# what's return from active factor selection?

Anyone knows the formula of it? This is inspired by question 59 choice C, from CFA Mock01.

Is there a formula? Active factor risk is just choosing which factors to have exposure to.

Given: Active risk squared decomposition Percent of total active risk in parenthesis Portfolio Industry | Risk Indexes | Total factor | Active Specific | Active Risk Squared S 10(28%) 12(33%) 22(61%) 14(39%) 36 T 2(5%) 26(65%) 28(70%) 12(30%) 40 Information ratio for S is 0.25 or T is 0.55 Choic C: Portfolio T earned a higher return from active factor selection. How to calculate this?

Hi Nibs, there is a formula for active facotr risk. AFR= (active sensitivity to the factor)^2 (factor variance) Where, active sensitivity to the factor=portfolio sensitivity- benchmark sensitivity.

I only remember active risk squared = active risk + active specific risk That’s a new one for me. I can’t even begin to understand what that table says.

WTF

Portfolio Industry | Risk Indexes | Total factor | Active Specific | Active Risk Squared S 10(28%) 12(33%) 22(61%) 14(39%) 36 T 2(5%) 26(65%) 28(70%) 12(30%) 40 Information ratio for S is 0.25 or T is 0.55 Portfolio T has higher Information ratio(active return per unit of active risk) as compared to Portfolio S. Looking at the data it is due to Portfolio T higher total factor risk (70%) as compared to port S (61%)…active risk of both the portfolio is almost same (T 6.32 and S 6) Therefore T has earned more active retrun by active factor selection (Risk Index 65%)

I got the same thing as Rakesh, but the answer is not C. So C should be incorrect. Donnot know why.