Chapter 24

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# Chapter 24 - PowerPoint PPT Presentation

Chapter 24. Portfolio Performance Evaluation. Introduction. Complicated subject Theoretically correct measures are difficult to construct Different statistics or measures are appropriate for different types of investment decisions or portfolios

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Presentation Transcript

### Chapter 24

Portfolio PerformanceEvaluation

24-1

Introduction
• Complicated subject
• Theoretically correct measures are difficult to construct
• Different statistics or measures are appropriate for different types of investment decisions or portfolios
• Many industry and academic measures are different
• The nature of active management leads to measurement problems

24-2

Dollar- and Time-Weighted Returns

Dollar-weighted returns

• Internal rate of return considering the cash flow from or to investment
• Returns are weighted by the amount invested in each stock

Time-weighted returns

• Not weighted by investment amount
• Equal weighting

24-3

Text Example of Multiperiod Returns

PeriodAction

0 Purchase 1 share at \$50

1 Purchase 1 share at \$53

Stock pays a dividend of \$2 per share

2 Stock pays a dividend of \$2 per share

Stock is sold at \$108 per share

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Dollar-Weighted Return

Period Cash Flow

0 -50 share purchase

1 +2 dividend -53 share purchase

2 +4 dividend + 108 shares sold

Internal Rate of Return:

24-5

Time-Weighted Return

Simple Average Return:

(10% + 5.66%) / 2 = 7.83%

24-6

Averaging Returns

Arithmetic Mean:

Text Example Average:

(.10 + .0566) / 2 = 7.81%

Geometric Mean:

Text Example Average:

[ (1.1) (1.0566) ]1/2 - 1

= 7.83%

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Comparison of Geometric and Arithmetic Means
• Past Performance - generally the geometric mean is preferable to arithmetic
• Predicting Future Returns- generally the arithmetic average is preferable to geometric
• Geometric has downward bias

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Abnormal Performance

What is abnormal?

Abnormal performance is measured:

• Benchmark portfolio
• Market model / index model adjusted
• Reward to risk measures such as the Sharpe Measure:

E (rp-rf) / p

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Factors That Lead to Abnormal Performance
• Market timing
• Superior selection
• Sectors or industries
• Individual companies

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rp = Average return on the portfolio

• rf = Average risk free rate

= Standard deviation of portfolio

return

p

1) Sharpe Index

rp - rf

p

24-11

M2 Measure
• Developed by Modigliani and Modigliani
• Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolio
• If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market

24-12

M2 Measure: Example

Managed Portfolio: return = 35% standard deviation = 42%

Market Portfolio: return = 28% standard deviation = 30% T-bill return = 6%

Hypothetical Portfolio:

30/42 = .714 in P (1-.714) or .286 in T-bills

(.714) (.35) + (.286) (.06) = 26.7%

Since this return is less than the market, the managed portfolio underperformed

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rp = Average return on the portfolio

• rf = Average risk free rate
• ßp = Weighted average for portfolio

rp - rf

ßp

2) Treynor Measure

24-14

3) Jensen’s Measure

= rp - [ rf + ßp ( rm - rf) ]

p

= Alpha for the portfolio

p

rp= Average return on the portfolio

ßp = Weighted average Beta

rf = Average risk free rate

rm = Avg. return on market index port.

24-15

Appraisal Ratio

Appraisal Ratio = ap / s(ep)

Appraisal Ratio divides the alpha of the portfolio by the nonsystematic risk

Nonsystematic risk could, in theory, be eliminated by diversification

24-16

Which Measure is Appropriate?

It depends on investment assumptions

1) If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market.

2) If many alternatives are possible, use the Jensen or the Treynor measure

The Treynor measure is more complete because it adjusts for risk

24-17

Limitations
• Assumptions underlying measures limit their usefulness
• When the portfolio is being actively managed, basic stability requirements are not met
• Practitioners often use benchmark portfolio comparisons to measure performance

24-18

Market Timing

Adjusting portfolio for up and down movements in the market

• Low Market Return - low ßeta
• High Market Return - high ßeta

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rp - rf

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rm - rf

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Example of Market Timing

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• Decomposing overall performance into components
• Components are related to specific elements of performance
• Example components
• Industry
• Security Choice
• Up and Down Markets

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Process of Attributing Performance to Components

Set up a ‘Benchmark’ or ‘Bogey’ portfolio

• Use indexes for each component
• Use target weight structure

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Process of Attributing Performance to Components
• Calculate the return on the ‘Bogey’ and on the managed portfolio
• Explain the difference in return based on component weights or selection
• Summarize the performance differences into appropriate categories

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Where B is the bogey portfolio and p is the managed portfolio

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Contributions for Performance

Contribution for asset allocation (wpi - wBi) rBi

+ Contribution for security selection wpi (rpi - rBi)

= Total Contribution from asset class wpirpi -wBirBi

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Complications to Measuring Performance
• Two major problems
• Need many observations even when portfolio mean and variance are constant
• Active management leads to shifts in parameters making measurement more difficult
• To measure well
• You need a lot of short intervals
• For each period you need to specify the makeup of the portfolio

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