Volatility

Finance's stand-in for risk: measured from the past, traded in the present, feared about the future — and an asset class of its own.

What the number means

Volatility is the annualised standard deviation of returns — the market's unit for "how much does this thing move". An asset at 20% vol delivers one-year outcomes roughly ±20% around its trend two times in three, and ±40% (two standard deviations) in 19 years of 20. It is not risk itself — permanent loss is risk — but it is the part of risk you can measure daily, price, and trade.

$$ \sigma_{\text{ann}} = \sigma_{\text{daily}} \cdot \sqrt{252} \qquad\qquad \text{expected move over } d \text{ days} \approx \sigma_{\text{ann}} \sqrt{\tfrac{d}{252}} $$

Interactive: volatility converter

The √time rule in one tool: turn an annualised vol into daily and monthly terms and into the expected move over any horizon.

Daily vol
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Monthly vol
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Expected move (1σ)
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95% range (2σ)
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√252 for trading days; the same rule scales any horizon. It assumes independent daily moves — volatility clustering (below) is exactly where that assumption bends.

Realised vs. implied: the two volatilities

  • Realised (historical) vol — measured from past returns: what the asset did.
  • Implied vol — backed out of option prices (try the IV solver): what the market pays for going forward. The VIX condenses 30-day S&P implied vol into one number — mechanically, a variance-swap strike (see variance swaps).
Implied usually sits above subsequent realised — the volatility risk premium. In shocks, realised briefly overtakes: the insurer's loss year.
ShockImplied (bought today)Realised (delivered later)TimeVolatility
  • The vol risk premium: implied exceeds subsequently-delivered realised most of the time — option buyers systematically overpay, like insurance customers. Harvesting that gap (selling options, short VIX futures) earns steady carry with rare violent losses: "Volmageddon" (Feb 2018) erased short-vol ETPs in one afternoon.
  • Volatility clusters: calm days follow calm days, wild days follow wild ones (the GARCH observation). Vol is far more forecastable than returns — the whole vol-trading industry lives in that gap.
  • The leverage effect: equity vol rises when prices fall — one driver of the skew and of why long-vol positions hedge equity portfolios.

Volatility as a control variable

  • Vol targeting: funds scale positions to keep portfolio vol constant — mechanically selling after vol spikes, buying after calm. Stabilises the ride; adds pro-cyclical flows the market now anticipates.
  • Position sizing: the honest use — at 60% vol (crypto) a "small" position delivers big-position outcomes; the risk-based sizing tool and the leverage-decay calculator both run on vol inputs.
  • Vol term structure: like the yield curve, implied vol has a curve across expiries — upward in calm (near-dated cheap), inverted in panic (near-dated explosive). VIX futures trade this curve, with the same roll costs commodities know.

Reading vol like a practitioner

  • Vol is a price, not just a statistic — ask what level you're implicitly buying or selling in any position with optionality (every structured product page in this atlas is an example).
  • High vol ≠ sell, low vol ≠ safe: the calmest markets breed the positions that detonate (2017 → 2018, 2006 → 2008). Vol mean-reverts, but from when and where is the entire question.
  • Annualised numbers hide daily reality: 80% annualised vol is ~5% per day — run the converter above before judging any crypto or single-stock position.