Explainer, in Risk & Portfolio Construction
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.
1 question. Published May 10, 2026. By AI Fin Hub Research.
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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Questions people ask next
Why does vol cluster?
Empirically, large moves are followed by large moves and small by small. The mechanism is contested (leverage feedback, regime switching, information arrival) but the autocorrelation of squared returns is one of the most robust stylized facts in finance.
Sources
- GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics , Engle (2001), Journal of Economic Perspectives 15(4)
Keep the topic connected
- Learn Sharpe Ratio
Sharpe ratio defined, when it lies (skew, fat tails, autocorrelation), and how to read a Sharpe number you didn't compute yourself.
- Learn Drawdown
Drawdown explained: peak-to-trough decline, why max drawdown alone is misleading, and the recovery math that actually matters.