Lecture Presentation Software
to accompany
Investment Analysis and
Portfolio Management
Seventh Edition
by
Frank K. Reilly & Keith C. Brown
Chapter 26
Chapter 26 - Evaluation of
Portfolio Performance
Questions to be answered:
• What major requirements do clients expect
from their portfolio managers?
• What can a portfolio manager do to attain
superior performance?
• What is the peer group comparison method of
evaluating an investor’s performance?
Chapter 26 - Evaluation of
Portfolio Performance
• What is the Treynor portfolio performance
measure?
• What is the Sharpe portfolio performance
measure?
• What is the critical difference between the
Treynor and Sharpe portfolio performance
measures?
Chapter 26 - Evaluation of
Portfolio Performance
• What is the Jensen portfolio performance
measure, and how does it relate to the Treynor
measure?
• What is the information ratio and how is it
related to the other performance measures?
• When evaluating a sample of portfolios, how
do you determine how well diversified they
are?
Chapter 26 - Evaluation of
Portfolio Performance
• What is the bias found regarding the
composite performance measures?
• What is the Fama portfolio performance
measure and what information does it provide
beyond other measures?
• What is attribution analysis and how can it be
used to distinguish between a portfolio
manager’s market timing and security
selection skills?
Chapter 26 - Evaluation of
Portfolio Performance
• What is the Roll “benchmark error” problem,
and what are the two factors that are affected
when computing portfolio performance
measures?
• What is the impact of global investing on the
benchmark error problem?
• What are customized benchmarks?
• What are the important characteristics that
any benchmark should possess?
Chapter 26 - Evaluation of
Portfolio Performance
• How do bond portfolio performance measures
differ from equity portfolio performance
measures?
• In the Wagner and Tito bond portfolio
performance measure, what is the measure of
risk used?
• What are the components of the Dietz, Fogler,
and Hardy bond portfolio performance
measure?
Chapter 26 - Evaluation of
Portfolio Performance
• What are the sources of return in the Fong,
Pearson, and Vasicek bond portfolio
performance measure?
• What are the time-weighted and dollarweighted returns and which should be
reported under AIMR’s Performance
Presentation Standards?
What is Required of
a Portfolio Manager?
1.The ability to derive above-average returns for a
given risk class
Superior risk-adjusted returns can be derived from
either
– superior timing or
– superior security selection
2. The ability to diversify the portfolio completely to
eliminate unsystematic risk. relative to the
portfolio’s benchmark
Composite Portfolio
Performance Measures
• Portfolio evaluation before 1960
– rate of return within risk classes
• Peer group comparisons
– no explicit adjustment for risk
– difficult to form comparable peer group
• Treynor portfolio performance measure
– market risk
– individual security risk
– introduced characteristic line
Treynor Portfolio
Performance Measure
• Treynor recognized two components of risk
– Risk from general market fluctuations
– Risk from unique fluctuations in the securities in the
portfolio
• His measure of risk-adjusted performance
focuses on the portfolio’s undiversifiable risk:
market or systematic risk
Treynor Portfolio
Performance Measure

R
T
i
 RFR 
i
• The numerator is the risk premium
• The denominator is a measure of risk
• The expression is the risk premium return per unit of
risk
• Risk averse investors prefer to maximize this value
• This assumes a completely diversified portfolio
leaving systematic risk as the relevant risk
Treynor Portfolio
Performance Measure
• Comparing a portfolio’s T value to a similar measure for
the market portfolio indicates whether the portfolio would
plot above the SML
• Calculate the T value for the aggregate market as follows:
Tm

R

m
 RFR
m

Treynor Portfolio
Performance Measure
• Comparison to see whether actual return of
portfolio G was above or below expectations
can be made using:
ER G   RFR   i R m  RFR 
Sharpe Portfolio
Performance Measure
• Risk premium earned per unit of risk
Si 
R i  RFR
i
Treynor versus Sharpe Measure
• Sharpe uses standard deviation of returns as the
measure of risk
• Treynor measure uses beta (systematic risk)
• Sharpe therefore evaluates the portfolio manager
on the basis of both rate of return performance
and diversification
• The methods agree on rankings of completely
diversified portfolios
• Produce relative not absolute rankings of
performance
Jensen Portfolio
Performance Measure
• Also based on CAPM
• Expected return on any security or portfolio is
ER j   RFR   j ER m   RFR 
Jensen Portfolio
Performance Measure
• Also based on CAPM
• Expected return on any security or portfolio is
ER j   RFR   j ER m   RFR 
Where: E(Rj) = the expected return on security
RFR = the one-period risk-free interest rate
j= the systematic risk for security or portfolio j
E(Rm) = the expected return on the market portfolio of
risky assets
The Information Ratio
Performance Measure
• Appraisal ratio
• measures average return in excess of
benchmark portfolio divided by the standard
deviation of this excess return
IR j 
R j  Rb
 ER

ER j
 ER
j

U
Application of Portfolio
Performance Measures
EPit  Div it  Cap.Dist .it  BPit
Rit 
BPit
Potential Bias of One-Parameter
Measures
• positive relationship between the composite
performance measures and the risk involved
• alpha can be biased downward for those
portfolios designed to limit downside risk
Components of Investment
Performance
• Fama suggested overall performance, which
is its return in excess of the risk-free rate
Portfolio Risk + Selectivity
• Further, if there is a difference between the
risk level specified by the investor and the
actual risk level adopted by the portfolio
manager, this can be further refined
Investor’s Risk + Manager’s Risk + Selectivity
Components of Investment
Performance
• The selectivity measure is used to assess the
manager’s investment prowess
• The relationship between expected return
and risk for the portfolio is:


 Em Rˆ  RFR  Cov R̂ j , R̂ m
E Rˆ  RFR  

  Rm    Rm 


Components of Investment
Performance
• The market line then becomes a benchmark
for the manager’s performance
 Rm  RFR 
Rx  RFR  
 x
   Rm  
Selectivit y  Ra  Rx  a 
Components of Investment
Performance
• The selectivity component can be broken
into two parts
– gross selectivity is made up of net selectivity
plus diversification
Selectivit y
Diversific ation
Ra  R x  a   Net Selectivit y  R x  Ra   R x  a 
Components of Investment
Performance
• Assuming the investor has a target level of
risk for the portfolio equal to T, the portion
of overall performance due to risk can be
assessed as follows:
 Manager' s Risk  Investor' s Risk
Rx  a   RFR   Rx  a   Rx  T   Rx  T   RFR 
Risk
Relationship Among
Performance Measures
• Treynor
• Sharpe
• Jensen
• Information Ratio
• Fama net selectivity measures
Highly correlated, but not perfectly so
Performance Attribution Analysis

  W   R

• Allocation effect   i Wai  W pi  R pi  R p 
• Selection effect
i
ai
ai

 R pi 
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
Measuring Market Timing Skills
R pt  RFRt  max Rst  RFRt , Rbt  RFRt ,0
R
pt
 RFRt      b Rbt  RFRt    s Rst  RFR 
  max Rst  RFRt , Rbt  RFRt ,0  U t
Factors That Affect Use of
Performance Measures
• Market portfolio difficult to approximate
• Benchmark error
–
–
–
–
can effect slope of SML
can effect calculation of Beta
greater concern with global investing
problem is one of measurement
• Sharpe measure not as dependent on market
portfolio