Chapter 19

Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

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Bodie • Kane • Marcus1

Chapter 19

Performance Evaluation and Active Portfolio Management



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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 ExamplePort. P. Market

Risk Prem. (r-rf) 13% 10%

Beta 0.80 1.0

Alpha 5% 0%

Treynor Measure 16.25 10

Weight to match Market w = M/P = 1.0 / 0.8

Adjusted Return RP* = w (RP) = 16.25%

T2P = RP

* - RM = 16.25% - 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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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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Example of Market Timing

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rrpp - r - rff

rrmm - r - rff

Steadily Increasing the BetaSteadily Increasing the BetaIrwin/McGraw-Hill ©The McGraw-Hill Companies,

Inc., 199819-1119-11



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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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• 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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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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rrff

rrff

rrMM

Rate of Return of a Perfect Market Timer



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Numerical ExampleYearYear7171727273737474757576767777787879798080

Stock Ret.Stock Ret..1431 .1431 .1898 .1898

-.1466 -.1466 -.2647 -.2647 .3720 .3720 .2384 .2384

-.0718 -.0718 .0656 .0656 .1844 .1844 .3242.3242

T-Bill RetT-Bill Ret.0439.0439.0384.0384.0693.0693.0800.0800.0580.0580.0508.0508.0512.0512.0718.0718.1038.1038.1124.1124

Avg. Ret.Avg. Ret.S.D. Ret.S.D. Ret.

.1034.1034

.2068.2068.0680.0680.0248.0248

Irwin/McGraw-Hill

21-521-5 ©The McGraw-Hill Companies, Inc., 1998



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With Perfect Forecasting Ability

• Switch to T-Bills in 73, 74, 77, 78• No negative returns or losses• Average Ret. = .1724• S.D. Ret. = .1118• Results with perfect timing

– 70% increase in mean return– 46% lower S.D.



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With Imperfect Ability to Forecast

• Long horizon to judge the ability

• Judge proportions of correct calls

• Bull markets and bear market calls

• Evidence from boxed item: “Market Timing Also Stumps Many Pros”



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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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Reward to Variability Measures

Passive Portfolio Passive Portfolio ::

m

fm rrESm

2

2



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Appraisal RatioAppraisal Ratio

AA = Alpha for the active portfolio= Alpha for the active portfolio

((eA)eA)= Unsystematic standard= Unsystematic standard deviation for activedeviation for active


eA

A

2



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Combined Portfolio Combined Portfolio ::

eA

A

m

fm rrES P

22

2



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M

AP

E(r)E(r)

CMLCMLCALCALTreynor-Black AllocationTreynor-Black Allocation

Rf



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Summary Points: Treynor-Black Model

• Sharpe Measure will increase with added ability to pick stocks

• Slope of CAL>CML

(rp-rf)/p > (rm-rf)/p

• P is the portfolio that combines the passively managed portfolio with the actively managed portfolio

• The combined efficient frontier has a higher return for the same level of risk

Chapter 19

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