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	2.3	%	0.5	0.3	2.8% (S&P 500)
Bonds	1.3		0.4	0.2	1.4 (Barclay’s Aggregate)
Cash	0.5		0.1	0.5	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.)

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.

Manager’s return in the month = Return on security x Weight of the security

R(M)     = (2.3% x 0.5) + (1.3% x 0.4) + (0.5% x 0.1)

              = 1.15% + 0.52% + 0.05%

              = 1.72%

A-2.

For finding out underperformance or overperformance of the Manager we first need to find out the Market performance.

Market return = (2.8% x 0.3) + (1.4% x 0.2) + (0.5% x 0.5)                         

                             = 0.84% + 0.28% + 0.25%

                             = 1.37%

As Manager’s return is more than the Market return, the Manager has overperformed by 0.35% (1.72% - 1.37%)

B.

Now we know that Manager has outperformed the market by 0.35%.

The extra return can be attributed to Asset Allocation and Security Selection. i.e.

Return from Security Selection can be calculated as follows –

Return (SS)         = [Actual return x Actual weight] +[Index return x Actual weight]

= [(2.3% x 0.5) + (1.3% x 0.4) + (0.5% x 0.1)] – [(2.3% x 0.3) + (1.3% x 0.2) + (0.5% x 0.5)]

                             = [1.15% + 0.52% + 0.05%] – [0.69% + 0.26% + 0.25%]

                             = 1.72% - 1.2%

                             = 0.52%

C.

Return from Asset Allocation can be calculated as follows -

Return (AA)        = [Actual Return x Benchmark Weights] – [Index Return x Benchmark Weights)]

                             = [(2.3% x 0.3) + (1.3% x 0.2) + (0.5% x 0.5)] – [(2.8% x 0.3) + (1.4% x 0.2) + (0.5% x 0.5)]

                             = [0.69% + 0.26% + 0.25%] – [0.84% + 0.28% + 0.25%]

                             = 1.2% - 1.37%

                             = - 0.17%

Total Extra Return = Return (SS) + Return (AA) = 0.52% + (-0.17%) = 0.35%