Version 1.2 Copyright © 2000 by Harcourt, Inc. All rights reserved. Requests for permission to make copies of any part of the work should be mailed to: Permissions Department Harcourt, Inc Sea Harbor Drive Orlando, Florida Lecture Presentation Software to accompany Investment Analysis and Portfolio Management Sixth Edition by Frank K. Reilly & Keith C. Brown Chapter 27

Copyright © 2000 by Harcourt, Inc. All rights reserved. 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, or –luck! 2. The ability to diversify the portfolio completely to eliminate unsystematic risk –OTOH, Buffett focuses not on eliminating unsystematic risk, but on betting on the right sources of unsystematic risk (i.e., on +ve  stocks)

Copyright © 2000 by Harcourt, Inc. All rights reserved.  For most investors, the expected utility of an investment is a positive function of the expected return of the investment and a negative function of the variance of these returns : E(U) = f [ E(R), -  2 ]  Other relevant risk measures may include beta (for a stock portfolio) or duration (for a fixed income portfolio).  But, how do you actually adjust for risk? Risk, Return, and Utility  Proper performance evaluation should recognize both the return and the riskiness of the investment.

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

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

Copyright © 2000 by Harcourt, Inc. All rights reserved. Treynor Portfolio Performance Measure 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

Copyright © 2000 by Harcourt, Inc. All rights reserved. Treynor Portfolio Performance Measure 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:

Copyright © 2000 by Harcourt, Inc. All rights reserved. Treynor Portfolio Performance Measure Comparison to see whether actual return of portfolio G was above or below expectations can be made using:

Copyright © 2000 by Harcourt, Inc. All rights reserved. Sharpe Portfolio Performance Measure Risk premium earned per unit of risk

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

Copyright © 2000 by Harcourt, Inc. All rights reserved. Jensen Portfolio Performance Measure Also based on CAPM Expected return on any security or portfolio is

Copyright © 2000 by Harcourt, Inc. All rights reserved. Jensen Portfolio Performance Measure Also based on CAPM Expected return on any security or portfolio is Where: E(R j ) = the expected return on security RFR = the one-period risk-free interest rate  j = the systematic risk for security or portfolio j E(R m ) = the expected return on the market portfolio of risky assets

Copyright © 2000 by Harcourt, Inc. All rights reserved. Jensen Portfolio Performance Measure Jensen’s alpha is: E(R j ) could also be determined by APT instead of CAPM, and alpha can be estimated through regression.

Copyright © 2000 by Harcourt, Inc. All rights reserved. Recap So, to summarize the measures thus far …

Copyright © 2000 by Harcourt, Inc. All rights reserved.  The Sharpe measure relates return to total risk. It can be used effectively with a portfolio where unsystematic risk has been diversified away. Traditional Performance Measures where= arithmetic mean return of security i = risk free rate = standard deviation of returns on security i

Copyright © 2000 by Harcourt, Inc. All rights reserved.  The Treynor measure relates return to systematic risk, as measured by the security (or portfolio) beta. It is an appropriate measure for both single securities as well as for portfolios. Traditional Performance Measures

Copyright © 2000 by Harcourt, Inc. All rights reserved.  According to finance theory,  i should be zero. So, a positive alpha that is statistically different from zero indicates an above- average performance, and vice versa.  The Jensen measure stems directly from the implications of the capital asset pricing model as estimated by the market model. Traditional Performance Measures or

Copyright © 2000 by Harcourt, Inc. All rights reserved.  The line extending from the risk-free rate through the market portfolio on the efficient frontier is the capital market line.  Securities plotted above the capital market line show better-than-expected performance, and vice versa. Traditional Performance Measures mean return standard deviation  The Sharpe performance measure can be interpreted as the slope of a line relating the security’s return with its risk.

Copyright © 2000 by Harcourt, Inc. All rights reserved.  The standard of comparison in this case is the security market line. This line extends from the risk-free rate through the point corresponding to the return associated with a beta of 1.0. Traditional Performance Measures mean return beta  It is also possible to plot the returns of securities against their levels of systematic risk, or beta, cf. both Treynor and Jensen.

Copyright © 2000 by Harcourt, Inc. All rights reserved. Additional Performance Measures In addition to the overall summary measures of portfolio performance just described, There are a number of additional ways to measure and allocate and attribute the performance of a portfolio and its causes …

Copyright © 2000 by Harcourt, Inc. All rights reserved. The Information Ratio Performance Measure Appraisal ratio measures average return in excess of benchmark portfolio divided by the standard deviation of this excess return

Copyright © 2000 by Harcourt, Inc. All rights reserved. Application of Portfolio Performance Measures

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

Copyright © 2000 by Harcourt, Inc. All rights reserved. Components of Investment Performance Fama suggested overall performance, which is its return in excess of the risk-free rate Portfolio 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 refined Investor’s Risk + Manager’s Risk + Selectivity

Copyright © 2000 by Harcourt, Inc. All rights reserved. Components of Investment Performance The selectivity measure is used to assess the manager’s investment prowess The relationship between expected return and risk for the portfolio is:

Copyright © 2000 by Harcourt, Inc. All rights reserved. Components of Investment Performance The market line then becomes a benchmark for the manager’s performance

Copyright © 2000 by Harcourt, Inc. All rights reserved. Components of Investment Performance The selectivity component can be broken into two parts –gross selectivity is made up of net selectivity plus diversification

Copyright © 2000 by Harcourt, Inc. All rights reserved. Components of Investment Performance 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:

Copyright © 2000 by Harcourt, Inc. All rights reserved. Relationship Among Performance Measures Treynor Sharpe Jensen Information Ratio Fama net selectivity measures Highly correlated, but not perfectly so

Copyright © 2000 by Harcourt, Inc. All rights reserved. Performance Attribution Analysis Allocation effect Selection effect

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

Copyright © 2000 by Harcourt, Inc. All rights reserved. Measuring Market Timing Skills

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

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

Copyright © 2000 by Harcourt, Inc. All rights reserved. Characteristics of Benchmarks Unambiguous Investable Measurable Appropriate Reflective of current investment opinions Specified in advance

Copyright © 2000 by Harcourt, Inc. All rights reserved. Building a Benchmark Specialize as appropriate Provide value weightings Provide constraints to portfolio manager

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

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

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

Copyright © 2000 by Harcourt, Inc. All rights reserved. Decomposing Portfolio Returns Into 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

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

Copyright © 2000 by Harcourt, Inc. All rights reserved. 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) and the unexpected return (U) on default-free securities I = E + U

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

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

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

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

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

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

Copyright © 2000 by Harcourt, Inc. All rights reserved. The Internet Investments Online

Copyright © 2000 by Harcourt, Inc. All rights reserved. End of Chapter 27 –Evaluation of Portfolio Performance

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