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 0.36 % 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

a-1)

Manager's return = (Return on Equity * Weight of Equity) + (Return of Bond * Weight of Bond) + (Return of Cash * Weight of Cash)

= (2.8%*0.40) + (1.1%*0.40) + (0.9%*0.20)

= 0.0112 + 0.0044 + 0.0018

= 0.0174 or 1.74%

Therefore, Manager's return is 1.74%.

a-2)

a) Equity under performed by 0.1% (2.9% - 2.8%)

Bond under performed by 0.7% (1.8% - 1.1%)

Cash is not either under performed or over performed as both are 0.9% only.

b) Contribution of Security Selection = (Weight of Equity*Over or Under performed) + (Weight of Bond*Over or Under performed) + (Weight of cash*Over or Under performed)

= (0.40*-0.1%) + (0.40*-0.7%) + (0.20*-0)

= -0.04% + -0.28% + -0%

= -0.32%

Therefore, Contribution of Security Selection is -0.32%.

c) Contribution of Asset Allocation = (Weight of Equity - Benchmark Weight) * Over or Under performance + (Weight of Bond - Benchmark Weight)* Over or Under performance + (Weight of Cash - Benchmark Weight)*Over or Under performance

= (0.40 - 0.30)*-0.1% + (0.40 - 0.50) * -0.7% + (0.20 - 0.20)*-0%

= 0.01% + (-0.07%) + 0%

= -0.06%

Therefore. contribution of asset allocation is -0.06%.