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Lecture Presentation Software to accompany

Investment Analysis and Portfolio Management

Seventh Editionby

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?


• 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?


• 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?


• 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?


• 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?


• 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?


• What are the sources of return in the Fong, Pearson, and Vasicek bond portfolio performance measure?

• What are the time-weighted and dollar-weighted 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 classSuperior 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


• 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


• 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


• 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

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

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

Components of Investment Performance

• Fama suggested overall performance, which is its return in excess of the risk-free ratePortfolio 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 refinedInvestor’s Risk + Manager’s Risk + Selectivity


• 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


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

xm

mx R

RFRRRFRR

axa RR y Selectivit


• 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


• 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:

RFRRRRRFRR TxTxaxax

Risk sInvestor' Risk sManager' Risk

Relationship Among Performance Measures

• Treynor

• Sharpe

• Jensen

• Information Ratio

• Fama net selectivity measures

Highly correlated, but not perfectly so

Performance Attribution Analysis

• Allocation effect

• Selection effect

ppipiaii RRWW

piaiaii RRW

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 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

Characteristics of Benchmarks

• Unambiguous

• Investable

• Measurable

• Appropriate

• Reflective of current investment opinions

• Specified in advance

Building a Benchmark

• Specialize as appropriate

• Provide value weightings

• Provide constraints to portfolio manager

Evaluation of Bond Portfolio Performance

• How did performance compare among portfolio managers relative to the overall bond market or specific benchmarks?

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

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 Market Line Evaluation• Policy effect

– Difference in expected return due to portfolio duration target

• Interest rate anticipation effect– Differentiated returns from changing duration

of the portfolio• Analysis effect

– Acquiring temporarily mispriced bonds• Trading effect

– Short-run changes

Decomposing Portfolio ReturnsInto maturity, sector, and quality effects

• Total return during a period is the income effect and a price change effect

• The yield-to-maturity (income) effect is the return an investor would receive if nothing had happened to the yield curve during the period

• Interest rate effect measures changes in the term structure of interest rates during the period

Decomposing Portfolio Returns• The sector/quality effect measures expected

impact on returns because of changing yield spreads between bonds in different sectors and ratings

• The residual effect is what is left after accounting for the first three factors

• A large positive residual would indicate superior selection capabilities

• Time-series plot demonstrates strengths and weaknesses of portfolio manager

Analyzing Sources of Return

• Total return (R) made up of the effect of the interest rate environment (I) and the contribution of the management process (C)

R = I + C• I is the expected rate of return (E) on a portfolio of

default-free securities and the unexpected return (U) on the Treasury Index

I = E + U

Analyzing Sources of Return

• C is composed of

M = return from maturity management

S = return from spread/quality management

B = return attributable to the selection of specific securities

R = I + C

= (E + U) + (M + S + B)

Consistency of Performance

• A study by Kritzman revealed no relationship between performance in the two periods examined in the study

• A further test also revealed no relationship between past and future performance even among the best and worst performers

• Based on these results, Kritzman concluded that it would be necessary to examine something besides past performance to determine superior bond portfolio managers

Computing Portfolio Returns

• To evaluate portfolio performance, we have to measure it

• From Chapter 1 we learned how to calculate a holding period yield, which equals the change in portfolio value plus income divided by beginning portfolio value:

1

Value Beginning

Value EndingHPY

Computing Portfolio Returns

• Dollar-weighted rate of return (DWRR)– Internal rate of return on the portfolio’s cash flows

• Time-weighted rate of return (TWRR)– Geometric average return

• TWRR is better– Considers actual period by period portfolio returns– No size bias - inflows and outflows could affect

results

Performance Presentation Standards

• AIMR PPS have the following goals:– 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• Total return must be used• Time-weighted rates of return must be used• Portfolios valued quarterly and periodic returns geometrically linked• Composite return performance (if presented) must contain all actual

fee-paying accounts• Performance calculated after trading expenses• Taxes must be recognized when incurred• Annual returns for all years must be presented• Disclosure requirements

The InternetInvestments Online

www.nelnet.com

www.styleadvisor.com

www.valueline.com

www.morningstar.com

www.valueline.com

www.aimr.org

http://www.nelnet.com/

http://www.styleadvisor.com/

http://www.valueline.com/

http://www.morningstar.com/

http://www.valueline.com/

http://www.aimr.org/

End of Chapter 26–Evaluation of Portfolio Performance

document26

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