AppliedNumeric answerFree solution
A name moves a day. What is a one-standard-deviation move over a five-day week, in per cent?
Answer with a number in %. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.
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Answer
Variance adds over independent periods, so volatility scales with , not with . Five days therefore gives . Multiplying by five instead would give , which overstates the move by more than double and is the standard error. The same square root is why a one-year option has roughly times the vega of a one-month one, and why doubling your sample only cuts an estimation error by .
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Takeaway: Scale volatility by the square root of time, never by time.
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