Impact of Increasing Active Risk on Active Return

Hi all,

Question is in relation to CFAI EOC question #8:

The active return of the portfolio was 1.5 with a tracking risk (active risk) of 2. The client’s liabilities are higher than assets so the client wants the manager to increase tracking risk to 4 to generate an active return (alpha) of 3. the answer speaks towards this notion of not being able to increase alpha by the same amount as the active risk increase because of the long-only constraint (although it doesn’t say there is a long only constraint).

I’m fine with that answer but it got me thinking. Can you increase active risk and receive the same active return assuming no portfolio constraints? based ont the IR equation it doens’t look like you can but wanted to see what others thought.