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. Equity Bonds Cash Actual Return 2.5% 1.4 0.8 Actual Weight 0.5 0.2 Benchmark Weight 0.7 0.2 Index Return 3% (S&P 500) 1.9 (Barclay's Aggregate) 0.9 0.3 0.1 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 1.76 % 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

Answer 1

Ans:- (a-1) Managers actual return in the month will be given by

=(Equity weights * Return on equity + weights of bond * Return on Bond + weights of cash * Return on cash,)

= 0.5 * 2.5% + 0.2 * 1.4% + 0.3 * 0.8 = 1.77%

(a-2) In this question we need to find the underperformance or overperformance by the manger for that first we need to find the Benchmark return.

Benchmark return = Benchmark weights of equity * Index return on equity + Benchmarks weights of Bond * Index return on Bond + Benchmark weights of cash * Index return on cash.

= 0.7 * 3% + 0.2 * 1.9% + 0.1 * 0.9

= 2.57%.

Now clearly there is an Underperformance by the manager because Benchmark return > Actual Return (2.57 >1.77)

Now the mangers underperformance will be the difference between (Benchmark return - Actual return)

= 2.57% - 1.77% = 0.80%.

(b) Contribution of security selection to relative performance will be given by

= Actual weights of equity * ( Actual return of equity - Benchmark return on equity) + Actual weights of Bond * ( Actual return of bond - Benchmark return on Bond) + Actual weights of cash * ( Actual return - Benchmark return)

= 0.5 * ( 2.5% - 3%) + 0.2 * ( 1.4% - 1.9%) + 0.3 * (  0.8% - 0.9%) = - 0.38%.

(c) Contribution of Asset allocation will be given by

= Excess weights of equity * Index return of equity + Excess weights of Bond * Index return on Bond + Excess weights of cash * Index return on cash.

= ( 0.5 - 0.7 ) * 3% + (0.2 - 0.2) * 1.9% + ( 0.3 - 0.1) * 0.9% = -0.42%.

Note:- Excess return is (Actual weights - Benchmark weights).

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