Information ratio

Hey guys,

Would someone know why the information ratio changes if I add cash but not if I combine it with the benchmark portfolio?

Many thanks.

Take a look at the formula and actually work out an example and it will make more sense.

The IR= Rp-Rb / st. deva (active return / active risk) - If you add cash the return on the portfolio will go down (likely) yet the return on the bechmark will be unchanged.

Adding to the benchmark portfolio would cause the active return to go down and would also cause the ative risk to go down by the same amount. This is similar to adding cash/leverage and the effects on the Sharpe Ratio.

Again putting some numbers to this will show you that it holds.

Many thanks!

Partyl I can agree with brfry.

  1. senario: If we have unconstrained portfolio in that case leverage © will cause “c” times higher active return (increase all active weight with “c”) and increase altimately active risk with “c” (higher leverage higher risk)

  2. senario: If we have constrained portfolio “the information ratio for the combined portfolio will generally shrink” (page 424.).IR will degrees because “investor will not be able to adjust the active risk of an existing fund by changing the individual asset activie weight position” (investor has a constrain)