Converting annual volatility back to daily

Question

A fund reports an annualized volatility of 20\%. Assume returns are independent across days and there are 252 trading days in a year. What is the implied daily volatility?

Accepted Answer

This runs the square-root-of-time rule in reverse. The annual volatility is the daily volatility scaled up by \sqrt{252}: \sigma{	ext{year}} = \sigma{	ext{day}} 	imes \sqrt{252}. To recover the daily figure, divide instead of multiply: \sigma{	ext{day}} = \frac{\sigma{	ext{year}}}{\sqrt{252}} = \frac{20\%}{15.87} \approx 1.26\%. So a fund that swings 20\% over a year typically moves only about 1.26\% on a given day. The daily number is much smaller because a year packs in 252 days and the swing only grows with the square root of time. Takeaway. To go from a long horizon back to a short o…

Converting annual volatility back to daily

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