chapter 24
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Chapter 24. Performance Evaluation and Active Portfolio Management. Introduction. Complicated subject Theoretically correct measures are difficult to construct Different statistics or measures are appropriate for different types of investment decisions or portfolios - PowerPoint PPT PresentationTRANSCRIPT
Chapter 24
Performance Evaluation and Active Portfolio
Management
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
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 managements leads to measurement problems
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Abnormal Performance
What is abnormal?Abnormal performance is measured:
• Benchmark portfolio
• Market adjusted
• 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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Risk Adjusted Performance: Sharpe
1) Sharpe Index
rrpp - r - rff
rrpp = Average return on the portfolio= Average return on the portfolio
rrff = Average risk free rate= Average risk free rate
pp= Standard deviation of portfolio = Standard deviation of portfolio
returnreturn
pp
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Risk Adjusted Performance: Treynor
2) Treynor Measure rrpp - r- rff
ßßpp
rrpp = Average return on the portfolio = Average return on the portfolio
rrff = Average risk free rate = Average risk free rate
ßßp p = Weighted average = Weighted average for portfoliofor portfolio
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= r= rpp - [ r - [ rff + ß + ßpp ( r ( rmm - r - rff) ]) ]
3) 3) Jensen’s MeasureJensen’s Measure
pp
p
rrpp = Average return on the portfolio = Average return on the portfolio
ßßpp = Weighted average Beta = Weighted average Beta
rrff = Average risk free rate = Average risk free rate
rrmm = Avg. return on market index port. = Avg. return on market index port.
Risk Adjusted Performance: Jensen
= = Alpha for the portfolioAlpha for the portfolio
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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
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M2 Measure: Example
Managed Portfolio Market T-bill
Return 35% 28% 6%
Stan. Dev 42% 30% 0%
Hypothetical Portfolio: Same Risk as Market
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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T2 (Treynor Square) Measure
• Used to convert the Treynor Measure into percentage return basis
• Makes it easier to interpret and compare• Equates the beta of the managed portfolio
with the market’s beta of 1 by creating a hypothetical portfolio made up of T-bills and the managed portfolio
• If the beta is lower than one, leverage is used and the hypothetical portfolio is compared to the market
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T2 Example Port. P. Market
Risk Prem. (r-rf) 18% 15%
Beta 0.80 1.0
Alpha 5% 0%
Treynor Measure 16.25 10
Risk Free rate 5%
T2P = (RP – rf)/Bp – (RM – rf) =13/.8 – 10 = 6.25%
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Which Measure is Appropriate?
It depends on investment assumptions1) 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 measureThe Treynor measure is more complete because it adjusts for risk
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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
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Performance Attribution
• Decomposing overall performance into components
• Components are related to specific elements of performance
• Example components• Broad Allocation• 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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Appropriate Benchmark
• Unambiguous – anyone can reproduce it
• Investable
• Measurable
• Specified in Advance
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• 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
Process of Attributing Performance to Components
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See Example
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Lure of Active Management
Are markets totally efficient?• Some managers outperform the market for
extended periods• While the abnormal performance may not be
too large, it is too large to be attributed solely to noise
• Evidence of anomalies such as the turn of the year exist
The evidence suggests that there is some role for active management
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Market Timing
• Adjust the portfolio for movements in the market
• Shift between stocks and money market instruments or bonds
• Results: higher returns, lower risk (downside is eliminated)
• With perfect ability to forecast behaves like an option
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Style Analysis
• Introduced by Bill Sharpe
• Explaining percentage returns by allocation to style
• Style Analysis has become popular with the industry
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Morning Star’s Risk Adjusted Rating
• Similar to mean Standard Deviation rankings
• Companies are put into peer groups
• Stars are assigned• 1-lowest• 5-highest
• Highly correlated to Sharpe measures
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Superior Selection Ability
• Concentrate funds in undervalued stocks or undervalued sectors or industries
• Balance funds in an active portfolio and in a passive portfolio
• Active selection will mean some unsystematic risk
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Treynor-Black Model
• Model used to combine actively managed stocks with a passively managed portfolio
• Using a reward-to-risk measure that is similar to the the Sharpe Measure, the optimal combination of active and passive portfolios can be determined
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Treynor-Black Model: Assumptions
• Analysts will have a limited ability to find a select number of undervalued securities
• Portfolio managers can estimate the expected return and risk, and the abnormal performance for the actively-managed portfolio
• Portfolio managers can estimate the expected risk and return parameters for a broad market (passively managed) portfolio
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Appraisal Ratio =Appraisal Ratio =
AA//eAeA
AA = Alpha for the active portfolio= Alpha for the active portfolio
((eA)eA)= Unsystematic standard= Unsystematic standard deviation for activedeviation for active
Reward to Variability Measures