Exercise 6 on page 138. We are supposed to calculate the optimal amount of active risk and the weights allocated to each portfolio to achieve it.
S&P 500 expected annual return: 9.0%, STD: 18.0%, SR: 0.33.
Indigo Fund expected annual return: 10.5%, STD: 25.0%, SR: 0.30, active return: 1.2%, active risk 8%.
The formula is STD (RA) = IR/SRB * STD (RB) = 0,15/0,33 * 18% = 8,11% optimal active risk.
Now I have some doubts regarding determing the weights for Indigo Fund & benchmark. I don’t understand why it’s doing: 8,11% / 8% = 1.014 as the weight for Indigo fund.
Wouldn’t it be: Benchmark risk + active risk / (Benchmark risk + active risk + Benchmark risk) … i.e… portfolio risk / total risk ?