Essentials of Investments: Chapter 18 - Active Management and Performance Measurement

Essentials of Investments: Chapter 18 - Active Management and Performance Measurement to introduce the most widespread approaches to risk adjustment for performance evaluation. It includes Introduction, The Conventional Theory of Performance Evaluation, Market Timing.

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

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

The Objective of Active

Management

 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

Introduction to Performance Appraisal

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) / sp

Abnormal Performance

Summary Reminder

 Objective: To introduce the most

widespread approaches to risk

adjustment for performance evaluation

 Introduction

 The Conventional Theory of Performance Evaluation

 Market Timing

1) Sharpe Index

rp = Average return on the portfolio

rf = Average risk free rate

sp = Standard deviation of portfolio return

Risk Adjusted Performance: Sharpe

2) Treynor Measure

Risk Adjusted Performance: Treynor

rp = Average return on the portfolio

rf = Average risk free rate

bp = Weighted average b for portfolio

Risk Adjusted Performance: Jensen

3) Jensen’s Measure

p = 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

Appraisal Ratio

Appraisal Ratio = p / s(ep)

Appraisal Ratio divides the alpha of the

portfolio by the nonsystematic risk

Nonsystematic risk could, in theory, be

eliminated by diversification

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

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

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

Which Measure is

Appropriate?

 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

Limitations

 Wilfred Vos proposed a new measure

that also captures skewness: VVR (Vos

Value Ratio)

Summary Reminder

 Objective: To introduce the most

widespread approaches to risk

adjustment for performance evaluation

 Introduction

 The Conventional Theory of Performance Evaluation

 Market Timing

 Adjust the portfolio for movements in the market

 Shift between stocks and money market

r

rM

Rate of Return of a Perfect Market Timer

 Switch to T-Bills in 90 and 94

 Long horizon to judge the ability

 Judge proportions of correct calls

 Bull markets and bear market calls

With Imperfect Ability to

Forecast

Adjusting portfolio for up and down movements in the market

 Low Market Return - low ßeta

 High Market Return - high ßeta

Identifying Market

Timing

 Concentrate funds in undervalued stocks

or undervalued sectors or industries

 Balance funds in an active portfolio and

 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

Complications to Measuring Performance