investment analysis and portfolio management first canadian edition

Investment Analysis and Portfolio Investment Analysis and Portfolio ManagementManagement

First Canadian EditionFirst Canadian EditionBy Reilly, Brown, Hedges, ChangBy Reilly, Brown, Hedges, Chang1818

Copyright © 2010 by Nelson Education Ltd. 18-2

•Peer Group Comparison•Risk-Adjusted Composite Performance Measures•Other Performance Measures•Challenges of Benchmarking•Evaluation of Bond Portfolio Performance•Reporting Investment Performance

Chapter 18 Evaluation of Portfolio Performance


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


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


• The Formula

• 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

Treynor Portfolio Performance Measure

i

ii

RFRRT


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?

i

ii

RFRRT

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%


Portfolio Performance Measures: Treynor’s Measure


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



i

i

i

RFRRS

where:

σi = the standard deviation of the rate of return for Portfolio i



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?

i

ii

RFRRS

SM = (14%-8%) / 20% =0.300

SD = (13%-8%) / 18% =0.278

SE = (17%-8%) / 22% =0.409

SF = (16%-8%) / 23% =0.348


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


• Jensen Portfolio Performance MeasureRjt - 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

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:

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




• 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


• The Information Ratio Performance Measure• The Formula

where: Rb = the average return for the benchmark portfolio

σER = the standard deviation of the excess return

ER

j

ER

bj

j

ERRRIR



it

itititit

itBP

BPDistCapDivEPR

..

Where

Rit = the total rate of return on Fund i during month tEPit = the ending price for Fund i during month tDivit = the dividend payments made by Fund i during month tCap.Dist.it = the capital gain distributions made by Fund i during month tBPit = the beginning price for Fund i during month t

Application of Portfolio Performance Measures

Total Rate of Return on A Mutual Fund



• 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



• 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



• Measuring Performance with Multiple Risk Factors• Form of Estimation Equation

• 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

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


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


Application of Portfolio Performance Measure


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 Effectwhere:wai, wpi = the investment proportions of the ith market segment the

manager’s portfolio and the policy portfolio, respectivelyRai, Rpi = the investment return to the ith market segment in the

manager’s portfolio and the policy portfolio, respectively

ppipiaii RRWW

piaiaii RRW


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

Performance Attribution Analysis


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• Can effect slope of SML• Can effect calculation of beta• Greater concern with global investing• Problem is one of measurement



• 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



• 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



• Required Characteristics of Benchmarks• Unambiguous• Investable• Measurable• Appropriate• Reflective of current investment opinions• Specified in advance



• 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


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 curveDEF = the default premium and is calculated by the credit spread


Evaluation of Bond Portfolio Performance


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

where: DW = factor represents portion of period that contribution is actually held in account

Ending Value of InvestmentHPY = - 1

Beginning Value of Investment

Ending Value of Investment – (1 – DW) ContributionAdjusted HPY =

Beginning Value of Investment + (DW ) Contribution



• 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



• 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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