CHAPTER TWENTY-TWO Evaluation of

Investment Performance

Cleary / Jones Investments: Analysis and

Management

Learning ObjectivesLearning Objectives To outline the framework for To outline the framework for

evaluating portfolio performanceevaluating portfolio performance To use measures of return and risk To use measures of return and risk

to evaluate portfolio performanceto evaluate portfolio performance To distinguish between the three To distinguish between the three

composite measures of portfolio composite measures of portfolio performanceperformance

Learning ObjectivesLearning Objectives To discuss problems with portfolio To discuss problems with portfolio

measurementmeasurement To explain issues in portfolio To explain issues in portfolio

evaluation such as performance evaluation such as performance attributionattribution

How Should Portfolio How Should Portfolio Performance Be Performance Be

Evaluated?Evaluated? ““Bottom line” issue in investingBottom line” issue in investing Is the return after all expenses Is the return after all expenses

adequate compensation for the risk?adequate compensation for the risk? What changes should be made if the What changes should be made if the

compensation is too small?compensation is too small? Performance must be evaluated Performance must be evaluated

before answering these questionsbefore answering these questions

ConsiderationsConsiderations Without knowledge of risks taken, Without knowledge of risks taken,

little can be said about performancelittle can be said about performance– Intelligent decisions require an Intelligent decisions require an

evaluation of risk evaluation of risk andand return return– Risk-adjusted performance bestRisk-adjusted performance best

Relative performance comparisons Relative performance comparisons – Benchmark portfolio must be legitimate Benchmark portfolio must be legitimate

alternative that reflects objectivesalternative that reflects objectives

ConsiderationsConsiderations Evaluation of portfolio manager or the Evaluation of portfolio manager or the

portfolio itself?portfolio itself?– Portfolio objectives and investment Portfolio objectives and investment

policies matterpolicies matter Constraints on managerial behaviour affect Constraints on managerial behaviour affect

performanceperformance How well-diversified during the How well-diversified during the

evaluation period?evaluation period?– Adequate return for diversifiable risk?Adequate return for diversifiable risk?

AIMR’s Presentation AIMR’s Presentation StandardsStandards

Minimum standards for reporting Minimum standards for reporting investment performanceinvestment performance

Standard objectives:Standard objectives:– Promote full disclosure in reportingPromote full disclosure in reporting– Ensure uniform reporting to enhance Ensure uniform reporting to enhance

comparabilitycomparability Requires the use of total return to Requires the use of total return to

calculate performancecalculate performance

Return MeasuresReturn Measures Change in investor’s total wealth over Change in investor’s total wealth over

an evaluation periodan evaluation period(V(VEE - V - VBB)/V)/VBB

VVEE = ending portfolio value = ending portfolio valueVVBB = beginning portfolio value = beginning portfolio value

Assumes no funds added or withdrawn Assumes no funds added or withdrawn during evaluation periodduring evaluation period– If not, timing of flows importantIf not, timing of flows important

Dollar-weighted returnsDollar-weighted returns– Captures cash flows during the Captures cash flows during the

evaluation periodevaluation period– Equivalent to internal rate of returnEquivalent to internal rate of return– Equates initial value of portfolio Equates initial value of portfolio

(investment) with cash inflows or (investment) with cash inflows or outflows and ending value of portfoliooutflows and ending value of portfolio

– Cash flow effects make comparisons to Cash flow effects make comparisons to benchmarks inappropriatebenchmarks inappropriate

Return MeasuresReturn Measures

Time-weighted returnsTime-weighted returns– Captures cash flows during the evaluation Captures cash flows during the evaluation

period period andand permits comparisons with permits comparisons with benchmarksbenchmarks

– Calculate a return relative for each time Calculate a return relative for each time period defined by a cash inflow or outflowperiod defined by a cash inflow or outflow

– Use each return relative to calculate a Use each return relative to calculate a compound rate of return for the entire compound rate of return for the entire periodperiod

Return MeasuresReturn Measures

Which Return Measure Which Return Measure Should Be Used?Should Be Used?

Dollar- and Time-weighted Returns Dollar- and Time-weighted Returns can give different resultscan give different results– Dollar-weighted returns appropriate for Dollar-weighted returns appropriate for

portfolio ownersportfolio owners– Time-weighted returns appropriate for Time-weighted returns appropriate for

portfolio managersportfolio managers No control over inflows, outflowsNo control over inflows, outflows Independent of actions of clientIndependent of actions of client

AIMR requires time-weighted returnsAIMR requires time-weighted returns

Risk MeasuresRisk Measures Risk differences cause portfolios to Risk differences cause portfolios to

respond differently to market changesrespond differently to market changes Total risk measured by the standard Total risk measured by the standard

deviation of portfolio returns deviation of portfolio returns Systematic risk measured by a Systematic risk measured by a

security’s betasecurity’s beta– Estimates may vary, be unstable and Estimates may vary, be unstable and

change over timechange over time

Risk-Adjusted Risk-Adjusted PerformancePerformance

The Sharpe reward-to-variability The Sharpe reward-to-variability ratioratio– Benchmark based on the ex post Benchmark based on the ex post

capital market linecapital market line /SDRFTRRVAR pp

= Average excess return / total risk= Average excess return / total riskRisk premium per unit of riskRisk premium per unit of risk– The higher the RVAR, the better The higher the RVAR, the better the performancethe performance– Provides a ranking measure for Provides a ranking measure for portfoliosportfolios

The Treynor reward-to-volatility The Treynor reward-to-volatility ratioratio– Distinguishes between total and Distinguishes between total and

systematic risksystematic risk

Risk-Adjusted Risk-Adjusted PerformancePerformance

/RFTRRVOL pp

= Average excess return / market risk= Average excess return / market risk– Risk premium per unit of market riskRisk premium per unit of market risk– The higher the RVOL, the better the The higher the RVOL, the better the performanceperformance– Implies a diversified portfolioImplies a diversified portfolio

RVAR or RVOL?RVAR or RVOL? Depends on the definition of riskDepends on the definition of risk

– If total (systematic) risk is the relevant If total (systematic) risk is the relevant risk, use RVAR (RVOL)risk, use RVAR (RVOL)

– If portfolios are perfectly diversified, If portfolios are perfectly diversified, rankings based on either RVAR or RVOL rankings based on either RVAR or RVOL are the sameare the same

– Differences in diversification cause Differences in diversification cause ranking differencesranking differences

RVAR captures portfolio diversificationRVAR captures portfolio diversification

Measuring DiversificationMeasuring Diversification How correlated are portfolio’s How correlated are portfolio’s

returns to market portfolio?returns to market portfolio?– RR22 from estimation of from estimation of

RRptpt - RF - RFtt = = pp + + pp[R[RMtMt - RF - RFtt] + e] + eptpt

– RR22 is the coefficient of determination is the coefficient of determination– Excess return form of characteristic lineExcess return form of characteristic line– The lower the RThe lower the R22, the greater the , the greater the

diversifiable risk and the less diversifieddiversifiable risk and the less diversified

Jensen’s AlphaJensen’s Alpha The estimated The estimated coefficient in coefficient in

RRptpt - RF - RFtt = = pp + + pp[R[RMtMt - RF - RFtt] + e] + eptpt

is a means to identify superior or inferior is a means to identify superior or inferior portfolio performanceportfolio performance

– CAPM implies CAPM implies is zerois zero– Measures contribution of portfolio manager Measures contribution of portfolio manager

beyond return attributable to riskbeyond return attributable to risk If If > 0 (< 0, = 0), performance is superior > 0 (< 0, = 0), performance is superior

(inferior, equal) to market, risk-adjusted(inferior, equal) to market, risk-adjusted

Measurement ProblemsMeasurement Problems Performance measures based on Performance measures based on

CAPM and its assumptionsCAPM and its assumptions– Riskless borrowing?Riskless borrowing?– What should market proxy be?What should market proxy be?

If not efficient, benchmark errorIf not efficient, benchmark error Global investing increases problemGlobal investing increases problem

How long of an evaluation period?How long of an evaluation period?– AMIR stipulates a 10 year periodAMIR stipulates a 10 year period

Other Evaluation IssuesOther Evaluation Issues Performance attribution seeks an Performance attribution seeks an

explanation for success or failureexplanation for success or failure– Analysis of investment policy and asset Analysis of investment policy and asset

allocation decisionallocation decision– Analysis of industry and security selectionAnalysis of industry and security selection– Benchmark (bogey) selected to measure Benchmark (bogey) selected to measure

passive investment resultspassive investment results– Differences due to asset allocation, market Differences due to asset allocation, market

timing, security selectiontiming, security selection