1. Past performance SCU Finance Department research seminar, 10/23/2007

2. Top ability quartileTop performance quartile Little overlap = largely luck

3. Top ability quartileTop performance quartile Significant overlap = largely skill

4. Performance persistence captures “luck versus skill” Manager ability Past performance Future performance If ability consistently determines performance, past performance will correlate with future performance

5. Weak persistence example If 40% of the exceptional managers earn good returns –28% of the funds with good returns continue to earn good returns –76% of the mediocre performing funds remain mediocre –64% of the funds repeat their performance Top quartile returns Lower quartile returns exceptional ordinary 40 60 exceptional ordinary 60 240 16 24 48 12

6. Strong persistence example If 90% of the exceptional managers earn good returns –81% of the funds with good returns continue to earn good returns –94% of the mediocre performing funds remain mediocre –90% of the funds repeat their performance Top quartile returns Lower quartile returns exceptional ordinary 90 10 exceptional ordinary 10 290 81 9 10 <1

7. How investors use persistence in Private Equity Focus on performance persistence among “good” (top quartile) managers Studies in private equity suggest 35-45% top quartile persistence in PE –Kaplan and Schoar (2005) –Conner (2005) –Rouvinez (2006)

8. 40% 30% 20% 10% Top quartile 2 nd quartile 3 d quartile 4 th quartile Current top quartile Future distribution

9. Superior distribution = superior returns Based on PEI vintage IRRs, 1989-2000: Equally-weighted average return = 18.0% (25% in each quartile) Top quartile-weighted average return = 27.2% (40-30-20-10)

10. 30% 28% 23% 19% Top quartile 2 nd quartile 3 d quartile 4 th quartile Actual top quartile Future distribution Fall out of top quartile Top quartile after four years 50% Complicated in practice Weighted-average return = 21.4%

11. Model of luck versus skill 4N funds managed by 4N managers N exceptional managers and top quartile funds Probability x that an exceptional manger is in the top return quartile Probability FP that Fund t+1 is in the top return quartile, conditional on Fund t being in the top return quartile FP is observable, x is not.

12. x determines FP Expected number of current top return quartile managers that are exceptional = xN Expected number of current top return quartile managers that are ordinary = (1-x)N Probability that an ordinary manager is in the top return quartile = [(1-x)N]/3N = (1-x)/3 FP = [x 2 N + (1-x) 2 N/3]/N = x 2 + (1-x) 2 /3 If x=1 (all skill), perfect persistence (FP=1) If x=0.25 (all luck), no persistence (FP=0.25)

13. Infer x from FP x = [1 + (1 – 4(1-3FP)) ½ ]/4

14. Incomplete information Given FP = 0.4, the probability that a top quartile fund has an exceptional manger is 58.5% If the fund is immature, the probability is likely much lower

15. Multiple funds (3-yr investment cycle) A series of top quartile funds increases the probability that the manager is exceptional (FP = 0.4)

16. Dynamic managerial ability Exceptional managers become ordinary with probability p: FP = (N*[x 2 (1-p)+x(1-x)(p/3)] + N*[x(1-x)(p/3) + (1/3)(1-x) 2 (1-p/3)])/N x = [6-8p + [(8p-6)2 – 4(12-16p)(3-p-9FP)] ½ ]/[2(12-16p)]

17. Conclusion Past performance is a useful signal for making investment decisions Seasoned performance is a stronger signal A series of top quartile funds is a much stronger signal Requiring a series of top quartile funds creates two problems –Access to funds may be limited –Opportunity set shrinks rapidly Example: 1000 funds, 40% persistence