Practice Problem #6 Page 461

[melissabt]

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

 

[S2000magician]

The 6% is the excess return of the S&P 500 over the risk-free rate:
6% = 0.333 × 18%

 

[Hardj]

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?