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 portfolio 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		Actual Weight	Benchmark Weight	Index Return
Equity	2.6	%	0.4	0.6	3.1% (S&P 500)
Bonds	1.5		0.2	0.1	1.7 (Barclay’s Aggregate)
Cash	0.7		0.4	0.3	0.8

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.)

a-2. What was her overperformance or underperformance? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)

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.)

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.)

Answer 1

a-1. Manger's return = Sum of weight of assets*return of assets

Manager's return = 0.4*2.6 + 0.2*1.5 + 0.4*0.7 = 1.04 + 0.3 + 0.28 = 1.62%

a-2. over or under performance = Manager's return - benchmark return

benchmark return = Sum of benchmark weight of assets*benchmark return of assets

benchmark return = 0.6*3.1 + 0.1*1.7 + 0.3*0.8 = 1.86 + 0.17 + 0.24 = 2.27%

under performance = 1.62% - 2.27% = -0.65%

Manager's under performance is 0.65%.

b. contribution of security selection to relative performance = manager's return - sum of actual weights of assets*benchmark return of assets

contribution of security selection to relative performance = 1.62% - (0.4*3.1 + 0.2*1.7 + 0.4*0.8) = 1.62% - (1.24 + 0.34 + 0.32) = 1.62% - 1.9% = -0.28%

c.contribution of asset allocation to relative performance = sum of (Actual weight of assets - benchmark weight of assets)*benchmark return of assets

contribution of asset allocation to relative performance = (0.4 - 0.6)*3.1% + (0.2 - 0.1)*1.7% + (0.4 - 0.3)*0.8% = -0.2*3.1% + 0.1*1.7% + 0.1*0.8% = -0.62% + 0.17% + 0.08% = -0.37%