Square-root-of-time rule
Definition · Level 8 · Risk & portfolio
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Scale σ or VaR to a new horizon by multiplying by √T; strictly valid only for i.i.d. returns (no autocorrelation, stable volatility), and for VaR also a normal distribution with zero mean.
Example
1-day VaR $200k → 10-day ≈ $200k × 3.16 = $632k.
Where Tradecraft teaches it
Level 8 · Risk & portfolio, in the lesson “VaR, expected shortfall & fat tails”: Compute parametric VaR, scale it with √time, know its three flavours and why it understates the tail.
Related terms
- Expected shortfallAverage loss on the days worse than the VaR threshold — it answers “when it’s bad, how bad?”.
- Historical VaRReprices today’s portfolio over actual past daily moves (e.g. the last 500 days) and reads the loss at the chosen percentile — no normality…
- Monte Carlo VaRLoss percentile read from thousands of simulated scenarios drawn from a statistical model of the risk factors; suits option-heavy books.
- Scenario analysisEstimating P&L by replaying a historical or hypothetical episode (2008, March 2020, a rate shock) across all risk factors at once.
- VaRLoss threshold expected to be exceeded only with a stated probability over a given horizon; the parametric (normal) version = z × σ × position value.
- 1RThe dollar amount at risk on a trade — entry-to-stop distance × size — used as the unit for measuring every result.