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%	0.7	0.6	2.5%	(S&P 500)
Bonds	1	0.2	0.3	1.2	(Salomon Index)
Cash	0.5	0.1	0.1	0.5

a.         What was the manager's return for the month? What was her value-added performance for the month?

b.         What was the contribution of asset allocation to relative performance?

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

Answer 1

Part a:
Manager's return for the month= (Actual return on equity)*(Actual weight of equity)+(Actual return on bond)*(Actual weight of debt)+(Actual return on cash)*(Actual weight of cash)
=2%*0.7+1%*0.2+0.5%*0.1=1.65%

Benchmark (index) return=2.5%*0.6+1.2%*0.3+0.5%*0.1=1.91%
Manger's value added (under performance)=1.65%-1.91%=-0.26%

Part b:

Equity =(Equity portfolio wt- Benchmark weight)* Benchmark return =(0.7-0.6)*2.5%=0.25%
Bond = (Bond portfolio wt- Benchmark weight)* Benchmark return =(0.2-0.3)*1.2%=-0.12%
Cash = (Cash portfolio wt- Benchmark weight)* Benchmark return =(0.1-0.1)*0.5=0

Contribution of asset selection = 0.25%-0.12%+0=0.13%

Part c:

Equity = (Equity portfolio return-Benchmark return)*Actual weight = (2%-2.5%)*0.7=-0.35%
Bond = (Bond portfolio return-Benchmark return)*Actual weight = (1%-1.2%)*0.2=-0.04%
Cash = (Cash portfolio return-Benchmark return)*Actual weight = (0.5%-0.5%)*0.1=0

Contribution of security selection = -0.35%-0.04%+0=-0.39%