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Chapter 20. Active Management and Performance Measurement. Chapter Summary. Objective: To introduce the most widespread approaches to risk adjustment for performance evaluation. Introduction The Conventional Theory of Performance Evaluation Market Timing. The Objective of Active Management.

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Chapter 20

Active Management and Performance Measurement


Chapter summary
Chapter Summary

  • Objective: To introduce the most widespread approaches to risk adjustment for performance evaluation.

    • Introduction

    • The Conventional Theory of Performance Evaluation

    • Market Timing


The objective of active management
The Objective 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


Introduction to performance appraisal
Introduction to Performance Appraisal

  • 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


Abnormal performance
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


Factors that lead to abnormal performance
Factors That Lead to Abnormal Performance

  • Market timing

  • Superior selection

    • Sectors or industries

    • Individual companies


Summary reminder
Summary Reminder

  • Objective: To introduce the most widespread approaches to risk adjustment for performance evaluation.

    • Introduction

    • The Conventional Theory of Performance Evaluation

    • Market Timing


Risk adjusted performance sharpe

rp = Average return on the portfolio

rf = Average risk free rate

sp = Standard deviation of portfolio return

Risk Adjusted Performance: Sharpe

1) Sharpe Index


Risk adjusted performance treynor

rp = Average return on the portfolio

rf = Average risk free rate

bp = Weighted average b for portfolio

Risk Adjusted Performance: Treynor

2) Treynor Measure


Risk adjusted performance jensen

ap = alpha for the portfolio

rp = Average return on the portfolio

rf = Average risk free rate

bp = Weighted average b for portfolio

rm = Average return on market index portfolio

Risk Adjusted Performance: Jensen

3) Jensen’s Measure


Appraisal ratio
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


M 2 measure
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


M 2 measure example
M2 Measure: Example

Managed Portfolio: return = 35% st dev = 42%

Market Portfolio: return = 28% st dev = 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


Which measure is appropriate
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


Limitations
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


Alternative performance measures
Alternative Performance Measures

  • Mean-variance measures of performance are increasingly challenged

  • The normality or log-normality of returns is also questioned

  • Wilfred Vos proposed a new measure that also captures skewness: VVR (Vos Value Ratio)


Summary reminder1
Summary Reminder

  • Objective: To introduce the most widespread approaches to risk adjustment for performance evaluation.

    • Introduction

    • The Conventional Theory of Performance Evaluation

    • Market Timing


Market timing
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


Rate of return of a perfect market timer

rf

rM

rf

Rate of Return of a Perfect Market Timer



With perfect forecasting ability
With Perfect Forecasting Ability

  • Switch to T-Bills in 90 and 94

    • Mean = 18.94%,

    • Standard Deviation = 12.04%

  • Invested in large stocks for the entire period:

    • Mean = 17.41%

    • Standard Deviation = 14.11%

  • The results are clearly related to the period


With imperfect ability to forecast
With Imperfect Ability to Forecast

  • Long horizon to judge the ability

  • Judge proportions of correct calls

  • Bull markets and bear market calls


Identifying market timing
Identifying Market Timing

Adjusting portfolio for up and down movements in the market

  • Low Market Return - low ßeta

  • High Market Return - high ßeta


Example of market timing

rp - rf

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rm - rf

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Steadily Increasing the Beta

Example of Market Timing


Superior selection ability
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


Complications to measuring performance
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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