# Reading 54 Analysis of Active Portfolio Management [Sharpe Ratio Calculation]

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?

S&P Sharpe Ratio = 0,33333

Sharpe Ratio (Portfolio Return - RFR)/StD --> (9-x)/18=0,33 solve for x --> 6%

Thank you.

That is question is not from Level1. But thank you for the reply

Really? there is more on Sharpe Ratio in other levels?

Solving that equation gives me x–> 3%

Besides Level I it appears only at Level II and Level III.

are they using rm - rf = Market Risk premium … bcos as melissabt has pointed out

solving (9-x)/18 = 0.333 gives x = 3%

Solving for X in that equation gives you x=3% and this represents the risk free rate. However, the question references the excess return which would then be 9-3 = 6%. Make sense?