# Help with analysis of active portfolio management question

Hi everyone,

Could someone please help me out with the following question:

Text

Hwang Soi makes monthly allocation decisions between consumer discretionary and consumer staples based on a proprietary model. The historical correlation between the returns of the two sectors is 0.30 and Soi’s bets have been correct 60% of the time. Further information is below.

Sector // E® // Standard deviation // Benchmark weight

Consumer staples // 10.8% // 3.0% // 65%

Consumer discretionary // 13.2% // 5.0% // 35%

Question: What is the expected annualized active return of Soi’s sector rotation strategy?

Answer : Active return from this strategy using a probability weighted average (given that Soi makes correct calls 60% of time) of combined risk is: (0.60)(0.05) + (0.40)(–0.05) = 0.01 or 1% per month. Annual active return = 1% × 12 = 12%.

My question: Can someone please explain where the 0.05 and -0.05 come from in the answer?

Thank you.

that’s the monthly active risk taken from point 1 of the same question

Monthlyactiverisk=σ=σ2−2σσr +σ212 cX XXXYY

= [0.032 + 0.052 – 2 (0.03)(0.05)(0.30)]1/2 = 0.05 or 5%

(Tolia 178)

Tolia, Dr. B., CFA, CA. SchweserNotes™ 2016 Level II CFA® Book 5: Derivatives and Portfolio Management (eBook). Kaplan Schweser, 09/2014. VitalBook file.