Performance Evaluation and Prediction in Investment Management

1. Chapter 22 Performance evaluation and prediction

2. Measuring past performance and predicting future performance • Predictions based on past performance are generally unreliable (Discuss readings) • If you cannot predict whether you can trade profitably, you should not trade. • If you cannot predict which managers will be successful, you should not employ active investment managers. • Passive investment managements use buy and hold strategies, e.g., Index replicators

3. Luck or skill? • Good performance evaluations must discriminate between luck and skill. Skilled Unskilled Lucky Blessed Insufferable Unlucky Cursed Doomed

4. Performance evaluation methods • Absolute performance measurement • Total returns • IRR • Holding period return • Relative performance measurement • Difference between a portfolio return and benchmark return (see Table 22-1) • Market-adjusted returns • Risk-adjusted returns

5. Market timing Raw return = (Raw return – Beta x Market return) + (Beta x Market return – Market return) + Market return = Excess return (selection) + Market timing return + Market return

6. Past performance can be used to predict future performance if • Past performance reflects skills • The manager’s skill will continue to generate good future returns • The manager still has the skills In general, correlation between past and future performance is low!!

7. Statistical test Null Hypothesis (H0) Not True True Test Reject Power α (Type I error) Result Accept Type II error Confidence Level (CL) • Power = 1 – Type II error • CL = 1 – Type I error

8. Testing manager’s skill Manager is (H0) Skilled Not Skilled Test Skilled Power α (Type I error) Result Not Type II error Confidence Skilled Level (CL)

9. Student’s t-test and confidence level • t-ratio = Adjusted return/SE of Adjusted return = (Rp – Rm)/SE of (Rp - Rm) If t-ratio is greater than critical value, adjusted return cannot be due to luck. The critical value is determined by confidence level. Confidence level = 1 – significance level (alpha) If confidence level is 95% (i.e., significance level is 5%), critical value is 1.64. It means that there is 5% chance that t-ratio will be greater than 1.64 even if the manager has no skills. Null hypothesis Ho: No skills There is 5% chance that null hypothesis is rejected even if Ho is true. This is also called Type I error.

10. Power of test – want to maximize • The power of test is the probability of rejecting Ho when it is false. • The probability that Ho is rejected when the manager is skilled, i.e., the probability that the t-ratio is greater than the critical value, given that the manager is skilled. • Recall that Type II error is the probability of accepting Ho when it is false. • Power of test = 1 – Type II error

11. Power of test • Increases when confidence level decreases (i.e., when alpha increases) • Increases with the manager’s skills • Decreases with the importance of luck • Increases with the number of observations (years) • Discuss Table 22-2 and Table 22-3

12. Determining the optimal confidence and power levels • Suppose we choose active manager if the test indicates that he is skilled and index fund otherwise. • Suppose we choose CL and PL to maximize the expected market-adjusted return.

13. Other assumptions and Table 22-5 Annual expected net excess return True manager status Test resultSkilledNot skilled Skilled (Active mgr.) 1.00% -2.00% Not skilled (Index) -0.15% -0.15% Probability True manager status Test resultSkilledNot skilled Skilled 1/3xPL 2/3 x (1 – CL) Not skilled 1/3x(1-PL) 2/3 x CL

14. Discuss Table 22-6 and Table 22-7

15. Important problems with statistical performance evaluation • Distributional shape • Normality • Peso problem • Fraudulent returns • Return smoothing • Pyramid schemes

16. Sample selection bias • Sample selection in the mutual fund industry • Avoiding the sample selection bias