Investment Analysis and Portfolio Management First Canadian Edition

1. Investment Analysis and Portfolio Management First Canadian Edition By Reilly, Brown, Hedges, Chang 18

2. Chapter 18Evaluation of Portfolio Performance • Peer Group Comparison • Risk-Adjusted Composite Performance Measures • Other Performance Measures • Challenges of Benchmarking • Evaluation of Bond Portfolio Performance • Reporting Investment Performance

3. 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

4. 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

5. Treynor Portfolio Performance Measure • 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

6. 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? • 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%

7. Portfolio Performance Measures: Treynor’s Measure

8. 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

9. - R RFR i = S i s i Portfolio Performance Measures: Sharpe’s Measure • where: • σi = the standard deviation of the rate of return for Portfolio i

10. - R RFR i = S i s i Portfolio Performance Measures: Sharpe’s Measure 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? • SM = (14%-8%) / 20% =0.300 • SD = (13%-8%) / 18% =0.278 • SE = (17%-8%) / 22% =0.409 • SF = (16%-8%) / 23% =0.348

11. 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

12. Risk-Adjusted Performance Measures • Jensen Portfolio Performance Measure Rjt- 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

13. Risk-Adjusted Performance Measures

14. 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:

15. Risk-Adjusted Performance Measures • Information Ratio Performance Measure • Measures average return in excess that of a benchmark portfolio divided by the standard deviation of this excess return • σERcan be called the tracking errorof the investor’s portfolio and it is a “cost” of active management

16. - R R ER j b j = = IR j s s ER ER Risk-Adjusted Performance Measures • The Information Ratio Performance Measure • The Formula where: Rb= the average return for the benchmark portfolio σER = the standard deviation of the excess return

17. + + - EP Div Cap . Dist . BP = it it it it R it BP it Application of Portfolio Performance Measures Total Rate of Return on A Mutual Fund • Where • Rit= the total rate of return on Fund i during month t • EPit= the ending price for Fund i during month t • Divit= the dividend payments made by Fund i during month t • Cap.Dist.it= the capital gain distributions made by Fund i during month t • BPit= the beginning price for Fund i during month t

18. Application of Portfolio Performance Measures • 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

19. Application of Portfolio Performance Measures • 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

20. Application of Portfolio Performance Measures • 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

21. 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

22. Application of Portfolio Performance Measure

23. [ ] ( ) ( ) = S - ´ - W W R R i [ ai pi pi ] p ( ) ( ) = S ´ - W R R i ai ai pi 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 Effect where: wai, wpi = the investment proportions of the ith market segment the manager’s portfolio and the policy portfolio, respectively Rai, Rpi = the investment return to the ith market segment in the manager’s portfolio and the policy portfolio, respectively

24. Performance Attribution Analysis

25. 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

26. 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

27. Challenges in Benchmarking • 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

28. Challenges in Benchmarking • 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

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

30. Challenges in Benchmarking • 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

31. 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 intothe Treasury yield curve DEF = the default premium and is calculatedby the credit spread

32. Evaluation of Bond Portfolio Performance

33. Ending Value of Investment HPY = - 1 Beginning Value of Investment ( ) Ending Value of Investment – (1 – DW) Contribution Adjusted HPY = -1 ( ) Contribution Beginning Value of Investment + (DW ) 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

34. Reporting Investment Performance • 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

35. Reporting Investment Performance • 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