Portifolio Measure

Copyright © 2000 by Harcourt, Inc. All rights reserved.

Chapter 15Performance Measurement


Chapter 15Outline

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 15Outline

• 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 15Outline

• 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 15Outline

• 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 15Outline

• 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 15Outline

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


How Should Investors Measure Risk?

• Standard Deviation

– Investors with limited holdings

• Beta

– Investors with a wide array of holding


How Should Investors Select Funds?

Performance Indexes

Provide a method of comparing

funds with different

risk-return characteristics


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


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


Performance Indexes

• Sharpe’s Performance Index (PIS)

• Treynor’s Performance Index (PIT)

• Jensen’s Performance Index (PIJ)

• Performance Indexes With APT(PIA)


Treynor’s Performance Index

• Based on SML

• Uses Beta to measure Risk

• The Higher the Index– The better the performance

• Investors Hold Many Assets

• For Investors Only Interested in Whether They Beat the Market


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’s Performance Index

• Based on the Slope of the CML

• Uses Standard Deviation to Measure Risk

• The Higher the Index

– The better the performance

• Investors Only Hold the Mutual Fund


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’s Performance Index

• Based on CAPM• Uses Beta to Measure Risk• “Alpha” = average return less expected return

given by CAPM / SML• Determines How Much One Fund

Outperforms or Underperforms Another Fund• Determines the Significance of Results• Investors Hold Many Assets


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


Performance Indexes With APT

• One or More Factors Determine Risk

• Jensen’s Performance Measure

• Examine the Difference Between – Actual and expected average rate of return

• Determines the Significance of Results

• For Investors Who Want to Compare Their Performance With Other Fund Managers


Summary

• Standard Deviation Appropriate– Sharpe’s index

• Beta Appropriate– Treynor’s index– Jensen’s index

• One or More Factors Determine Risk– APT


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

..


Empirical Evidence For MFs • MFs performance Fall Behind the Market• MFs can not Outperform

– Buy-the-market and-hold policy

• International MFs Tend to do Better– Outperform the S&P 500

– Choice of market portfolio critical

• Bond Funds Underperform the Indexes– Relationship

• underperformance and the expense ratio


Pension Funds Outperformed By The S&P 500

0

10

20

30

40

50

60

70

80

81 82 83 84 85 86 87 88 89 90 91

%


Performance Attribution

Assessing the performance of

the activities that make up

portfolio management


Levels Of Decisions Causing Excess Returns

• Top-Down Approach– Asset allocation– Sector Allocation– Industry allocation– Security selection


Flow Chart Top -Down Money Management

Process

A sse t A lloca tion s

S ec to r A lloca tion s

In d u s try A lloca tion

S ecu rity S e llec tion s A m W ater W orks

W ater

U tilit ies

S tocks B on d s C ash

Portfolio


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


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


Can Fund Managers Time The Market?

• Newsletters Failed

• Performance Attributed To– Problems with performance indexes


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


Caution About Performance Indexes

• Problems– Historical performance is used to infer future performance– Difficult to measure the risk of actively traded accounts– Beta is not stable

• Depends on the choice of market index– Overall performance indexes cannot identify

• What activities of the portfolio manager resulted in the performance

• Performance attribution done as a separate step


What is the “Market Portfolio”?

• 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


Consistency of Performance

• For bond managers, no relationships between performance in two periods, nor between past and future performance among the best and worst performers


Computing Portfolio Returns

• To evaluate portfolio performance, we have to measure it

• From Chapter 5 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

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Portifolio Measure

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