 # information ratio

does a high information neccessarily mean that the value added for an investor would be high?

i have this question in KS that compares three porfolios to determine the highest value added to some granny, and they have residual risk and residual return given.

so they calculate the information ratio and based on that they justify that the highest information ratio means highest value added.

VA = IR*residualrisk - lambda*residualrisksquared

so it would appear to me that information ratio alone cannot be the decision standard for the highest value added

For simplicity we can take residual return = 1000% and residual risk = 1000% and see that the VA is negative for decent lambda

is there anything that i am missing here?

as long as IR > lambda x omega, yes

I think there will be value added.

VA = IR x w - lambda x w^2

if VA = 0

IR x w = lambda x w^2

IR = lambda x w (threshold point, I think) - Could be wrong - will think abt it more

Just think of it in a simple manner – Just like the sharpe ratio. Want the greatest return per unit of risk. Whichever has the greatest return per unit risk will add the most value.

The key word is “highest” value added. What you have listed is just the VA formula, which can keep changing for various values. The optimal VA for a given residual risk and aversion is simply 2* residual risk* aversion=IR

No the question gives me three (residual return, residual return) values aand asks me to tell which one has the highest value added.

and in the answer they have calculated just the information ratio to answer the question

I think that is not the way to do it.

What is the question ID? I can take a look.

Assuming Manager takes optimum level of Risk, with higher IR, VA increases, at same level of Risk Aversion. Can you post the question here for more clarity.

VA = alpha - (lambda * optimum residual risk square). I am assuming Granny would have fixed Lambda and Manager taking on optimum level of residual risk, the manager which has highest IR would eventually have more VA for poor Granny!

I was asking about the Question ID in KS. I thought I can look at the question before commenting any further.

KS practice exams

volume 2

exam 1

question 94

While you are at it can you send me the image of page 43 and page 178 from same book i.e. KS practice exams volume 2… my book has it completely blank for some reason.