Portfolio active risk

Alternative active return active risk 1 -0.1% 0.01% 2 2.71% 4.55% A question asked for active return, active risk and information ratio based on 80% to alternative 1 and 20% to alternative 2. Active return is a simple weighted average 0.8(-0.1%) + 0.2(2.71% = 0.46% For active risk, our formula is to use: [(0.8^2)(0.0001^2) + (0.2^2)(0.04555^2)]^0.5 = 0.91% Using a weighted average for active risk gives an approximation, but why is using the weighted average wrong?

if you assume that the correlation of the two alternatives is zero, that is correct. except you have an extra 5 for alternative 2 in the active risk calculation