2. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 15 Performance Measurement

3. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 15 Outline 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?

4. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 15 Outline 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?

5. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 15 Outline 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?

6. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 15 Outline 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?

7. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 15 Outline 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?

8. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 15 Outline What are the time-weighted and dollar- weighted returns and which should be reported under AIMR’s Performance Presentation Standards?

9. Copyright © 2000 by Harcourt, Inc. All rights reserved. How Should Investors Measure Risk? Standard Deviation –Investors with limited holdings Beta –Investors with a wide array of holding

10. Copyright © 2000 by Harcourt, Inc. All rights reserved. How Should Investors Select Funds? Performance Indexes Provide a method of comparing funds with different risk-return characteristics

11. 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 2. The ability to diversify the portfolio completely to eliminate unsystematic risk

12. 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

13. Copyright © 2000 by Harcourt, Inc. All rights reserved. Performance Indexes Sharpe’s Performance Index (PI S ) Treynor’s Performance Index (PI T ) Jensen’s Performance Index (PI J ) Performance Indexes With APT(PI A )

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

15. 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

16. 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

17. 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:

18. 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:

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

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

21. 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

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

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

24. 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

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

26. Copyright © 2000 by Harcourt, Inc. All rights reserved. Summary Standard Deviation Appropriate –Sharpe’s index Beta Appropriate –Treynor’s index –Jensen’s index One or More Factors Determine Risk –APT

27. 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

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

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

30. Copyright © 2000 by Harcourt, Inc. All rights reserved. Pension Funds Outperformed By The S&P 500

31. Copyright © 2000 by Harcourt, Inc. All rights reserved. Performance Attribution Assessing the performance of the activities that make up portfolio management

32. Copyright © 2000 by Harcourt, Inc. All rights reserved. Levels Of Decisions Causing Excess Returns Top-Down Approach –Asset allocation –Sector Allocation –Industry allocation –Security selection

33. Copyright © 2000 by Harcourt, Inc. All rights reserved. Flow Chart Top -Down Money Management Process

34. 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

35. 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:

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

37. 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

38. 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:

39. 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

40. Copyright © 2000 by Harcourt, Inc. All rights reserved. Can Fund Managers Time The Market? Newsletters Failed Performance Attributed To –Problems with performance indexes

41. 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

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

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

44. 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

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

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

47. 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?

48. 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

49. 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

50. 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

51. 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

52. 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

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

54. 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

55. 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

56. 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