Ex post risk report

The following table describes the ex-post risk statistics currently calculated by the FIA engine.

Statistic	Notes	Formula
mean	Average return over N samples	<math>\mu=\frac{1}{N}\sum_i{r_i}</math>
sigma	Standard deviation of return over interval. Also referred to as volatility, sigma.	<math>\sigma=\sqrt{\frac{1}{N}\sum_i{(r_i-\mu)}^2}</math>
population_sigma	Sample standard deviation of return. Includes Bessel's sample count correction N-1 instead of N.	<math>sd=\sqrt{\frac{1}{N-1}\sum_i{(r_i-\bar{x})}^2}</math>
variance	Square of standard deviation of return over interval.	<math>\sigma^2</math>
population_variance	Square of sample standard deviation of return over interval.	<math>{sd}^2</math>
tracking_error	Standard deviation of active return (portfolio return minus benchmark return)
information_ratio	Active return (portfolio return minus benchmark return) divided by tracking error
covariance	Covariance of portfolio return against benchmark return
correlation	Correlation of portfolio return against benchmark return
correlation_squared	Square of correlation of portfolio return against benchmark return
beta	Beta of portfolio against benchmark
omega	Omega statistic
jensen_alpha	Jensen's alpha
Sharpe ratio	Sharpe ratio for portfolio return
Active Sharpe ratio	Sharpe ratio for portfolio return against benchmark return	<math>S = \frac{R_P-R_B}{sd}</math>
Treynor ratio		<math>T = \frac{R_P-R_B}{\beta}</math>
upside_volatility
downside_volatility
Skewness	A measure of the asymmetry of the distribution of returns about their mean	<math>S=\frac{N}{(N-1)(N-2)}\sum_{i=1}^N\left[\frac{(r_i-\bar{r})}{sd}\right]^3</math>
Kurtosis	A measure of the "peakedness" of the distribution of returns	<math>S=\frac{N(N+1)}{(N-1)(N-2)(N-3)}\sum_{i=1}^N\left[\frac{(r_i-\bar{r})}{sd}\right]^4</math> <math>+\frac{3(N-1)(N-1)}{(N-2)(N-3)}</math>