes accordingly - **Identifying mispricings**: stocks with chronically low RV relative to IV (consumer staples, large-cap tech in calm regimes) are good premium-selling candidates - **Event analysis**: actual realized move post-earnings vs the implied move tells you whether long-options strategies would have been profitable RV calculation methods vary in sophistication. Simple close-to-close RV is the most common. More advanced methods include: - **Parkinson estimator** (uses high-low range — more efficient for small samples) - **Garman-Klass** (uses OHLC — even more efficient) - **Yang-Zhang** (handles overnight gaps separately) The Parkinson and Garman-Klass estimators can produce smoother RV estimates with less noise than close-to-close, but most retail traders work with the simpler version.