Active management fundamental law

CFA Level II Portfolio Management
#1

A security selector typically makes 50 active stock selections annually, has an information coefficient of 0.04 and constructs unconstrained portfolios.

What’s his information ratio?

The solution apparently is 0.04 * sqr(50) = 0.28

But don’t we have to multiply this by the optimal active risk?

Thanks!!

#2

Fundamental law for unconstrained portfolio is IR = IC √ BR so solution is as you stated.

For constrained portfolio is IR = (TC) IC √ BR

if TC is < 1.