Practice Problem #6 Page 461
S&P 500 Indigo Fund
E(annual return) 9% 10.5%
Return Std Dev 18% 25%
Sharpe Ratio 0.333 0.30
Active Return 1.2%
Active Risk 8%
Information Ratio 0.15
I understand that the optimal amount of active risk is caluculated as IR/SR(b) * STD(Rb).
Optimal active risk is 0.15/0.333(18%)= 8.11%
Weight on active portfolio would be 8.11%/8.0% = 1.014 and
Weight on benchmark would be 1- 1.014 = -0.014
To further prove that this is correct the author goes to prove the optimal sharpe ratio is 0.365
How are they calculating total excess return as 6.0% + (1.014* 1.2)= 7.217% where is 6% coming from? I would have thought that Sharpe Ratio = (Portfolio Return - RFR)/StD –> (9%-x)/18%=0.333 solve for x –> 3% and therefore the total excess return would be 3.0% + (1.014*12) = 4.217% Does anyone know where this 6% comes from? Thank you