How to calculate weighted IR?

If we have two managers with weight 50% each and IR of 1 and 1,5.

Is the IR for the whole portfolio: 0,5x1 + 0,5x1,5

or (0,5x1)^2 + (0,5x1,5)^2

Ideally you would want to start with the individual active returns and active risk measures. Arrive at the weighted average for both and then calculate the IR by dividing the combined measures.

I proceed with weighting risk variables same as return variables in one of Qs but guideline provides classical portfolio stdevp formula for risk variable.

Yes. That’s what I meant. Sorry if I was ambiguous, will use the weighted average formula for the return component and the w2*variance formula to compute active risk (assuming 0 correlation unless stated otherwise).

Thanks

I agree: If you have the separate active returns and active risk you calculate it that way. But if you are only gived the weights and IRs and nothing else. How is it calculated? Refer to my original question. I cannot find this formula in the curriculum.

If you weight IR of each manager to get IR of total portfolio it is just approximation but if none of details provided, seems as only rational solution.

I’m pretty sure you cannot work a weighted IR out without knowing the portfolio’s respective active risk and return. Just take an example where two portfolios have IRs both equal to 1. Now imagine in one case that’s because they both have active return and active risk equal to 1 and do the math. Then imagine instead one of them has active return and risk both equal to 10 and the other one still equal to 1. Keep the weights the same and re-do the math. You’ll get a vastly different outcome, so unless you know the underlying active risk and return you cannot really perform a weighted IR calc given just 2 IR and the portfolio weights.

can someone reference this to an actual example in the book/ mocks

+1