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	2.1	%	0.7	0.5	2.6% (S&P 500)
Bonds	1.1		0.1	0.2	1.3 (Barclay’s Aggregate)
Cash	0.5		0.2	0.3	0.5

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 %

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.)

	Underperformed by %

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

Answer : (a-1.) Calculation of Managers Return for month

Managers Return of Month = Sum of (Actual Return * Actual Weights)

= (2.1% * 0.7) + (1.1% * 0.1) + (0.5 * 0.2)

= 1.47% + 0.11% + 0.1%

= 1.68%

(a-2.) Calculation of Underperformance or over performance

UnderPerformance = (Benchmark Return - Actual Return )

Managers Benchmark's Return of Month = Sum of (Index Retun * Benchmark Weights)

= (2.6% * 0.5) + (1.3% * 0.2) + (0.5 * 0.3)

= 1.3% + 0.26% + 0.15%

=1.71%

UnderPerformance = (1.71% - 1.68%)

= 0.03%

(b.) Calculation of Contribution from security selection :

Contribution from security selection = Sum of [(Actual Return - Index Return ) * Actual Weights]

= [(2.1% - 2.6%) * 0.70] + [(1.1% - 1.3%) * 0.10] + [(0.5% - 0.5%) * 0.20]

= [-0.5% * 0.70] + [-0.2% * 0.10] + 0

= -0.35 - 0.02

= (-0.37%)

(c.) Calculation of Contribution from asset allocation :

Contribution from security selection = Sum of [(Actual Weight - Benchmark Weight ) * Index Return]

= [(0.7 - 0.5) * 2.6%] + [(0.1 - 0.2) * 1.3%] + [(0.2 - 0.3) * 0.5%]

= 0.52% + (-0.13%) + (-0.05%)

= 0.34%