Reading 43: Evaluating Portfolio Performance－LOS e market, active, returns, management

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CFA Institute Area 3-5, 7, 12, 14-18: Portfolio Management
Session 16: Performance Evaluation and Attribution
Reading 43: Evaluating Portfolio Performance
LOS e: Demonstrate the analysis of portfolio returns into components due to the market, to style, and to active management.

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What is the Treynor measure for the Miranda Fund and the S& 500?

Miranda Fund S& 500

A) 0.2216 -0.5568

B) 0.1109 -0.2050

C) 0.0745 -0.2450

D) 0.3515 -0.2227

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Answer and Explanation

To calculate the Treynor measure, use the following formula:

Treynor measure = (R R_f) / b

where:
R = return
R_f = risk-free return
b = beta

The Treynor measure for the Miranda Fund is:

(0.102 -0.02)/1.10 = 0.0745

The Treynor measure for the S& 500 is:

(-0.225 0.02)/1.00 = -0.2450

Based on the Treynor measure, Blakely outperformed the S& 500 on a risk-adjusted basis (when risk is defined as systematic risk). The Treynor ratio is meaningful for portfolios that are well-diversified.

To calculate the Treynor measure, use the following formula:

Treynor measure = (R R_f) / b

where:
R = return
R_f = risk-free return
b = beta

The Treynor measure for the Miranda Fund is:

(0.102 -0.02)/1.10 = 0.0745

The Treynor measure for the S& 500 is:

(-0.225 0.02)/1.00 = -0.2450

Based on the Treynor measure, Blakely outperformed the S& 500 on a risk-adjusted basis (when risk is defined as systematic risk). The Treynor ratio is meaningful for portfolios that are well-diversified.

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What is the Jensen measure for the Miranda Fund?

A) 0.0745.

B) 0.2216.

C) 0.3515.

D) 0.3270.

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Answer and Explanation

To calculate the Jensen measure, use the following formula:

Jensens alpha = R_a [R_f + b(R_m R_f)]

where:
R_a = return on actual portfolio
R_f = risk-free return
R_m = market return
b = beta of portfolio

The Jensen measure for Miranda Fund is:

0.102 [0.02 + 1.10(0.225 0.02)] = 0.3515

Jensens Alpha measures the excess return for a given level of systematic risk. It also measures the value added of an active strategy. Jensens Alpha indicates that the excess return for the Miranda Fund was 35.15 percentage points more than the return implied by the CAPM/Security Market Line. Because Jensens Alpha should be used to compare well-diversified portfolios having the same betas, it would not be the best measure for assessing the value added by Blakely.

To calculate the Jensen measure, use the following formula:

Jensens alpha = R_a [R_f + b(R_m R_f)]

where:
R_a = return on actual portfolio
R_f = risk-free return
R_m = market return
b = beta of portfolio

The Jensen measure for Miranda Fund is:

0.102 [0.02 + 1.10(0.225 0.02)] = 0.3515

Jensens Alpha measures the excess return for a given level of systematic risk. It also measures the value added of an active strategy. Jensens Alpha indicates that the excess return for the Miranda Fund was 35.15 percentage points more than the return implied by the CAPM/Security Market Line. Because Jensens Alpha should be used to compare well-diversified portfolios having the same betas, it would not be the best measure for assessing the value added by Blakely.

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What are the one-year asset class returns (stocks, cash) for Miranda and the benchmark?

Miranda Fund (stocks, cash) S& 500(stocks, cash)

A) 22.4%, 2% -23.13%, 2%

B) 18.4%, 2% -23.10%, 3%

C) 18.4%, 2% -23.26, 2%

D) 22.4%, 2% -23.29%, 3%

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Answer and Explanation

To calculate the overall actual returns for the Miranda Fund and the benchmark returns for S& 500, use the following formula:

Total return = ∑ (W_i × R_i)

where:
W_i = weights of each individual asset class
R _i = returns of each individual asset class

Blakely decided to alter the asset allocation weights to 50% stocks and 50% cash. Since the actual total return for the Miranda Fund was 10.2% and the cash return was 2%, then the asset class return for stocks is:

0.102 = [(0.50 × R_i) + (0.50 × 0.02)]

0.0920 = 0.50 R_i

R_i = 0.1840 = 18.4%

Therefore for the Miranda Fund, the asset class returns for stocks and cash are 18.4% and 2% respectively.

The benchmark S& 500 had constant weights of 97% stocks and 3% cash. Since the actual total return for the S& 500 was 22.5% and the cash return was 2%, then the asset class return for stocks is:

0.225 = [(0.97 × R_i) + (0.03 × 0.02)]

0.2256 = 0.97 R_i

R_I = 0.2326 = - 23.26%

Therefore, for the S&P 500, the asset class returns for stocks and cash are 23.26% and 2% respectively.

Total return = ∑ (W_i × R_i)

where:
W_i = weights of each individual asset class
R _i = returns of each individual asset class

Blakely decided to alter the asset allocation weights to 50% stocks and 50% cash. Since the actual total return for the Miranda Fund was 10.2% and the cash return was 2%, then the asset class return for stocks is:

0.102 = [(0.50 × R_i) + (0.50 × 0.02)]

0.0920 = 0.50 R_i

R_i = 0.1840 = 18.4%

Therefore for the Miranda Fund, the asset class returns for stocks and cash are 18.4% and 2% respectively.

The benchmark S&P 500 had constant weights of 97% stocks and 3% cash. Since the actual total return for the S&P 500 was 22.5% and the cash return was 2%, then the asset class return for stocks is:

0.225 = [(0.97 × R_i) + (0.03 × 0.02)]

0.2256 = 0.97 R_i

R_I = 0.2326 = - 23.26%

Therefore, for the S&P 500, the asset class returns for stocks and cash are 23.26% and 2% respectively.

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What was the effect of Blakely's active management decision on the Miranda Fund's one-year performance?

A) 11.87%.

B) 20.83%.

C) 32.70%.

D) 22.84%.

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Answer and Explanation

Active management decisions are assumed to generate the difference between the portfolio and benchmark returns.

 A = P - B

where:
A = Active management decision
P = the investment manager's portfolio return
B = the benchmark return

 A = 10.2% - ( -22.5%) = +32.7%.

 A = P - B

where:
A = Active management decision
P = the investment manager's portfolio return
B = the benchmark return

 A = 10.2% - ( -22.5%) = +32.7%.

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What was the effect of Blakely's within-sector selection ability on the Miranda Fund's one-year performance?

A) 11.87%.

B) 0.43%.

C) 40.41%.

D) 22.83%.

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Answer and Explanation

To calculate the within-sector selection effect, use the formula below:

within-sector selection effect = ∑ [(w_Bj) × (R_Pj R_Bj)]

where:
w_Bj = investment weight given to the asset class in the benchmark portfolio
R_Pj, R_Bj = investment return to the asset class in the managers actual portfolio and the benchmark portfolio, respectively
within-sector selection effect = [0.97 × (0.184 (0.2326)] + [0.03 × (0.02 0.02)] = 0.4041 = 40.41%

Blakely gained an additional 40.41% by selecting securities that were superior to the securities within the benchmark. This higher return was attributable to her stock selection skills in picking specific stocks that outperformed the market benchmark. This enabled her to capture excess returns (alpha) in excess of the S&P 500 benchmark.

To calculate the within-sector selection effect, use the formula below:

within-sector selection effect = ∑ [(w_Bj) × (R_Pj R_Bj)]

where:
w_Bj = investment weight given to the asset class in the benchmark portfolio
R_Pj, R_Bj = investment return to the asset class in the managers actual portfolio and the benchmark portfolio, respectively
within-sector selection effect = [0.97 × (0.184 (0.2326)] + [0.03 × (0.02 0.02)] = 0.4041 = 40.41%

Blakely gained an additional 40.41% by selecting securities that were superior to the securities within the benchmark. This higher return was attributable to her stock selection skills in picking specific stocks that outperformed the market benchmark. This enabled her to capture excess returns (alpha) in excess of the S&P 500 benchmark.

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Which of the following is the most appropriate method of calculating the managers active return? The managers active return is the:

A) market return minus the benchmark return.

B) portfolio return minus the benchmark return.

C) benchmark return minus the market return.

D) portfolio return minus the market return.

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Answer and Explanation

The managers active return is the portfolio return minus the benchmark return, where the benchmark is appropriate to the managers style. The managers style return is the benchmark return minus the market return, where the market is a broad market index.

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Given the following data, how is the managers performance most accurately characterized?

Manager's Return

5.2%

Benchmark Return

6.3%

Market Index Return

4.3%

A) The manager earned an excess return from style but not from active management.

B) The manager earned an excess return from style and active management.

C) The manager did not earn an excess return from style or active management.

D) The manager earned an excess return from active management but not from style.

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Answer and Explanation

The manager earned a return from style, where the style return is the benchmark return minus the market return (6.30% - 4.30% = 2.00%). The manager did not earn a return from active management, where the active return is the managers return minus the benchmark return (5.20% - 6.30% = -1.10%).

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Given the following data, how is the managers performance most accurately characterized?

Manager's Return

7.6%

Benchmark Return

6.2%

Market Index Return

8.8%

A) The manager earned an excess return from style and active management.

B) The manager did not earn an excess return from style or active management.

C) The manager earned an excess return from style but not from active management.

D) The manager earned an excess return from active management but not from style.

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Answer and Explanation

The manager earned a return from active management, where the active return is the managers return minus the benchmark return (7.60% - 6.20% = 1.40%). The manager did not earn a return from style, where the style return is the benchmark return minus the market return (6.20% - 8.80% = -2.60%).