Hi guys! Need clarification on two questions from CFAI text reading 47: Performance Evaluation pgs 244 questions 7 and 8. The solution to the questions are hazy. Can anyone please explain the approach of the answers provided in the book? Thanks : )
For Q7. Return of portfolio w/o foreign asset = 10% (given) Return of portfolio w/ foreign asset = (0.9*10)+(0.1*11) = 10.1% Std dev of portfolio w/o foreign asset = 15% (given) Std dev of portfolio w/ foreign asset = [(W1^2*sd1^2)+(W2^2*sd2^2)+(2*W1*W2*sd1*sd2*correlation)]^(1/2) = (0.9^2*0.15^2+0.1^2*0.2^2+2*0.9*0.1*0.15*0.2*(-0.1))^(1/2) = 13.5% So. addition of foreign asset reduced the portfolio std dev/ risk by 1.5% (15%-13.5%) and increase the portfolio return from 10% to 10.1%
For Q8. Tracking error = std dev of active return. Active return = portfolio return - benchmark return.
Thanks a lot B_C. Can you please shed some light on the solution to question 6 as well?
Same logic as question 7. Only difference is that Q6 does not specify the weight of foreign asset they want to invest. If we assume 80% invest in domestic and 20% foreign assets. We will get the following results. Return of portfolio w/o foreign asset = 10% (given) Return of portfolio w/ foreign asset = (0.8*10%)+(0.2*11%) = 10.2% Std dev of portfolio w/o foreign asset = 12% (given) Std dev of portfolio w/ foreign asset (0.8^2*0.12^2+0.2^2*0.2^2+2*0.8*0.2*0.12*0.2*0.2)^(1/2) = 11.11% We still can see the impact of addition of foreign asset are 1. reduce the portfolio std dev/ risk from 12% to 11.11% 2. increase in the portfolio return from 10% to 10.2%