Chapter 22 Performance evaluation and prediction

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

Luck or skill? Good performance evaluations must discriminate between luck and skill. SkilledUnskilled LuckyBlessedInsufferable UnluckyCursedDoomed

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

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

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!!

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

Testing manager’s skill Manager is (H0) SkilledNot Skilled Test Skilled Powerα (Type I error) Result Not Type II errorConfidence Skilled Level (CL)

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 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.

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

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

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.

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 Skilled1/3xPL2/3 x (1 – CL) Not skilled1/3x(1-PL)2/3 x CL

Discuss Table 22-6 and Table 22-7

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

Sample selection bias Sample selection in the mutual fund industry Avoiding the sample selection bias