Volatility
Realized volatility is the sample standard deviation of periodic returns, usually annualized by multiplying by sqrt(N) where N is periods per year (252 for daily, 12 for monthly). Implied volatility is what option markets price in for the future. The two diverge constantly — vol risk premium is the persistent gap.
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Definition
Volatility
Realized volatility is the sample standard deviation of periodic returns, usually annualized by multiplying by sqrt(N) where N is periods per year (252 for daily, 12 for monthly). Implied volatility is what option markets price in for the future. The two diverge constantly — vol risk premium is the persistent gap.
Why it matters
Volatility is the risk denominator in Sharpe, the input to options pricing, the gate in volatility-targeting strategies, and the variable that drives most leverage decisions. Treating it as constant is the single most common quant mistake — vol clusters and vol-of-vol is itself a tradable factor.
How it works
Compute log returns or simple returns over consistent intervals. Take the sample standard deviation. Annualize: σ_ann = σ_period × sqrt(N). For daily data with 252 trading days, multiply daily σ by 15.87. Be honest about the window — a 30-day vol on a portfolio that just had a tail event tells you about the past, not the next 30 days.
Example
Daily realized vol on an equity index
Daily return σ
1.05%
Trading days per year
252
Annualized σ
1.05% × sqrt(252) = 16.7%
Implied vol (1-month ATM)
18.5%
Implied vol exceeds realized by 1.8 points — the vol risk premium. Selling that gap is the archetypal short-vol trade. It pays consistently until it doesn't.
Key Takeaways
Volatility itself is volatile — single-window estimates can be off by a factor of 2 versus the next window.
Annualization assumes IID returns; vol clustering breaks that assumption.
Implied vol is forward-looking and includes a risk premium; realized vol is backward-looking. They are not the same number.
Related Terms
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FAQ
Questions people ask next
The short answers readers usually want after the first pass.
Sources & References
- GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics — Engle (2001), Journal of Economic Perspectives 15(4)
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