# Information Ratio

IR = active return/active risk active return = return portfolio - return benchmark active risk = risk portfolio - risk benchmark what if the manager generates a positive active return with less risk? i.e. active return = 5%, active risk = -2.5%. I would assume you ignore the negative and the IR is 2 (not -2) but then the formula is somewhat flawed. also if the manager underperforms the benchmark with more risk is the IR negative?

Std Deviation can’t be negative…Its the Square Root of the Variance which is a squared term…so you can’t have negative Tracking Error. The IR is always positive…the other one I can’t think of right now can be negative…Oh the Treynor Ratio b/c its uses Beta in the denominator, and yes Beta can be negative. But a negative Treynor ratio doesn’t mean bad if the manager has a negative beta.

In such cases, when the Treynor measure or IR give you negative numbers, you should use Jenson’s alpha.

bigwilly: risk portfolio = 5% risk benchmark = 8% both positive yet active risk is negative I’ll look into Jenson’s alpha - I don’t recall it from the schweser readings

Jenson’s aplha is simply between the actual portfolio return and the return expected by CAPM: Alpha = Rp - [Rf - beta(Rm-Rf)]

Active Risk is not Risk of Port - Risk Of Bench. Active Risk is the Std Deviation of your Active Returns.

Std Deviations can’t be simply added or divided to get anotehr std deviation.

IR can be negative but the active risk can never be negative… It can be negative because active return can be negative if actual

Zidane, good point didnt think of that, need another cup of coffee