Annualized Volatility

In this research note, we compare S&P 500 volatility figures calculated with the popular “square-root-n rule” to volatility figures derived from time-aggregated daily returns and try to reconcile the differences with popular time-series models featuring serial correlation in returns or volatilities. We show that the deviations from the square-root-n rule cannot be explained with serial correlation in returns, rather with a GARCH model. We conclude that volatility figures annualized with the square-root-n rule should not be interpreted as accurate estimates for true annual volatility. The square-root-n rule is also not suitable to standardize volatility figures for reporting purposes.