Weights to obtain optimal active risk

CFA Level II Portfolio Management
#1

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 ?

#2

I’m not seeing exercise 6 on p. 460. Is this the 2022 curriculum, or 2023? Which volume?

#3

Sorry this would be 2022 curriculum.
Exercise 6 in page 138

#4

Gotcha.

Indigo has an active risk of 8%, and you want 8.11%. 100% Indigo gives you only 8% active risk. 8.11 / 8 = 101.4% Indigo gives you 8.11% active risk. Then you short the S&P 500 1.4% so that your total allocation is 100%.

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