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).

a. What was the manager’s return in the month? What was her over- or under - performance?

b. What was the contribution of security selection to relative performance?

c. What was the contribution of asset allocation to relative performance? Confirm that the sum of selection and allocation contributions equals her total “excess” return relative to the bogey.

Short answer

a. Underperformance

b. -0.39%

c. 0.13%; -.26%

Step-by-step solution

 Step 1: Calculation of manager’s return and explanation on performance

Actual: (Sum of Multiplication of column 2 by column 1)

= (.70 x .02) + (.20 x .01) + (.10 x .005)

= .0165

or 1.65%

Bogey: (Sum of Multiplication of column 3 by column 4)

= (.60 x .025) + (.30 x .012) + (.10 x .005)

= .0191

or 1.91%

Underperformance = .0191 - .0165 = .0026 = 26%

Calculation of contribution of security selection

Market	Portfolio performance	Index performance	Excess performance	Manager's portfolio weight	Contribution
	1	2	3	4	5 = 3 x 4
Equity	2.00%	2.50%	-0.50%	0.70	-0.35%
Bonds	1.00%	1.20%	-0.20%	0.20	-0.04%
Cash	0.50%	0.50%	0%	0.10	0.00%
		Contribution of security selection			-0.39%

Calculation of contribution of asset allocation

Market	Actual weight	Benchmark weight	Excess weight	Index return	Contribution
	1	2	3	4	5 = 3 x 4
Equity	0.70	0.60	0.10	2.50%	0.25%
Bonds	0.20	0.30	-0.10	1.20%	-0.12%
Cash	0.10	0.10	0.00	0.50%	0.00%
		Contribution of Asset allocation			0.13%

Validation on sum selection and asset allocation contribution equalling to excess performance 

From the above calculation, it implies:

Security selection: -.39%

Asset Allocation: .13%

Excess performance: -.39% +.13% = -.26%