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Past performance. SCU Finance Department research seminar, 10/23/2007. Top ability quartile. Top performance quartile. Little overlap = largely luck. Top ability quartile. Top performance quartile. Significant overlap = largely skill. Performance persistence captures “luck versus skill”.

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Past performance l.jpg

Past performance

SCU Finance Department research seminar, 10/23/2007


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Top ability quartile

Top performance quartile

Little overlap = largely luck


Slide3 l.jpg

Top ability quartile

Top performance quartile

Significant overlap = largely skill


Performance persistence captures luck versus skill l.jpg

Performance persistence captures “luck versus skill”

Manager ability

Past performance

Future performance

If ability consistently determines performance, past performance will correlate with future performance


Weak persistence example l.jpg

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

16

exceptional

Top quartile returns

40

12

ordinary

60

24

exceptional

60

48

Lower quartile returns

ordinary

240


Strong persistence example l.jpg

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

81

Top quartile returns

exceptional

90

<1

ordinary

10

9

exceptional

10

10

Lower quartilereturns

ordinary

290


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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)


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Future distribution

Top quartile

40%

Current top quartile

30%

2nd quartile

20%

3d quartile

10%

4th quartile


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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)


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Future distribution

Complicated in practice

Top quartile

30%

Actual top quartile

50%

28%

Top quartile after four years

2nd quartile

23%

3d quartile

50%

Fall out of top quartile

19%

4th quartile

Weighted-average return = 21.4%


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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.


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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 = [x2N + (1-x)2N/3]/N = x2 + (1-x)2/3

  • If x=1 (all skill), perfect persistence (FP=1)

  • If x=0.25 (all luck), no persistence (FP=0.25)


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Infer x from FP

x = [1 + (1 – 4(1-3FP))½ ]/4


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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


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Multiple funds (3-yr investment cycle)

A series of top quartile funds increases the probability that the manager is exceptional (FP = 0.4)


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Dynamic managerial ability

Exceptional managers become ordinary with probability p:

FP = (N*[x2(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)]


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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


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