Analysis of active portfolio management example 3

dishantgakhar · April 24, 2019, 5:40pm

In example 3, Q1, it states that the fund with the highest information ratio would add more value to the Sharpe ratio. So it chooses IR =0.05 over IR = -0.23

But we have,

SR_p² = SR_b² + IR²

So, should the sign of IR matter? Shouldn’t we look at the absolute value of IR.

S2000magician · April 24, 2019, 5:49pm

(−0.23)² = (+0.23)²

dishantgakhar · April 25, 2019, 1:52pm

That is what I am saying. We need to have the maximum possible sharpe ratio for the optimal portfolio. When we use IR= -0.23 we get sharpe ratio of the portfolio as 0.523 ( sharpe ratio of benchmark is 0.47) . But when we use IR = 0.05 we get sharpe ratio of the portfolio as 0.473. So shouldn’t we prefer IR =-0.23 ?