Bài giảng Essentials of Investments - 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
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Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-1
Chapter 20
Active Management
and Performance
Measurement
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-2
Chapter Summary
Objective: To introduce the most
widespread approaches to risk
adjustment for performance evaluation.
Introduction
The Conventional Theory of Performance
Evaluation
Market Timing
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-3
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
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-4
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
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-5
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
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-6
Market timing
Superior selection
Sectors or industries
Individual companies
Factors That Lead to
Abnormal Performance
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-7
Summary Reminder
Objective: To introduce the most
widespread approaches to risk
adjustment for performance evaluation.
Introduction
The Conventional Theory of Performance
Evaluation
Market Timing
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-8
1) Sharpe Index
rp = Average return on the portfolio
rf = Average risk free rate
sp = Standard deviation of portfolio return
Risk Adjusted
Performance: Sharpe
p
fp rr
s
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-9
2) Treynor Measure
Risk Adjusted
Performance: Treynor
p
fp rr
b
rp = Average return on the portfolio
rf = Average risk free rate
bp = Weighted average b for portfolio
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-10
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
fmpfpp rrrr b
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-11
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
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-12
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
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-13
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
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-14
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?
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-15
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
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-16
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)
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-17
Summary Reminder
Objective: To introduce the most
widespread approaches to risk
adjustment for performance evaluation.
Introduction
The Conventional Theory of Performance
Evaluation
Market Timing
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-18
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
Market Timing
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-19
rf
rf
rM
Rate of Return of a
Perfect Market Timer
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-20
Returns from 1987 -
1996
Year Lg Stocks T-Bills
1990 -3.20 7.86
1991 30.66 5.65
1992 7.71 3.54
1993 9.87 2.97
1994 1.29 3.91
1995 37.71 5.58
1996 23.07 5.58
1998 28.58 5.11
1999 21.04 4.80
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-21
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 Perfect Forecasting
Ability
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-22
Long horizon to judge the ability
Judge proportions of correct calls
Bull markets and bear market calls
With Imperfect Ability to
Forecast
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-23
Adjusting portfolio for up and down
movements in the market
Low Market Return - low ßeta
High Market Return - high ßeta
Identifying Market
Timing
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-24
Example of Market
Timing
*
**
*
*
*
*
*
*
*
*
**
***
*
**
*
*
**
rp - rf
rm - rf
Steadily Increasing the Beta
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-25
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
Superior Selection Ability
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-26
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