Fin2802: Investments Spring, 2010 Dragon Tang

1. Lectures 21&22 Performance Evaluation April 13 & 15, 2010 Readings: Chapter 24 Practice Problem Sets: 4,6,8,9,10-14 Fin2802: InvestmentsSpring, 2010Dragon Tang Chapter 24: Performance Evaluation

2. You have a large jar containing 999 fair pennies and one two-headed penny. Suppose you pick one coin out of the jar and flip it 10 times and get all heads. What is the probability that the coin you chose is the two-headed one? Wall Street Interview Question Chapter 24: Performance Evaluation

3. Performance Evaluation • Objectives: • Compute risk-adjusted rates of return. • Decompose excess returns into components attributable to asset allocation choices versus security selection choices. • Assess the performance of portfolio managers. • Assess the value of Market Timing Ability Chapter 24: Performance Evaluation

4. Skill Timing ability (asset allocation) Selection ability (security selection) Luck Goal of performance evaluation is to distinguish skill (and specific components) from luck! Performance Chapter 24: Performance Evaluation

5. Risk-Adjusted Returns Comparison groups: • Blindly comparing rates of return ignores risk • Comparison groups with similar investment styles and portfolio characteristics can be used for performance comparison Chapter 24: Performance Evaluation

6. Figure 24.1 Universe Comparison Chapter 24: Performance Evaluation

7. Risk Adjustments • Sharpe measure • Treynor measure • Jensen measure Chapter 24: Performance Evaluation

8. Sharpe Method Reward-to-volatility ratio: _ _ Appropriate for measuring the relative performance of an entire portfolio. Chapter 24: Performance Evaluation

9. Developed by Modigliani and Modigliani Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolio If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market M2 Measure Chapter 24: Performance Evaluation

10. Figure 24.2 M2 of Portfolio P Chapter 24: Performance Evaluation

11. M2 Measure: Example Managed Portfolio: return = 35% standard deviation = 42% Market Portfolio: return = 28% standard deviation = 30% T-bill return = 6% Hypothetical Portfolio: 30/42 = .714 in P (1-.714) or .286 in T-bills (.714) (.35) + (.286) (.06) = 26.7% Since this return is less than the market, the managed portfolio underperformed Chapter 24: Performance Evaluation

12. Treynor Measure Excess return to beta ratio: _ _ Appropriate for measuring the relative performance of parts of a portfolio. Chapter 24: Performance Evaluation

13. Jensen Measure Alpha of an investment (from CAPM): Appropriate for measuring the absolute performance of a portfolio. Chapter 24: Performance Evaluation

14. Information Ratio Information Ratio = ap / s(ep) Information Ratio divides the alpha of the portfolio by the nonsystematic risk Nonsystematic risk could, in theory, be eliminated by diversification Chapter 24: Performance Evaluation

15. Sharpe measure: Useful when assets are concentrated within a single portfolio managers Treynor and Jensen measures: Useful when assets are spread across many portfolio managers. Which one to use? Chapter 24: Performance Evaluation

16. Figure 24.3 Treynor’s Measure Chapter 24: Performance Evaluation

17. Table 24.2 Excess Returns for Portfolios P and Q and the Benchmark M over 12 Months Chapter 24: Performance Evaluation

18. Table 24.3 Performance Statistics Chapter 24: Performance Evaluation

19. Risk and Changing Portfolio Composition (Limitation of Performance Measures) • Risk adjustment techniques assume that portfolio risk is constant over the relevant time period. • However, changing the mean return and risk will add to the appearance of higher volatility. Chapter 24: Performance Evaluation

20. Market Timing and Luck • If the portfolio manager can time the market, she would shift funds from the safe asset to the market portfolio (from cash to stocks or bonds) just before the market upturn. • This would increase the portfolio beta. • Empirical evidence indicates that betas did not increase prior to market advances indicating no evidence of successful market timing. (EMH strikes again)! Chapter 24: Performance Evaluation

21. Performance Attribution Procedures • Understand which decisions lead to superior or inferior performance • Attribution studies start from the broadest asset allocation choices and progress towards every-finer details of portfolio choice. Chapter 24: Performance Evaluation

22. Performance Attribution Process Components of Decomposition: 1. Broad asset market allocation choices (equity, fixed income and money market funds) 2. Industries (sectors) choices within each market 3. Security choices within each sector Chapter 24: Performance Evaluation

23. Performance Attribution Procedures • The Bogey is the return an investment manager is compared to for performance evaluation. • The bogey portfolio indicates the returns of a completely passive strategy. • Performance at each step is to be compared to a benchmark or bogey portfolio. Chapter 24: Performance Evaluation

24. Performance of the Managed Portfolio Chapter 24: Performance Evaluation

25. Asset allocation Security selection Equity Sector allocation Security allocation Fixed Income Performance Attribution Chapter 24: Performance Evaluation

26. Performance Attribution:Asset Allocation Contribution Was superior performance due to asset allocation? • Compare the return from the active allocation procedure to a hypothetical passive portfolio composed of indices in every category (stocks, bonds…). Chapter 24: Performance Evaluation

27. Performance Attribution Chapter 24: Performance Evaluation

28. Sector and Security Selection Was superior performance due to sector and security selection decisions? • Compare portfolio’s equity performance to the S&P 500 Index • Compare your fixed-income performance to the Lehman Brothers or Merrill Lynch index • Compare sector weights in your portfolio to the S&P 500 Chapter 24: Performance Evaluation

29. Sector Allocation Within the Equity Market Chapter 24: Performance Evaluation

30. Portfolio Attribution: Summary Chapter 24: Performance Evaluation

31. Asset Allocation in which investment in the market is increased when the market is expected to outperform T-bills. Perfect timing from 1927 to 1978: 34.71% p.a.! Extremely hard to implement (forecasting) Value of market timing is like the value of a call option on the index (in the money when index does better than T-bill) Market Timing Chapter 24: Performance Evaluation

32. Table 24.5 Performance of Bills, Equities and (Annual) Timers – Perfect and Imperfect Chapter 24: Performance Evaluation

33. Rate of Return of a Perfect Market Timer rf rM rf Chapter 24: Performance Evaluation

34. Being “right most of the time” does not necessarily mean having forecasting abilities. Need to examine the proportion of correct “bull market forecast” (P1) and correct “bear market forecast” (P2). Measure of market timing ability: P1+P2-1 Value of imperfect forecasting: (P1+P2-1)xC where C=call option value of a perfect market timer Value of Imperfect Forecasting Chapter 24: Performance Evaluation

35. Morningstar mutual fund rankings Similar to mean Standard Deviation rankings Companies are put into peer groups Stars are assigned: 1-lowest; 5-highest Highly correlated to Sharpe measures Style analysis Explaining percentage returns by allocation to style Popular with the industry Treynor-Black Model: combine actively managed stocks with a passively managed portfolio Practical Measures Chapter 24: Performance Evaluation

36. Introduced by William Sharpe 1992 study of mutual fund performance 91.5% of variation in return could be explained by the funds’ allocations to bills, bonds and stocks Later studies show that 97% of the variation in return could be explained by the funds’ allocation to a broader range of asset classes Style Analysis Chapter 24: Performance Evaluation

37. Table 24.6 Sharpe’s Style Portfolios for the Magellan Fund Chapter 24: Performance Evaluation

38. Figure 24.8 Fidelity Magellan Fund Cumulative Return Difference: Fund versus Style Benchmark and Fund versus SML Benchmark Chapter 24: Performance Evaluation

39. Figure 24.9 Average Tracking Error for 636 Mutual Funds Chapter 24: Performance Evaluation

40. Summary • Measures of portfolio performance • Sharpe measure; Treynor measure; Jensen measure • Shifting mean and variance of actively managed portfolios creates problems with performance measures • Performance attribution procedures allow evaluator to judge performance based on asset allocation, industry (sector) allocation and security selection • Market timing as a call option • Value of imperfect forecasting • April 22: Project Presentation • 10 minutes per group: 8 minute presentation, 2 minutes Q&A • Send your presentation to TA before presentation day! Chapter 24: Performance Evaluation