Question

Consider the following information regarding the performance of a money manager in a recent month. The table represents the actual return of each sector of the manager's portfolio in column 1, the fraction of the portfolie allocated to each sector in column 2, the benchmark or neutral sector allocations in column 3, and the returns of sector indices in column 4. Actual Return 2.2% 1.2 0.5 Actual Weight Benchmark Weight 0.4 0.3 0.3 Index Return Equity Bonds 0.6 2.7% ( S&P 500) 1.5 (Barclay's Aggregate) 0.5 0.2 Cash 0.2 a-1. What was the manager's return in the month? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.) The manager's return in the month is % underperformance? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.) a-2. What was her overperformance % b. What was the contribution of security selection to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign. % Contribution of security selection c. What was the contribution of asset allocation to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.) % Contribution of asset allocation

Answer 1

a.1) Manager's return(R_p)=W₁R₁+W₂R₂+W₃R₃

=(0.6×2.2+0.2×1.2+0.2×0.5)

=(1.32+0.24+0.10)%

=1.66%

a.2) Benchmark return(R_b)=(0.4×2.7+0.3×1.5+0.3×0.5)%

=(1.08+0.45+0.15)%

=1.68%

Active return (R_A)= R_p-R_b

=(1.66-1.68)%

=-0.02%

The negative R_A​​​​​​ indicates that the security has underperformed as compared to the benchmark by 0.02%.

Excess return on each security is :

Equity=(0.6×2.2)-(0.4×2.7)

=1.32-1.08

= 0.24%

Bonds=(0.2×1.2)-(0.3×1.5)

=0.24-0.45

=-0.21%

Cash = (0.2×0.5)-(0.3×0.5)

=0.10-0.15

=-0.05%

Contribution of security selection on relative performance

= (0.6×0.24)+(0.2×-0.21)+(0.2×-0.05)

=0.144-0.042-0.010

= 0.092%