Explain where active risk comes from, and interpret the information ratio and tracking risk

Active risk, or tracking risk, is the standard deviation of the portfolio's return minus the benchmark's. In a factor model, active risk squared equals active factor risk squared plus active specific risk squared. Active factor risk comes from differences between the portfolio's and benchmark's factor sensitivities; active specific risk comes from active weights on individual securities times their residual risk, and falls as positions are diversified. The information ratio, mean active return divided by active risk, measures reward per unit of benchmark-relative risk and is used to compare managers. The trap is adding the two components as standard deviations, or computing their shares from standard deviations rather than variances.