chapter #4all rights reserved1 chapter 4 evaluating portfolio performance

Chapter #4Chapter #4 All Rights ReservedAll Rights Reserved 11

Chapter 4

Evaluating Portfolio Evaluating Portfolio PerformancePerformance


Student Learning Objectives

Issues in Measuring PerformanceIssues in Measuring Performance Three measures of investment Three measures of investment

performance based on MPTperformance based on MPT Past performance as a predictor of Past performance as a predictor of

future performancefuture performance Applying MPT to investment Applying MPT to investment

decisionsdecisions Applying the Treynor-Black modelApplying the Treynor-Black model


Issues in Measuring Issues in Measuring PerformancePerformance

Cash inflows and outflows mean that Cash inflows and outflows mean that different, legitimate methods of computing different, legitimate methods of computing returns will provide different performance returns will provide different performance results.results. Time-weighted (Geometric Average)Time-weighted (Geometric Average) dollar weighted (Arithmetic average)dollar weighted (Arithmetic average) Internal Rate of Return (IRR; makes NPV = 0)Internal Rate of Return (IRR; makes NPV = 0)

NN

N

1tt

t0

r1

Value

r1

CFValue0


Issues in Measuring Issues in Measuring PerformancePerformance

Additions of cash to or removals of cash from a portfolio Dividends or interest payments left in

portfolio are not interim cash flows Charges in a margin account added to

the debit balance, or offset against a cash position are not interim cash flows


BenchmarkingBenchmarking

Selection of market indexSelection of market index DJIA: Price-weightedDJIA: Price-weighted SP500: Value-weighted (price * shares)SP500: Value-weighted (price * shares) NASDAQ: Value-weightedNASDAQ: Value-weighted Bond IndexesBond Indexes Foreign Market indexesForeign Market indexes


BenchmarkingBenchmarking

Selection of comparison methodSelection of comparison method Should be risk-adjusted comparisonShould be risk-adjusted comparison Can adjust risk based on:Can adjust risk based on:

BetaBeta Variance (or standard deviation)Variance (or standard deviation)


Performance Measures

Sharpe Performance Index (1966)Sharpe Performance Index (1966) Reward to Variability (risk) (CML Reward to Variability (risk) (CML

construct)construct)

S = (RS = (Rpp – R – Rff) / ) / pp

S is the slope of a line whose intercept is S is the slope of a line whose intercept is

the risk free rate (Rthe risk free rate (Rff))

the STEEPER the line, the better the the STEEPER the line, the better the

performance.performance.

Best used to [performance] rank portfoliosBest used to [performance] rank portfolios


Source:

Investments, Haim Levy & Thierry Post

Prentice-Hall (2005).

Chapter 22, page 771.



Treynor Performance IndexTreynor Performance Index Reward per Beta Risk (SML construct)Reward per Beta Risk (SML construct) T = (RT = (Rpp – R – Rff) / ) / pp

Beta computed using historical rates of Beta computed using historical rates of returnreturn

How well did the investment portfolio do How well did the investment portfolio do in terms of percentage return on a in terms of percentage return on a risk-risk-adjustedadjusted basis. basis.


Source:Investments, Haim Levy & Thierry PostPrentice-Hall (2005). Chapter 22, page 774.



Jensen’s Alpha: Jensen’s Alpha: Mean Excess Return minus the CAPM returnMean Excess Return minus the CAPM return

Excess return = RExcess return = Rpp – R – Rff

CAPM Return = CAPM Return = (R (Rmm – R – Rff))

= (R= (Rp – R – Rf) – ) – (R (Rmm – R – Rff)) One problem with Jensen’s measure is that One problem with Jensen’s measure is that

we do not know the magnitude of non-we do not know the magnitude of non-systematic risk incurred in order to achieve systematic risk incurred in order to achieve the excess.the excess.



Information Ratio A portfolio’s alpha divided by the

standard deviation of the error term from the estimation of a portfolio’s characteristic line IR = /

The larger the value of the ratio, the more attractive the performance of the portfolio


Supplemental MaterialSupplemental Material

Gauging impact of MPT on Investor Gauging impact of MPT on Investor BehaviorBehavior How do investors implement efficient How do investors implement efficient

market theory?market theory? True BelieversTrue Believers DoubtfulDoubtful Percentage playersPercentage players


MPT and Investor Decisions

Different groups of investors apply MPT Different groups of investors apply MPT differently depending on how strongly differently depending on how strongly they believe in market efficiencythey believe in market efficiency Group 1 MPT investors believe the market is Group 1 MPT investors believe the market is

strong-form efficientstrong-form efficient and will invest in any and will invest in any naïve diversified portfolionaïve diversified portfolio

Passive or Passive or naïve strategy invests in a well-naïve strategy invests in a well-diversified portfoliodiversified portfolio because one cannot because one cannot “beat the market” – index portfolio“beat the market” – index portfolio


MPT and Investor Decisions Group 2 MPT investors believe in Group 2 MPT investors believe in

Semistrong market efficiencySemistrong market efficiency and and invest in a well-diversified portfolio of invest in a well-diversified portfolio of growth stocks to gain both benefitsgrowth stocks to gain both benefits Group 2 investors will analyze securities Group 2 investors will analyze securities

to determine which stock to include in a to determine which stock to include in a well-diversified portfoliowell-diversified portfolio

Group 2 investors will also analyze Group 2 investors will also analyze optimal allocation of the portfoliooptimal allocation of the portfolio


MPT and Investor Decisions Third group is somewhere between Third group is somewhere between

group 1 and group 2group 1 and group 2 They believe the market offers They believe the market offers

undervalued and overvalued stocks, undervalued and overvalued stocks, but that finding them is nearly but that finding them is nearly impossible, so they may act as group impossible, so they may act as group 1 investors1 investors

Other investors scorn MPTOther investors scorn MPT Technicians may fall in this groupTechnicians may fall in this group


Treynor-Black Portfolio Combination Model Mathematical Model to determine Mathematical Model to determine

optimal combinations between optimal combinations between undervalued stocks and the well-undervalued stocks and the well-diversified diversified naïvenaïve portfolio portfolio

Shows the tradeoff between buying Shows the tradeoff between buying growth stocks and the naïve portfoliogrowth stocks and the naïve portfolio

Finds the optimal allocation of the Finds the optimal allocation of the stocksstocks

Appeals to group 2 MPT investorsAppeals to group 2 MPT investors


Applying the Treynor-Black Portfolio Combination Model Determine a well-diversified portfolio Determine a well-diversified portfolio

on the efficient frontier - a market on the efficient frontier - a market portfolioportfolio

Identify a group of undervalued stocks Identify a group of undervalued stocks using security analysisusing security analysis

Optimize the market portfolio using Optimize the market portfolio using the undervalued portfoliothe undervalued portfolio

Select the proportion of allocations Select the proportion of allocations using the Sharpe measureusing the Sharpe measure


Implications for investors Diversify by investing in several Diversify by investing in several

securities or in mutual fundssecurities or in mutual funds Measure performance using reward per Measure performance using reward per

risk to determine fund performancerisk to determine fund performance Measure performance over a long period Measure performance over a long period

of time, perhaps five years or moreof time, perhaps five years or more Understand the tradeoffs between Understand the tradeoffs between

picking high growth stocks over a well-picking high growth stocks over a well-diversified portfoliodiversified portfolio

chapter #4all rights reserved1 chapter 4 evaluating portfolio performance

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