Question

Consider the following information regarding the performance of a money manager in a recent month. The table presents 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 indexes in column (4). (1) Actual Return (2) Actual Weight (3) Benchmark Weight (4) Index Return Equity 2.8% 0.40 0.30 2.9% (S&P 500) Bonds 1.1 0.40 0.50 1.8 (Aggregate Bond Index) Cash 0.9 0.20 0.20 0.9 a-1. What was the manager’s return in the month? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Manager’s return % a-2. What was her over or underperformance? (Input the value as positive value. Do not round intermediate calculations. Round your answer to 2 decimal places.) % b. What was the contribution of security selection to relative performance? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.) 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.) Contribution of asset allocation %

Answer 1

	(1)	(2)	(3)	(4)
	Actual Return	Actual Weight	Benchmark Weight	Index Return
Equity	2.80%	0.4	0.3	2.90%
Bonds	1.10%	0.4	0.5	1.80%
Cash	0.90%	0.2	0.2	0.90%

a. Actual Return = Actual return of equity * actual weight of equity + return on bond *actual weight of bond+ return on cash * actual weight of cash

=0.028 * 0.4 + 0.011 * 0.4 + 0.009 * 0.2

= 0.0174 or 1.74%

Bogey = Aggregate of benchmark weight * index return

= 2.9% * 0.3 + 1.8% * 0.5 + 0.9% * 0.2

= 1.95%

Under-performance = 1.95% - 1.74% = 0.21%

b. Security Selection

		(1)	(2)	(3) = (1) - (2)	(4)	(5) = (3) * (4)
		Portfolio Performance	Index Performance	Excess performance	Managers Portfolio Weight	Contribution
	Equity	2.80%	2.90%	-0.10%	0.4	-0.04%
	Bonds	1.10%	1.80%	-0.70%	0.4	-0.28%
	Cash	0.90%	0.90%	0.00%	0.2	0.00%
				Contribution of Security Selection		-0.32%

c. Asset Allocation

	(1)	(2)	(3) = (1) - (2)	(4)	(5) = (3) * (4)
	Actual Weight	Benchmark Weight	Excess Weight	Index Return	Contribution
Equity	0.4	0.3	0.1	2.90%	0.29%
Bonds	0.4	0.5	-0.1	1.80%	-0.18%
Cash	0.2	0.2	0	0.90%	0.00%
			Contribution of Asset allocation		0.11%

Security Selection = -0.32%

Asset Allocation = 0.11%

Excess Performance = -0.21%

sum of selection and allocation contributions equals to total “excess” return relative to the bogey.