Transcript What do investors gain from chasing the top quartile? What

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”
Manager ability
Past
performance
Future
performance
If ability consistently determines performance, past
performance will correlate with future performance
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
16
exceptional
40
ordinary
60
12
24
exceptional
60
48
Lower
quartile
returns
ordinary
240
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
quartile
returns
ordinary
290
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)
Future distribution
40%
Current top
quartile
Top quartile
30%
2nd quartile
20%
3d quartile
10%
4th quartile
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)
Complicated in practice
Future distribution
30%
50%
Actual top
quartile
Top
quartile
after four
years
50%
Top quartile
Fall out of
top quartile
28%
2nd quartile
23%
3d quartile
19%
4th quartile
Weighted-average return = 21.4%
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.
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)
Infer x from FP
x = [1 + (1 – 4(1-3FP))½ ]/4
The Probability that an Exceptional Managers is in the Top Return Quartile
1.10
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Follow -on probability (FP)
0.9
1
1.1
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
Characteristics of the Top Quartile as a Vintage Seasons
100.00%
90.00%
80.00%
70.00%
Fraction that will end
up top quartile
60.00%
50.00%
Fraction with
exceptional managers
40.00%
30.00%
20.00%
10.00%
0.00%
0
1
2
3
4
5
6
7
Years into vintage
8
9
10
11
Multiple funds (3-yr investment cycle)
A series of top quartile funds increases the probability
that the manager is exceptional (FP = 0.4)
Series of top quartile funds Probability that the manager is exceptional
1
33%
2
53%
3
80%
4
95%
5
99%
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)]
Percentage of exceptional managers that
0%
10%
20%
Past funds observed
Probability
in that
top quartile
a manager is exceptional
1
33%
32%
31%
2
53%
51%
49%
3
80%
78%
74%
4
95%
93%
91%
5
99%
98%
97%
become ordinary each fund cycle
30%
40%
50%
31%
46%
71%
88%
96%
30%
44%
66%
84%
94%
29%
41%
60%
78%
90%
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
Pipeline if an investor demands N past top quartile funds
# past funds Opportunity set Exceptional managers % of population
1
250
83
33%
2
67
35
14%
3
25
20
8%
4
13
12
5%
5
7
7
3%