How many days until the swing triples?

Question

A stock's daily return volatility is 1\%, with independent daily returns. Over how many trading days does the cumulative return volatility grow to 3\%?

Accepted Answer

This solves the square-root-of-time rule for the horizon instead of the volatility. Over T days the volatility is \sigmaT = \sigma{	ext{day}} 	imes \sqrt{T} = 1\% 	imes \sqrt{T}. Set this equal to the target 3\%: 1\% 	imes \sqrt{T} = 3\% \quad\Rightarrow\quad \sqrt{T} = 3 \quad\Rightarrow\quad T = 9. So it takes 9 trading days for the swing to triple. Because volatility grows with the square root of time, tripling the swing takes 3^2 = 9 days, the same "factor squared" logic as the \sqrt{n} law for standard errors. Takeaway. To grow the swing by a factor k you need k^2 periods: tripling a…

How many days until the swing triples?

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