Standard Deviation Backtesting
The standard deviation backtesting screen compares forecasted standard deviation to realized standard deviation.
The test takes the daily P&L and divides it by the forecasted standard deviation from the close of the previous day. Assuming no trading, this series has an expected standard deviation of 1. In the test window, this value is displayed as “Normalized Standard Deviation”.
The statistical significance of this normalized standard deviation can be evaluated using a chi-squared distribution. More specifically, if s is the normalized standard deviation and there are n days in the sample, (n - 1) x s^2 will follow a chi-squared distribution with (n - 1) degrees of freedom.
If the normalized standard deviation were to be equal to exactly 1, then the p-value would be 0.50. A p-value of less than 0.025, or greater than 0.975, would warrant further investigation.