Scaling weekly volatility to a year

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An index's weekly return volatility is 4\%. Assume weekly returns are independent and there are 52 weeks in a year. What is the annualized volatility?

Accepted Answer

An annual return is the sum of 52 weekly returns. Independent variances add, so the annual variance is 52 times the weekly variance, and the volatility grows by \sqrt{52}: \sigma{	ext{year}} = \sigma{	ext{week}} 	imes \sqrt{52} = 4\% 	imes \sqrt{52}. Since \sqrt{52} \approx 7.21, \sigma{	ext{year}} \approx 4\% 	imes 7.21 \approx 28.8\%. The annual swing is only about 7 times the weekly one, not 52 times, because volatility scales with the square root of the number of periods. Takeaway. Annual volatility = \sigma{	ext{week}}\sqrt{52}: whatever the base period, you multiply by the square…

Scaling weekly volatility to a year

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