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Lecture Presentation Software to accompany

Investment Analysis and Portfolio Management

Eighth Editionby

Frank K. Reilly & Keith C. Brown

Chapter 25

Chapter 25 - 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?


• What is the Treynor portfolio performance measure?

• What is the Sharpe portfolio performance measure and how can it be adapted to include multifactor models of risk and expected return?

• What is information ratio and how it related to the other performance measures?


• When evaluating a sample of portfolios, how do you determine how well diversified they are?


• 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?


• What is the benchmark error problem, and what are the two factors that are affected when computing portfolio performance measures?

• What are customized benchmarks and What are the important characteristics that any benchmark should possess?


• How do bond portfolio performance measures differ from equity portfolio performance measures?


• What are the time-weighted and dollar-weighted returns and which should be reported under CFA’s Performance Presentation Standards?

• How can investment performance be measured by analyzing the security holdings of a portfolio?

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

Early Performance Measures Techniques

• 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

• Treynor portfolio performance measure– market risk– individual security risk– introduced characteristic line

• 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 ‘s CompositePerformance Measure

• 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

i

i RFRRT

Treynor ‘s Composite 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:

m

m

m

RFRRT

Demonstration of Comparative Treynor Measure

• Comparison to see whether actual return of portfolio G was above or below expectations can be made using:

RFRRRFRRE miG

Sharpe Portfolio Performance Measure

i

i

i

RFRRS

• Risk premium earned per unit of risk

Demonstration of Comparative Sharpe Measure

PortfolioAverage Annual Rate of

ReturnStandard Deviation of

Return

D 0.13 0.18

E 0.17 0.22

F 0.16 0.23

0.13 0.080.278

0.18DS

0.17 0.080.409

0.22ES

•The D portfolio had the lowest risk premium return per unit of total risk, failing even to perform as well as the aggregate market portfolio. In contrast, Portfolio E and F performed better than the aggregate market: Portfolio E did better than Portfolio F.

0.16 0.080.348

0.23FS

0.14 0.080.300

0.20MS

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

RFRRERFRRE mjj

Jensen Portfolio Performance Measure

• Also based on CAPM• Expected return on any security or portfolio is

Where: E(Rj) = the expected return on securityRFR = 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

RFRRERFRRE mjj

Applying the Jensen Measure

• Jensen Measure of performance requires using a different RFR for each time interval during the sample period

• It does not directly consider the portfolio manager’s ability to diversify because it calculates risk premiums in term of systematic risk

Jensen Measure and Multifactor Models

• Advantages:– It is easier to interpret

– Because it is estimated from a regression equation, it is possible to make statements about the statistical significance of the manger’s skill level

– It is flexible enough to allow for alternative models of risk and expected return than the CAPAM. Risk-adjusted performance can be computed relative to any of the multifactor models:

1 1 2 2[ ]jt t j j t j t jk kt jtR RFR b F b F b F e

The Information Ratio Performance Measure

• Appraisal ratio

• measures average return in excess of benchmark portfolio divided by the standard deviation of this excess return

ER

j

ER

bj

j

ERRRIR

U

j

Application of Portfolio Performance Measures

it

ititititit BP

BPDistCapDivEPR

..

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

Measuring Performance with Multiple Risk Factors

• Form of the estimation equation

1 2 3[ ( ) ]jt t j j Mt t j t j t jtR RFR b R RFR b SMB b HML e

Relationship between Performance Measures

• Although the measures provide a generally consistent assessment of portfolio performance when taken as a whole, they remain distinct at an individual level.

• Therefore it is best to consider these composites collectively

• The user must understand what each means

Components of Investment Performance

• Fama suggested overall performance, which is its return in excess of the risk-free rateOverall Performance=Excess return=Portfolio

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:

mm

m

RR

RFRRERFRRE

mj R̂,R̂Covˆ

ˆ

Evaluating Selectivity

• The market line then becomes a benchmark for the manager’s performance

xm

mx R

RFRRRFRR

axa RR y Selectivit

Evaluating Diversification

• The selectivity component can be broken into two parts– gross selectivity is made up of net selectivity

plus diversification

axaxaxa RRRRR ySelectivitNet

ationDiversific y Selectivit

Holding Based Performance Measurement

• There are two distinct advantages to assessing performance based on investment returns– Return are usually easy for the investor to

observe on a frequent basis– Represent the bottom line that the investor

actually takes away from the portfolio manager’s investing prowess

Holding Based Performance Measurement

• Returns-based measures of performance are indirect indications of the decision-making ability of a manager

• Holdings-based approach can provide additional insight about the quality of the portfolio manager

Grinblatt -Titman (GT) Performance Measure

• Among the first to assess the quality of the services provided by money managers by looking at adjustments they made to the contents of their portfolios

t 1j

GT ( )jt jt jtw w R t

t

GT

Average GT T

Characteristic Selectivity (CS) Performance Measure

• CS performance measure compares the returns of each stock held in an actively managed portfolio to the return of a benchmark portfolio that has the same aggregate investment characteristics as the security in question

tj

CS ( )jt jt Bjtw R R t

t

CS

Average CS T

Performance Attribution Analysis

• Allocation effect

• Selection effect

ppipiaii RRWW

piaiaii RRW

Performance Attribution Extensions

• Attribution methodology can be used to distinguish security selection skills from any of several other decisions that investor might make

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

0,,max tbttsttpt RFRRRFRRRFRR

ttbttst

ststbtbtpt

URFRRRFRR

RFRRRFRRRFRR

0,,max

Factors That Affect Use of Performance Measures

• Market portfolio is 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

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

Demonstration of the Global Benchmark Problem

• Two major differences in the various beta statistics:– For any particular stock, the beta estimates

change a great deal over time.– There are substantial differences in betas

estimated for the same stock over the same time period when two different definition of the benchmark portfolio are employed.

Implications of the Benchmark Problems

• Benchmark problems do not negate the value of the CAPM as a normative model of equilibrium pricing

• There is a need to find a better proxy for the market portfolio or to adjust measured performance for benchmark errors

• Multiple markets index (MMI) is major step toward a truly comprehensive world market portfolio.

Required Characteristics of Benchmarks

• Unambiguous

• Investable

• Measurable

• Appropriate

• Reflective of current investment opinions

• Specified in advance

Selecting a Benchmark

Must be selected at two levels:

• A global level that contains the broadest mix of risky asset available from around the world

• A fairly specific level consistent with the management style of an individual money manager (i.e., a customized benchmark).

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 addressed the flaw jt t j j1 mt t j2 t j3 t j4 t j4 t jtR - RFR = α + b R - RFR + b SMB + b HML + b TERM + b DEF + e

Bond Performance Attribution

• How did the performance levels of portfolio managers compare to the overall bond market?

• What factors lead to superior or inferior bond-portfolio performance?

Bond Performance Attribution

• A Bond Market Line – Need a measure of risk such as beta coefficient

for equities– Difficult to achieve due to bond maturity and

coupon effect on volatility of prices– Composite risk measure is the bond’s duration– Duration replaces beta as risk measure in a

bond market line

Bond Performance Attribution• This technique divides the portfolio return that differs from the

return on the Lehman Brothers Index into four components:– Policy effect

• Difference in expected return due to portfolio duration target

– Rate anticipation effect• Differentiated returns from changing duration of the

portfolio– Analysis effect

• Acquiring temporarily mispriced bonds– Trading effect

• Short-run changes

Reporting Investment Performance

• Time-Weighted and Dollar-Weight Returns– A better way to evaluate performance regardless of the

size or timing of the investment involved.

– The dollar-weighted and time-weighted returns are the same when there are no interim investment contributions within the evaluation period.

Ending Value of InvestmentHPY = - 1

Beginning Value of Investemnt

Ending Value of Investment - 1 - DW ContributionAdjusted HPY = 1

Beginning Value of Investemnt + DW Contribution


• Performance Presentation Standards (PPS)– The goals of the AIMR-PPS are:

• 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


• Performance Presentation Standards– Fundamental principles

• 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

The InternetInvestments Online

http://www.nelsons.com

http://www.styleadvisor.com

http://www.morningstar.com

http://www.cfainstitute.org

http://www.nelsons.com/

http://www.styleadvisor.com/

http://www.morningstar.com/

http://www.cfainstitute.org/

End of Chapter 25–Evaluation of Portfolio Performance

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