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

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Top ability quartileTop performance quartile Little overlap = largely luck

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Top ability quartileTop performance quartile Significant overlap = largely skill

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

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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

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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

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

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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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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%

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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 = [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)

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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*[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)]

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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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