# Practice Problem #6 Page 461

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

The 6% is the excess return of the S&P 500 over the risk-free rate:

6% = 0.333 × 18%

I had the same issue with this problem at first.

Sharpe Ratio (Portfolio Return - RFR)/StD –> (9-x)/18=.33 solve for 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 is equal to S&P 500 Expected Annual Return - Risk Free Rate which is 9-3 = 6%. Make sense?