Problem 1:

You are considering hiring one of two portfolios managers who have actively managed funds last year. Both of the funds these managers have managed are “value” funds that try to enhance the returns relative to the standard value strategy by being more selective within asset classes and timing market moves by reallocating across asset classes. Since you already have some market-timing skill, you are primarily interested in finding a fund manager with superior security picking skills. Using the data on the performances and allocations across asset classes below for each manager and value funds in general, answer the questions below.

Manager A Manager B Typical Value Fund
Allocation Return Allocation Return Allocation Return
Equity .60 20% .78 18% .75 15%
Bonds .30 6% .05 5% .10 4%
Cash .10 3% .17 3% .15 3%

1. Which manager had the highest return?

2. Relative to the performance of the typical value fund, how much better (in terms of returns) did each manager do?

3. How much of the performance of each manager can be attributed to timing?


4. How much of the performance of each manager can be attributed to selectivity? (6 points)

5. Which manager do you want to hire? Why? (4 points)

To determine the answers to these questions, we need to calculate the weighted return for each manager and compare their performance to the typical value fund. Here's how you can do it:

1. To find out which manager had the highest return, we need to calculate the weighted return for each manager. This can be done by multiplying each asset class's allocation by its respective return and summing up the results.

For Manager A:
Equity: 0.60 * 20% = 12%
Bonds: 0.30 * 6% = 1.8%
Cash: 0.10 * 3% = 0.3%
Total return for Manager A = 12% + 1.8% + 0.3% = 14.1%

For Manager B:
Equity: 0.78 * 18% = 14.04%
Bonds: 0.05 * 5% = 0.25%
Cash: 0.17 * 3% = 0.51%
Total return for Manager B = 14.04% + 0.25% + 0.51% = 14.80%

Therefore, Manager B had the highest return with a total return of 14.8%.

2. To calculate how much better each manager did relative to the typical value fund, we need to find the difference between their total returns and the return of the typical value fund.

For Manager A:
Manager A's excess return = Total return for Manager A - Return of typical value fund
Manager A's excess return = 14.1% - 15% = -0.9%

For Manager B:
Manager B's excess return = Total return for Manager B - Return of typical value fund
Manager B's excess return = 14.8% - 15% = -0.2%

So, relative to the performance of the typical value fund, Manager A did 0.9% worse, and Manager B did 0.2% worse.

3. To determine how much of each manager's performance can be attributed to timing, we need to compare their returns with the returns of the asset classes.

For Manager A:
Performance due to timing = [Return of Manager A - (Allocation of Manager A in Equity * Return of Equity + Allocation of Manager A in Bonds * Return of Bonds + Allocation of Manager A in Cash * Return of Cash)]
Performance due to timing = 14.1% - [(0.60 * 20%) + (0.30 * 6%) + (0.10 * 3%)]
Performance due to timing = 14.1% - [12% + 1.8% + 0.3%]
Performance due to timing = 14.1% - 14.1% = 0%

For Manager B:
Performance due to timing = [Return of Manager B - (Allocation of Manager B in Equity * Return of Equity + Allocation of Manager B in Bonds * Return of Bonds + Allocation of Manager B in Cash * Return of Cash)]
Performance due to timing = 14.8% - [(0.78 * 18%) + (0.05 * 5%) + (0.17 * 3%)]
Performance due to timing = 14.8% - [14.04% + 0.25% + 0.51%]
Performance due to timing = 14.8% - 14.8% = 0%

Therefore, none of the performance of each manager can be attributed to timing.

4. To determine how much of each manager's performance can be attributed to selectivity, we need to calculate the difference between their total returns and the weighted returns of the asset classes.

For Manager A:
Performance due to selectivity = Total return for Manager A - [(Allocation of Manager A in Equity * Return of Equity) + (Allocation of Manager A in Bonds * Return of Bonds) + (Allocation of Manager A in Cash * Return of Cash)]
Performance due to selectivity = 14.1% - [(0.60 * 15%) + (0.30 * 4%) + (0.10 * 3%)]
Performance due to selectivity = 14.1% - [9% + 1.2% + 0.3%]
Performance due to selectivity = 14.1% - 10.5% = 3.6%

For Manager B:
Performance due to selectivity = Total return for Manager B - [(Allocation of Manager B in Equity * Return of Equity) + (Allocation of Manager B in Bonds * Return of Bonds) + (Allocation of Manager B in Cash * Return of Cash)]
Performance due to selectivity = 14.8% - [(0.78 * 15%) + (0.05 * 4%) + (0.17 * 3%)]
Performance due to selectivity = 14.8% - [11.7% + 0.2% + 0.51%]
Performance due to selectivity = 14.8% - 12.41% = 2.39%

Therefore, 3.6% of Manager A's performance can be attributed to selectivity, and 2.39% of Manager B's performance can be attributed to selectivity.

5. Based on the analysis above, it is clear that Manager B had the highest return among the two managers. However, neither manager showed any performance when it comes to timing the market. Both managers had similar levels of selectivity, with Manager A having a slightly higher selectivity score of 3.6% compared to Manager B's 2.39%.

Therefore, considering their performance and attributes, it would be better to hire Manager B. While Manager A had a slightly higher selectivity score, Manager B outperformed in terms of total return.