Chapter 21

1. Chapter 21 EVALUATION OF PORTFOLIO MANAGEMENT

2. Chapter 21 Questions • What are some methods used to evaluate portfolio performance? • What are the differences and similarities between the various portfolio performance measures? • What are clients’ major requirements of their portfolio managers? • What important characteristics should any benchmark possess?

3. Chapter 21 Questions • What is the benchmark error problem, and how does it affect portfolio performance measures? • What two methods can be used to determine a portfolio’s style exposure over time? • What is portfolio performance attribution analysis? How does it assist the process of analyzing a manager’s performance?

4. Chapter 21 Questions • How do bond-portfolio performance measures differ from equity-portfolio performance measures? • What measure of risk is used in the Wagner and Tito bond-portfolio performance measure?

5. Judging Portfolio Performance Regardless of the style of management, it is important to evaluate whether portfolio results match the goals of the portfolio managers.

6. Composite Portfolio Performance Measures • How can we evaluate portfolio performance? • Calculate excess returns as the difference between portfolio returns and a returns from a return-generating model like the CAPM. • Relative return ratios, which measure return per unit of risk • Scaled return methods, which adjusts the portfolio return for risk so that it can be directly compared to the benchmark return

7. Composite Portfolio Performance Measures • Excess Returns Methods • Jensen Measure • Calculates excess returns based on the CAPM • Jensen’s alpha represents how much the manager contributes to portfolio (j) returns aj = Rjt –(RFRt + bj(Rmt-RFRt)) • Superior managers will generate a significantly positive alpha; inferior managers will generate a significantly negative alpha • Could use APT as the return-generating model

8. Composite Portfolio Performance Measures • Relative Return Ratios • Sharpe Portfolio Performance Measure • Based on the Capital Market Line, considers the total risk of the portfolio being evaluated S=(Rportfolio-RFR)/sportfolio • Shows the risk premium earned over the risk free rate per unit of total risk • Sharpe ratios greater than the ratio for the market portfolio indicate superior performance (plot above the CML)

9. Composite Portfolio Performance Measures • Relative Return Ratios • Treynor Portfolio Performance Measure • Based on the CAPM, considers the risk that cannot be diversified, systematic risk T=(Rportfolio-RFR)/bportfolio • Shows the risk premium earned over the risk free rate per unit of systematic risk • Treynor ratios greater than the market risk premium indicate superior performance (plot above the SML)

10. Traditional Performance Measures • Sharpe and Treynor Measures • Jensen Measure • Performance Measurement in Practice

11. Sharpe and Treynor Measures • The Sharpe and Treynor measures:

12. Sharpe and Treynor Measures (cont’d) • The Treynor measure evaluates the return relative to beta, a measure of systematic risk • It ignores any unsystematic risk • The Sharpe measure evaluates return relative to total risk • Appropriate for a well-diversified portfolio, but not for individual securities

13. Sharpe and Treynor Measures (cont’d) Example Over the last four months, XYZ Stock had excess returns of 1.86 percent, –5.09 percent, –1.99 percent, and 1.72 percent. The standard deviation of XYZ stock returns is 3.07 percent. XYZ Stock has a beta of 1.20. What are the Sharpe and Treynor measures for XYZ Stock?

14. Sharpe and Treynor Measures (cont’d) Example (cont’d) Solution: First, compute the average excess return for Stock XYZ:

15. Sharpe and Treynor Measures (cont’d) Example (cont’d) Solution (cont’d): Next, compute the Sharpe and Treynor measures:

16. Jensen Measure • The Jensen measure stems directly from the CAPM:

17. Jensen Measure (cont’d) • The constant term should be zero • Securities with a beta of zero should have an excess return of zero according to finance theory • According to the Jensen measure, if a portfolio manager is better-than-average, the alpha of the portfolio will be positive

18. Jensen Measure (cont’d) • The Jensen measure is generally out of favor because of statistical and theoretical problems

19. Information Ratios Let Rpt = the return on a portfolio in period t RBt = the return on the benchmark portfolio in period t Dt = the differential return in period t Dt = Rpt - RBt D = the average value of Dt over the period examined D = the standard deviation of the differential return during the period The historic (ex post) Sharpe Ratio (S) is:

20. Composite Portfolio Performance Measures • Scaled Returns • Risk-Adjusted Performance Measure (RAP) • Adjust the risk of the portfolio to equalize the risk of the market or benchmark portfolio • Compare the returns after risk adjustment to the benchmark portfolio returns • For instance, using the Sharpe index (S): RAPportfolio = RFR+(smarket)xS • Resulting values larger than the market return (or other benchmark used) would indicate superior performance

21. Composite Portfolio Performance Measures • Comparing Measures • Sharpe and RAP both use the portfolio standard deviation as the risk measure, so use total risk to evaluate performance • Treynor and Jensen use only systematic risk (beta) to evaluate performance

22. Composite Portfolio Performance Measures • Comparing Measures • All measures will give consistent results for completely diversified portfolios • When reviewing both diversified and undiversified portfolios, a poorly diversified portfolio could have high beta-adjusted performance but lower s-adjusted performance • Statistical analysis indicates high correlations across performance measures when evaluating mutual fund performance • They tend to rate and rank performance consistently • Still may make sense to use different measures at times

23. Benchmark Portfolios • In order to use as an evaluation tool, must first ask: What is required of a portfolio manager? 1. Follow the client’s policy statement 2. Earn above-average returns for a given risk class 3. Diversify the portfolio to eliminate unsystematic risk

24. Benchmark Portfolios • Provides a performance evaluation standard to judge whether the portfolio manager is meeting requirement • Usually a passive index or portfolio • May need benchmark for entire portfolio and separate benchmarks for segments to evaluate individual managers

25. Benchmark Portfolios Required Characteristics of Benchmarks • Unambiguous • Investable • Measurable • Appropriate • Reflective of current investment opinions • Specified in advance

26. Benchmark Portfolios • Sometimes no appropriate single benchmark exists, so you “build your own” • Specialize as appropriate • Be sure to consider risk and ensure that performance standards are not met simply through taking on additional risk.

27. Performance Measures and Benchmark Error The market portfolio problem • The theoretical market portfolio is an efficient, diversified portfolio that contains all risky assets in the economy, weighted by their market values • Typically use the S & P 500 Index • This is not a complete market proxy (this is benchmark error) • Further, betas derived using an incomplete benchmark may also differ from a company’s “true beta”

28. Performance Measures and Benchmark Error • Benchmark Errors and Global Investing • Concern with the benchmark error increases with global investing • The Dow 30 stocks have higher betas against the S&P 500 than against the Morgan Stanley World Stock Index • The benchmark problem is one of measurement in evaluating portfolio performance • Might want to give greater weight to the standard deviation-based portfolio performance measures (Sharpe measures)

29. Taxable Performance and Benchmarking • Another difficulty in evaluating performance • No standard way of adjusting pre-tax performance to after-tax performance • Need to adjust for capital gains and income flows to be reinvested • A difficult issue to resolve

30. Benchmarking and Portfolio Style • Two means of determining a portfolio manager’s style • Returns-based analysis • Characteristic analysis

31. Returns-based analysis • Also called effective mix analysis • Portfolio’s historical return pattern is compared to various well-specified indexes • Analysis uses sophisticated programming techniques to indicate styles most similar to the portfolio’s actual returns

32. Characteristic analysis • Based on the idea that current make-up will be a good predictor for the next period’s returns • Classifies manager into four styles: • Value, growth, market-oriented, small-capitalization • Decision tree approach to classify a portfolio’s stocks • Develop a “sector deviation measure” • Results combined to determine style

33. Attributions for Portfolio Performance • Possible explanations of superior performance: • Insightful asset allocation strategy that overweighted an asset class that earned high returns • Investing in undervalued sectors • Selecting individual securities that earned above average returns • Some combination of these reasons

34. Attributions for Portfolio Performance • Client’s policy statement is the place to start and compare against actual values • Effects of asset allocation decision • Compare actual performance against the policy statement allocation strategy earning benchmark returns across all allocations • Look for differences in allocations and returns within allocations to explain performance differences • Impact of sector and security selection • Repeat the same exercise as above, looking to explain either strong or weak performance

35. 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?

36. A Bond Market Line • Need a measure of risk such as the beta coefficient for equities • Difficult to achieve due to bond maturity differences and coupon effects on volatility of prices • Composite risk measure is the bond’s duration • Duration replaces beta as risk measure in a bond market line

37. Bond Market Line Evaluation Explains differences from benchmark returns as a function of the following: • 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

38. Bond Market Line Evaluation • A word of caution: duration is being used as a comprehensive measure of risk • Duration measures interest rate risk • Duration does not consider differences in default risk, which would also impact performance • May want to construct different bond market lines to evaluate bond portfolio performance for each bond rating