Question

Problem 24-11

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% 0.5 0.6 2.6% (S&P 500)

Bonds 1 0.2 0.3 1.2 (Salomon Index)

Cash 0.7 0.3 0.1 0.8

a.

What was the manager’s return in the month? What was her overperformance or underperformance?(Round your answer to 2 decimal places. Input all amounts as positive values. Do not round intermediate calculations. Omit the "%" sign in your response.)


The manager’s return in the month is %

(Click to select)OutperformedUnderperformed by %

b.

What was the contribution of security selection to relative performance? (Round your answer to 2 decimal places. Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Omit the "%" sign in your response.)


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. Omit the "%" sign in your response.)

Contribution of asset allocation: %

Expert Answer

Answer 1

To assess the performance of the money manager, the student must examine the portfolio's actual returns and investment weightings, compare them with the benchmark, and analyze the impact of security selection and asset allocation on performance attribution.

Step-by-step explanation:

The student inquires about the performance of a money manager by analyzing a portfolio, inclusive of actual returns, weights, benchmark weights, and index returns of different sectors. We calculate each sector's contribution to the overall portfolio return and compare it against the benchmark to determine the manager's overperformance or underperformance. The contributions of security selection and asset allocation to the relative performance are deduced by examining the differences in the actual weights and returns against the benchmark weights and index returns. It is important to note that these analyses are key components of performance attribution in portfolio management.

Answer 2

a. The manager's return in the month is 1.46%.

b. The manager underperformed by 1.14%.

c. The contribution of asset allocation to relative performance is 1.78%.

How did we get these values?

a. In order to calculate the manager's return in the month, sum up the product of the actual weight and actual return for each sector:

`\[ \text{Manager's Return} = \sum (\text{Actual Weight} * \text{Actual Return}) \]`

Manager's Return = (0.5 x 2.1) + (0.2 x 1) + (0.3 x 0.7)

Manager's Return = 1.05 + 0.2 + 0.21

Manager's Return = 1.46

So, the manager's return in the month is 1.46%.

Finding the overperformance or underperformance, subtract the benchmark return from the manager's return:

Overperformance/Underperformance} = Manager's Return - Benchmark Return

Overperformance/Underperformance = 1.46% - 2.6%

Overperformance/Underperformance = -1.14%

So, the manager underperformed by 1.14%.

b. Calculating the contribution of security selection to relative performance is by summing up the product of the benchmark weight, the difference between the actual return and index return for each sector:

`\[ \text{Contribution of Security Selection} = \sum (\text{Benchmark Weight} * (\text{Actual Return} - \text{Index Return})) \]`

Contribution of Security Selection} = (0.5 x (2.1% - 2.6%)) + (0.2 x (1% - 1.2%)) + (0.3 x (0.7% - 0.8%))

`\[ \text{Contribution of Security Selection} = (-0.25\%) + (-0.04\%) + (-0.03\%) \]`

Contribution of Security Selection} = -0.32%

So, the contribution of security selection to relative performance is -0.32%.

c. The contribution of asset allocation to relative performance is the difference between the total manager's return and the contribution of security selection:

`\[ \text{Contribution of Asset Allocation} = \text{Manager's Return} - \text{Contribution of Security Selection} \]`

Contribution of Asset Allocation = 1.46% - (-0.32%)

Contribution of Asset Allocation}= 1.78%

So, the contribution of asset allocation to relative performance is 1.78%.