Investment Analysis and Portfolio
Management
18
First Canadian Edition
By Reilly, Brown, Hedges, Chang
Chapter 18
Evaluation of Portfolio Performance
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•
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•
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Peer Group Comparison
Risk-Adjusted Composite Performance Measures
Other Performance Measures
Challenges of Benchmarking
Evaluation of Bond Portfolio Performance
Reporting Investment Performance
Copyright © 2010 by Nelson Education Ltd.
18-2
Peer Group Comparisons
• Peer Group Comparisons
• Collects the returns produced by a
representative universe of investors
over a specific period of time
• Potential problems
• No explicit adjustment for risk
• Difficult to form comparable peer group
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18-3
Risk-Adjusted
Composite Performance Measures
• Treynor Portfolio Performance Measure
• Market risk
• Individual security risk
• Introduced characteristic line
• Two components of risk
• General market fluctuations
• Uique fluctuations in the securities in the portfolio
• Focuses on the portfolio’s undiversifiable risk:
market or systematic risk
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18-4
Treynor Portfolio Performance Measure
• The Formula

R  RFR 
T 
i
i
•
•
•
•
•
i
Numerator is the risk premium
Denominator is a measure of risk
Expression is the risk premium return per unit of risk
Risk averse investors prefer to maximize this value
Assumes a completely diversified portfolio leaving
systematic risk as the relevant risk
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18-5
Portfolio Performance Measures:
Treynor’s Measure
Assume the market return is 14% and risk-free rate is 8%.
The average annual returns for Managers W, X, and Y are
12%, 16%, and 18% respectively. The corresponding betas
are 0.9, 1.05, and 1.20. What are the T values for the
market and managers?

R  RFR 
T 
i
i
i
TM = (14%-8%) / 1 =6%
TW = (12%-8%) / 0.9 =4.4%
TX = (16%-8%) / 1.05 =7.6%
TY = (18%-8%) / 1.20 =8.3%
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18-6
Portfolio Performance Measures:
Treynor’s Measure
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18-7
Portfolio Performance Measures:
Sharpe’s Measure
• Sharpe Portfolio Performance Measure
• Shows the risk premium earned over the risk free
rate per unit of standard deviation
• Sharpe ratios greater than the ratio for the
market portfolio indicate superior performance
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18-8
Portfolio Performance Measures:
Sharpe’s Measure
S
i

R
i
 RFR
s
i
where:
σi = the standard deviation of the rate of return for Portfolio i
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18-9
Portfolio Performance Measures:
Sharpe’s Measure
Assume the market return is 14% with a standard deviation of
20%, and risk-free rate is 8%. The average annual returns for
Managers D, E, and F are 13%, 17%, and 16% respectively.
The corresponding standard deviations are 18%, 22%, and
23%. What are the Sharpe measures for the market and
managers?
SM = (14%-8%) / 20% =0.300
i  RFR
R
Si 
si
SD = (13%-8%) / 18% =0.278
SE = (17%-8%) / 22% =0.409
SF = (16%-8%) / 23% =0.348
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18-10
Portfolio Performance Measures:
Treynor’s versus Sharpe’s Measure
• Treynor versus Sharpe Measure
• Sharpe uses standard deviation of returns as the
measure of risk
• Treynor measure uses beta (systematic risk)
• Sharpe evaluates the portfolio manager on basis
of both rate of return performance and
diversification
• Methods agree on rankings of completely
diversified portfolios
• Produce relative not absolute rankings of
performance
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18-11
Risk-Adjusted Performance Measures
• Jensen Portfolio Performance Measure
Rjt - RFRt = αj + βj [Rmt – RFRt ] + ejt
where:
αj = Jensen measure
• Represents the average excess return of the
portfolio above that predicted by CAPM
• Superior managers will generate a significantly
positive alpha; inferior managers will generate a
significantly negative alpha
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18-12
Risk-Adjusted Performance Measures
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18-13
Risk-Adjusted Performance Measures
• Applying the Jensen Measure
• Requires using a different RFR for each time interval
during the sample period
• Does not directly consider portfolio manager’s ability
to diversify because it calculates risk premiums in
term of systematic risk
• Flexible enough to allow for alternative models of risk
and expected return than the CAPM. Risk-adjusted
performance can be computed relative to any of the
multifactor models:
R jt  RFRt   j  [b j1F1t  b j 2 F2t 
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b jk Fkt ]  e jt
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Risk-Adjusted Performance Measures
• Information Ratio Performance Measure
• Measures average return in excess that of a
benchmark portfolio divided by the standard
deviation of this excess return
• σER can be called the tracking error of the
investor’s portfolio and it is a “cost” of active
management
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18-15
Risk-Adjusted Performance Measures
• The Information Ratio Performance Measure
• The Formula
IR j 
R j  Rb
s ER

ER j
s ER
where:
Rb = the average return for the benchmark portfolio
σER = the standard deviation of the excess return
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18-16
Application of Portfolio Performance
Measures
Total Rate of Return on A Mutual Fund
Rit 
EPit  Div it  Cap .Dist .it  BPit
BPit
Where
Rit = the total rate of return on Fund i during month t
EPit = the ending price for Fund i during month t
Divit = the dividend payments made by Fund i during month t
Cap.Dist.it = the capital gain distributions made by Fund i during
month t
BPit = the beginning price for Fund i during month t
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18-17
Application of Portfolio Performance
Measures
• Total Sample Results
• Selected 30 open-end mutual funds from nine
investment style classes and used monthly data
for 5-year period from April 2002 to March 2007
• Active fund managers performed much better
than earlier performance studies
• Primary factor was abnormally poor performance
of the index during first part of sample period
• Various performance measures ranked the
performance of individual funds consistently
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18-18
Application of Portfolio Performance
Measures
• Potential Bias of One-Parameter Measures
• Composite measures of performance should be
independent of alternative measures of risk
because they are risk-adjusted measures
• Positive relationship between the composite
performance measures and the risk involved
• Alpha measure can be biased downward for those
portfolios designed to limit downside risk
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18-19
Application of Portfolio Performance
Measures
• Measuring Performance with Multiple Risk
Factors
• Form of Estimation Equation
R jt  RFRt   j  [b j1 ( RMt  RFRt )  b j 2 SMBt  b j 3 HMLt ]  e jt
• Jensen’s alphas are computed relative to:
• Three-factor model including the market (Rm - RFR), firm
size (SMB), and relative valuation (HML) variables
• Four-factor model that also includes the return
momentum (MOM) variable
• One-factor and multifactor Jensen measures
produce similar but distinct performance rankings
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18-20
Application of Portfolio Performance
Measure
• Implications of High Positive Correlations
• Although the measures provide a generally
consistent assessment of portfolio performance
when taken as a whole, they remain distinct at an
individual level
• Best to consider these composites collectively
• User must understand what each means
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18-21
Application of Portfolio Performance
Measure
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18-22
Other Performance Measures
• Performance Attribution Analysis
• Attempts to distinguish the source of portfolio’s
overall performance
• Selecting superior securities
• Demonstrating superior timing skills
• The Formula
Allocation Effect
Selection Effect
[
]
 S i W ai  W pi  R pi  R p 
[
]
 S i Wai  Rai  R pi 
where:
wai, wpi = the investment proportions of the ith market segment the
manager’s portfolio and the policy portfolio, respectively
Rai, Rpi = the investment return to the ith market segment in the
manager’s portfolio and the policy portfolio, respectively
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Performance Attribution Analysis
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18-24
Performance Attribution Analysis
• Measuring Market Timing Skills
• Tactical asset allocation (TAA)
• Attribution analysis is inappropriate
• Indexes make selection effect not relevant
• Multiple changes to asset class weightings during an
investment period
• Regression-based measurement
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18-25
Challenges in Benchmarking
• Market Portfolio Is Difficult to Approximate
• Benchmark Portfolios
• Performance evaluation standard
• Usually a passive index or portfolio
• May need benchmark for entire portfolio and separate
benchmarks for segments to evaluate individual
managers
• Benchmark Error
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Can effect slope of SML
Can effect calculation of beta
Greater concern with global investing
Problem is one of measurement
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18-26
Challenges in Benchmarking
• Global Benchmark Problem
• Two major differences in the various beta
statistics:
• For any particular stock, the beta estimates change a
great deal over time
• Substantial differences exist in betas estimated for the
same stock over the same time period when two
different definition of the benchmark portfolio are
employed
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18-27
Challenges in Benchmarking
• Implications of the Benchmark Problems
• Benchmark problems do not negate the value of
the CAPM as a normative model of equilibrium
pricing
• Need to find a better proxy for market portfolio
or to adjust measured performance for
benchmark errors
• Multiple markets index (MMI) is major step
toward comprehensive world market portfolio
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18-28
Challenges in Benchmarking
• Required Characteristics of Benchmarks
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Unambiguous
Investable
Measurable
Appropriate
Reflective of current investment opinions
Specified in advance
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18-29
Challenges in Benchmarking
• Selecting a Benchmark
• Global level that contains the broadest mix
of risky asset available from around the
world
• Fairly specific level consistent with the
management style of an individual money
manager
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18-30
Evaluation of
Bond Portfolio Performance
• Returns-Based Bond Performance Measurement
• Early attempts to analyze fixed-income performance involved
peer group comparisons
• Peer group comparisons are potentially flawed because they
do not account for investment risk directly
• Fama and French Multifactor Model
Rjt-RFRt=αj+[bj1(Rmt-RFRt)+bj2SMBt+bj3HMLt+[bj4TERMt+bj5DEFt] + ejt
TERM = the term premium built into the Treasury yield curve
DEF = the default premium and is calculated by the credit spread
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18-31
Evaluation of
Bond Portfolio Performance
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18-32
Reporting Investment Performance
• Time-Weighted and Dollar-Weight Returns
• Better way to evaluate performance regardless of size or
timing of investment involved
• Dollar-weighted and time-weighted returns are the same
when there are no interim investment contributions within
the evaluation period
• Holding period yield computations
HPY =
Ending Value of Investment
-1
Beginning Value of Investment
Adjusted HPY =
Ending Value of Investment – (1 – DW) Contribution 
Beginning Value of Investment + (DW )  Contribution 
1
where:
DW = factor represents portion of period that contribution is
actually held in account
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Reporting Investment Performance
• Performance Presentation Standards (PPS)
• CFA Institute introduced in 1987 and formally
adopted in 1993 the Performance Presentation
Standards
• The Goals of PPS
• Achieve greater uniformity and comparability among
performance presentation
• Improve the service offered to investment management
clients
• Enhance the professionalism of the industry
• Bolster the notion of self-regulation
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Reporting Investment Performance
• Fundamental Principles of PPS
• Total return must be used
• Time-weighted rates of return must be used
• Portfolios must be valued at least monthly and periodic
returns must be geometrically linked
• Composite return performance (if presented) must contain
all actual fee-paying accounts
• Performance must be calculated after deduction of trading
expenses
• Taxes must be recognized when incurred
• Annual returns for all years must be presented
• Disclosure requirements must be met
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