© cumming & johan (2013) fund size cumming and johan (2013 chapter 18) 1

© Cumming & Johan (2013) Fund Size

Fund Size

Cumming and Johan (2013 Chapter 18)

1


A Growing Problem: the Problem of Growing!

IntroductionHypotheses

DataEmpirical Tests

Conclusions

• “We all had too much money. It was just too easy… The problem…was that the funds had grown so big that the 2 percent became just as important as the 20 percent… Success had less to do with performance or risk management…and more to do with bulking up.”— A Confession by a Private Equity Manager, The New York Times (September 22, 2009)

2


Chapter Objectives


DataEmpirical Tests

Conclusions

• Consider whether fund size affects:

• Valuation

• Performance

3


Factors at Play with Respect to Fund Size and Valuation


DataEmpirical Tests

Conclusions

• We project that the most reputable VCs are likely to pay a lower price, ceteris paribus.

• Larger VC funds are likely to pay a lower price as they have greater outside option.

• On the other hand, when funds become big, agency problem may kick in, which predicts a convex (U-shape) relationship between fund size and venture pre-money valuation.

• Further, if human capital does not keep up with the fund growth, the resulted diluted attention could reduce either funds’ outside option or continuation option, thus leads to a higher or lower pre-money valuation.

4


Hypotheses


DataEmpirical Tests

Conclusions

• Hypothesis 18.1: The most reputable VCs offer lower pre-money valuation given the quality of ventures equal.

• Hypothesis 18.2: VC fund size is negatively correlated with venture valuation

controlling for VC reputation and the quality of ventures.

• Hypothesis 18.3: There is a convex relation between fund size and venture valuation.

• Hypothesis 18.4a: Limited attention is negatively correlated with pre-money valuation if its impact on VCs’ continuation payoff is dominant.

• Hypothesis 18.4b: Limited attention is positively correlated with pre-money valuation if its impact on VCs’ outside option is dominant.

5


Factors at Play with Respect to Fund Size and Performance


DataEmpirical Tests

Conclusions

• Diseconomies of scale in the VC industry due to agency problems and limited attention.

• Agency problems with larger funds– If some fund managers (“bad” managers) seek large fund commitments to pursue

their pecuniary (for instance, greater fixed fee) and engage in inefficient investment behavior (for example, they may pursue larger but not necessarily highest NPV investments; they may pay more (offer higher valuation) to their portfolio companies; etc.), we expect a concave relation between fund size and portfolio companies’ exit performance.

• Limited attention with larger funds (see also Chapter 17)

6


Hypotheses


DataEmpirical Tests

Conclusions

• Hypothesis 18.5: There is a concave relation between fund size and portfolio companies’ exit performance (e.g., probability of successful exits).

• Hypothesis 18.6: VCs’ limited attention has a negative impact on the portfolio companies’ ultimate performance (e.g., probability of successful exits).

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Data


DataEmpirical Tests

Conclusions

• VentureXpert database provided by Thomason Financial Corporation. • 1991 – 2006 (Table 18.1)

• 27,754 rounds of VC investments. • Among the 27,754 rounds of VC investments, 9,266 observations (34.4% of

the sample) have the post-money valuation data

• Limited partnerships. – We do not include other types of VC investors, such as corporate VC,

financial institution affiliated VC funds, pension funds and university foundations, etc. The purpose is to avoid potential impact of organizational forms of VC investors on valuations.

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Year Number of financing rounds Rounds with valuation dataPercentage with valuation data

(%)

1991 1,136 78 6.9%

1992 1,302 265 20.4%

1993 1,058 230 21.7%

1994 1,111 312 28.1%

1995 1,014 343 33.8%

1996 1,328 429 32.3%

1997 1,497 535 35.7%

1998 1,581 755 47.8%

1999 2,457 1,296 52.7%

2000 3,571 1,966 55.1%

2001 2,314 1,137 49.1%

2002 1,726 615 35.6%

2003 1,684 494 29.3%

2004 1,800 351 19.5%

2005 1,987 250 12.6%

2006 2,188 210 9.6%

All Years 27,754 9,266 33.4%

Table 18.1 Number of Observations, by Year

9


Pre-Money Valuation Summary Statistics


DataEmpirical Tests

Conclusions

• Table 18.2 provides pre-money valuations– Valuations increase when the ventures are at their later stages of development;

ventures located in CA, MA, TX, and NY

• Pre pre-money valuation increases with the size of financing round. – The mean (median) pre-money valuation of the largest quartile of financing rounds is

103.8 (60.6) million, in 2006 dollars. In comparison, the mean (median) valuation of the smallest quartile of financing rounds is 18.8 (7.8) million, in 2006 dollars.

• Pre-money valuation of ventures increases with fund size.

– The pre-money valuation of ventures invested by VC funds in the largest quartile has a mean (median) pre-money valuation of $74.1 (34.2) million, while the mean (median) pre-money valuation of ventures invested by VC funds in the smallest quartile is $30.1 (12.8) million.

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Pre-money valuation ($M)Mean Median N

Round Size ($M)Highest Quartile 103.8 60.6 2316Second Quartile 36.1 22.2 2317Third Quartile 23.9 13.1 2315Lowest Quartile 18.8 7.8 2318

IndustryComputer Related 42.2 18.7 4032Communication 68.4 25.9 1771Medical/Health/Life Science 30.8 18.2 1395Biotechnology 40.0 19.2 790Semiconductor 46.9 20.5 623Non-Tech 42.3 17.7 655

StageStartup/Seed 11.2 6.0 1013Early Stage 20.2 10.7 2549Expansion 55.4 29.4 3843Later Stage 75.0 40.8 1502Other 102.8 38.5 359

LocationCA 47.1 21.1 3649MA 47.7 20.2 1091TX 59.1 20.4 500NY 57.2 24.1 305Elsewhere 40.3 18.0 3421

VC Fund Size ($M)Highest Quartile 74.1 34.2 2311Second Quartile 45.4 22.7 2293Third Quartile 33.1 17.1 2344Lowest Quartile 30.1 12.8 2318

Table 18.2 Pre-money Valuations of Financing Rounds

11


Measuring Limited Attention


DataEmpirical Tests

Conclusions

• To measure the performance-adjusted amount of excess capital managed per partner, we first group venture capital firms into quartiles based on their previous IPO market share.

• Then we compare the amount of capital managed per partner of a specific venture capital firm to the median measures of their peers with similar past performance (same quartile based on their previous IPO market share).

• The differences are our final measures of limited attention

12


Regression of Pre-Money Valuation (1 of 3)


DataEmpirical Tests

Conclusions

1. Valuation2. Exit Performance

• All specifications in Table 18.3 show that the relationship between venture valuation and VC past IPO market share is positive, albeit concave. – This finding suggests that more reputable VCs (of better past

performance) are often matched with higher quality ventures which typically are of higher value, nevertheless, the most reputable ones, on the other side, offer lower price holding the quality of ventures constant, supporting Hypothesis 18.1.

– This finding is consistent with the notion proposed in Hsu (2004) that entrepreneurs are willing to accept less favorable financial terms to be affiliated with more reputable VCs.

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DataEmpirical Tests

Conclusions


• We find a convex relationship between private firm valuation and VC fund size.

– The negative correlation between fund size and firm pre-money valuation indicates that larger VCs, in general, have greater negotiation power and thus pay lower price holding the quality of ventures constant, consistent with Hypothesis 18.2.

– However, this relationship is reversed when the fund gets very large, as suggested by the positive correlation between fund size square term and valuation, consistent with Hypothesis 18.3

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DataEmpirical Tests

Conclusions


• In models (2) and (3), we link limited attention to firm valuation. We find a significantly positive association between firm valuation and both measures of limited attention.

• For instance, a coefficient of 0.171 (p-value=0.003) on excess fund managed per partner, or Ln(Fund Size/N of Partners) adjusted by the median of the same measure of VCs with similar past performance, indicates that one standard deviation increase in excess capital managed per partner increases the valuation of the firm by 4.2% assuming other aspects similar.

• This set of findings are consistent with the prediction of Hypothesis 18.4b, implying that diluted attention when fund grows very large could reduce VCs’ outside option and thus decreases their bargaining power, which significantly increases the price of the investments.

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DV: Ln (Pre-money Valuation)(1) (2) (3) (4) (5)

Intercept 2.391*** 2.076*** 2.033*** 2.398*** 2.296***(0.000) (0.000) (0.000) (0.000) (0.000)

Variables of Key InterestLn(Fund Size) -0.122*** -0.121** -0.096*

(0.003) (0.035) (0.097)Ln(Fund Size) Square Term 0.015*** 0.009 0.007

(0.000) (0.121) (0.262)Ln(Fund Size/N of Partners): Comparable VCs Median Adjusted) 0.171*** 0.176**

(0.003) (0.013)Ln[Fund Size/(N of Partners/N of Parallel Funds)]: Comparable VCs Median Adjusted 0.027*** 0.028***

(0.001) (0.004)VC IPO Share 0.089*** 0.101*** 0.101*** 0.113*** 0.113***

(0.000) (0.000) (0.000) (0.000) (0.000)VC IPO Share Square Term -0.005** -0.006** -0.006** -0.007*** -0.007***

(0.014) (0.010) (0.011) (0.004) (0.004)Characteristics of FirmsStage of FirmSeed/Start-up Stage -1.432*** -1.466*** -1.473*** -1.462*** -1.469***

(0.000) (0.000) (0.000) (0.000) (0.000)Early Stage -1.093*** -1.120*** -1.114 -1.115*** -1.109***

(0.000) (0.000) (0.000) (0.000) (0.000)Expansion Stage -0.338*** -0.383*** -0.380*** -0.384*** -0.380***

(0.000) (0.000) (0.000) (0.000) (0.000)Industry of Firm Dummies Yes Yes Yes Yes YesLocation of Firm Dummies Yes Yes Yes Yes YesOther Control Variables Yes Yes Yes Yes YesYear Fixed Effect Yes Yes Yes Yes YesN 9266 6572 6572 6572 6572Adjusted R2(%) 47.52 48.15 48.32 48.22 48.38

Table 18.3 Regression Analysis: The Effect of Fund Size and Limited Attention on Valuation

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Robustness


DataEmpirical Tests

Conclusions


• Alternative specifications• Random effects• Heckman selection

17


Panel A: Company Random Effect Model

Variables of Key Interest

Ln(Fund Size) -0.104*** -0.102* -0.079

(0.008) (0.062) (0.160)

Ln(Fund Size) Square Term 0.013*** 0.008 0.005

(0.001) (0.172) (0.345)

Fund Size/N of Partners: Comparable VCs Median Adjusted 0131** 0.135**

(0.013) (0.43)

Fund Size/(N of Partners/N of Parallel Funds): Comparable VCs Median Adjusted 0.021*** 0.023**

(0.005) (0.020)

VC IPO Share 0.095*** 0.108*** 0.106*** 0.117*** 0.116***

(0.000) (0.000) (0.000) (0.000) (0.000)

VC IPO Share Square Term -0.007** -0.007*** -0.007*** -0.008*** -0.008***

(0.002) (0.001) (0.001) (0.000) (0.001)

LR Test Chi2 5181.29 4245.80 4209.22 4251.94 4213.83

Prob>Chi2 0.000 0.000 0.000 0.000 0.000

Table 18.4 Alternative Models: The Effect of Fund Size and Limited Attention on Valuation

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Panel B: Heckman Selection Model


Ln(Fund Size) -0.105*** -0.114** -0.090

(0.005) (0.034) (0.103)


(0.002) (0.159) (0.343)

Fund Size/N of Partners: Comparable VCs Median Adjusted 0.123** 0.143**

(0.012) (0.025)

Fund Size/(N of Partners/N of Parallel Funds): Comparable VCs Median Adjusted 0.020*** 0.023**

(0.005) (0.011)

VC IPO Share 0.097*** 0.102*** 0.102*** 0.117*** 0.118***

(0.000) (0.000) (0.000) (0.000) (0.000)

VC IPO Share Square Term -0.006*** -0.006*** -0.006*** -0.007*** -0.007***

(0.003) (0.003) (0.003) (0.001) (0.001)

Inverse Mills Ratio 1.019*** 0.751*** 0.768*** 0.758*** 0.778***

(0.000) (0.000) (0.000) (0.000) (0.000)

Wald Chi2 4700.22 4356.48 4329.07 4360.58 4327.35

Prob>Chi2 0.000 0.000 0.000 0.000 0.000 19


Panel C. Heckman-Correct Company Random Effect Model


Ln(Fund Size) -0.094** -0.099* -0.076

(0.016) (0.069) (0.172)


(0.004) (0.206) (0.401)

Fund Size/N of Partners: Comparable VCs Median Adjusted 0.091* 0.103

(0.087) (0.125)

Fund Size/(N of Partners/N of Parallel Funds): Comparable VCs Median Adjusted 0.016** 0.018*

(0.040) (0.059)

VC IPO Share 0.100*** 0.108*** 0.107*** 0.119*** 0.1119***

(0.000) (0.000) (0.000) (0.000) (0.000)

VC IPO Share Square Term -0.007*** -0.007*** -0.007*** -0.008*** -0.008***

(0.001) (0.001) (0.001) (0.000) (0.000)

Inverse Mills Ratio 2.489*** 1.995*** 1.966*** 2.018*** 2.001***

(0.000) (0.000) (0.000) (0.000) (0.000)

LR Test Chi2 5229.25 4270.45 4233.06 4277.16 4238.43

Prob>Chi2 0.000 0.000 0.000 0.000 0.000 20


Robustness


DataEmpirical Tests

Conclusions


• Similar performance quartiles

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Quartile 1 (Most Reputable VCs)


Ln(Fund Size) -0.024 0.117 0.113

(0.865) (0.587) (0.600)

Ln(Fund Size) Square Term 0.010 -0.002 -0.002

(0.422) (0.911) (0.930)

Fund Size/N of Partners: Comparable VCs Median Adjusted 0.165* 0.047

(0.065) (0.697)

Fund Size/(N of Partners/N of Parallel Funds): Comparable VCs Median Adjusted 0.023* 0.006

(0.085) (0.739)

N 2188 2006 2006 2006 2006

Adjusted R2 31.56 33.59 33.57 33.90 33.89

Table 18.5 The Effect of Fund Size and Limited Attention on Valuation among VCs with Similar Performance

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Quartile 2


Ln(Fund Size) -0.070 -0.231 -0.207

(0.624) (0.140) (0.217)

Ln(Fund Size) Square Term 0.023* 0.033** 0.030*

(0.068) (0.035) (0.079)

Fund Size/N of Partners: Comparable VCs Median Adjusted 0.108 -0.193*

(0.127) (0.094)

Fund Size/(N of Partners/N of Parallel Funds): Comparable VCs Median Adjusted 0.019** -0.018

(0.046) (0.278)

N 1970 1617 1617 1617 1617

Adjusted R2 36.88 31.91 31.96 32.44 32.38 23


Quartile 3


Ln(Fund Size) -0.389*** -0.503*** -0.506***

(0.008) (0.001) (0.001)

Ln(Fund Size) Square Term 0.061*** 0.072*** 0.072***

(0.000) (0.000) (0.000)

Fund Size/N of Partners: Comparable VCs Median Adjusted 1.220** -0.137

(0.018) (0.818)

Fund Size/(N of Partners/N of Parallel Funds): Comparable VCs Median Adjusted 0.258* -0.058

(0.058) (0.698)

N 1948 1529 1529 1529 1529

Adjusted R2 31.59 32.64 32.54 33.78 33.79 24


Quartile 4 (Least Reputable VCs)


Ln(Fund Size) -0.130* -0.251** -0.254**

(0.071) (0.018) (0.017)

Ln(Fund Size) Square Term 0.037*** 0.044*** 0.047***

(0.000) (0.001) (0.000)

Fund Size/N of Partners: Comparable VCs Median Adjusted 3.528*** 1.808**

(0.000) (0.013)

Fund Size/(N of Partners/N of Parallel Funds): Comparable VCs Median Adjusted 0.940*** 0.290

(0.000) (0.237)

N 2333 1574 1574 1574 1574

Adjusted R2 27.96 28.96 28.44 29.33 29.74 25


Fund Size and Performance


DataEmpirical Tests

Conclusions


• We find that fund size is positively associated with the probability of successful exit, while its square term is negatively associated with the probability of successful exit. This supports Hypothesis 18.5. Both coefficients, nevertheless, are only marginally significant (at the 15% and 10% confidence levels, respectively).

• We don’t find that limited attention is significantly associated with the probability of successful exits, thus rejecting Hypothesis 18.6.

• Also noteworthy:• More reputable VCs (higher IPO share) positively contribute to the

success of portfolio companies. • Technology companies overall and companies located in California and

Massachusetts are more likely to exit through IPOs or M&As.

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DV: Probability of Successful Exit(1) (2) (3) (4) (5)

Intercept -1.104*** -0.984*** -0.978*** -1.082*** -1.054***(0.000) (0.000) (0.000) (0.000) (0.000)

Variables of Key InterestLn(Fund Size) 0.086 0.078 0.063

(0.124) (0.336) (0.442)Ln(Fund Size) Square Term -0.010* -0.011 -0.009

(0.069) (0.187) (0.285)

Ln(Fund Size/N of Partners): Comparable VCs Median Adjusted) -0.024 0.096

(0.759) (0.350)

Ln[Fund Size/(N of Partners/N of Parallel Funds)]: Comparable VCs Median Adjusted -0.007 0.007

(0.551) (0.629)VC IPO Share 0.029*** 0.018** 0.018** 0.028*** 0.027**

(0.002) (0.036) (0.035) (0.008) (0.011)Characteristics of FirmsStage of FirmSeed/Start-up Stage -0.123** -0.154** -0.153** -0.146** -0.147**

(0.041) (0.022) (0.022) (0.030) (0.029)Early Stage -0.129*** -0.179*** -0.178*** -0.173*** -0.173***

(0.007) (0.001) (0.001) (0.001) (0.001)Expansion Stage -0.019 -0.054 -0.053 -0.052 -0.052

(0.667) (0.271) (0.274) (0.286) (0.288)Industry of Firm Dummies Yes Yes Yes Yes YesLocation of Firm Dummies Yes Yes Yes Yes YesOther Control Variables Yes Yes Yes Yes YesYear Fixed Effect Yes Yes Yes Yes YesN 7070 5608 5608 5608 5608Pseudo R2(%) 2.39 2.68 2.68 2.72 2.71

Table 18.6 Fund Size, Limited Attention, and Venture Performance

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Robustness: Fund Size and Performance


DataEmpirical Tests

Conclusions


• In Table 18.7, we group our sample into quartiles based on the pre-money valuation and repeat the regressions as shown in Table 18.6 for each quartile.

• We show that the influence of fund size on the probability of successful exits is particularly strong among the group with relatively high pre-money valuation (quartiles 1 and 2). Together with our findings in Section 18.4, this finding suggests that one of the mechanisms for the diseconomy of size documented in the literature is the overpricing of entrepreneurial firms by large VC funds.

• We provide empirical evidence, for the first time, that such agency problem exists in the venture capital investments and it has a negative impact on the performance of portfolio companies.

• Similar to Table 18.6, we do not find limited attention has a significant association with venture performance

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DV: Probability of Successful Exits

Quartile 1 (Highest Valuation)

Ln(Fund Size) 0.195* 0.183 0.176

(0.098) (0.289) (0.311)

Ln(Fund Size) Square Term -0.023** -0.026 -0.025

(0.038) (0.123) (0.141)

Ln(Fund Size/N of Partners): Comparable VCs Median Adjusted) -0.057 0.243

(0.636) (0.170)

Ln[Fund Size/(N of Partners/N of Parallel Funds)]: Comparable VCs Median Adjusted -0.007 0.029

(0.649) (0.207)

N 1813 1428 1428 1428 1428

Adjusted R2 2.91 3.74 3.74 4.72 4.02

Quartile 2

Ln(Fund Size) 0.259** 0.244* 0.229

(0.026) (0.097) (0.122)

Ln(Fund Size) Square Term -0.026** -0.023 -0.021

(0.023) (0.132) (0.171)

Ln(Fund Size/N of Partners): Comparable VCs Median Adjusted) -0.113 -0.011

(0.459) (0.956)

Ln[Fund Size/(N of Partners/N of Parallel Funds)]: Comparable VCs Median Adjusted -0.021 -0.008

(0.340) (0.765)

N 1777 1427 1427 1427 1427

Pseudo R2 3.66 4.12 4.14 4.27 4.27

Table 18.7 The Relation between Fund Size, Limited Attention and Exit Performance by Pre-Money Valuation Quartiles

29


Quartile 3

Ln(Fund Size) -0.010 0.024 0.030

(0.927) (0.887) (0.859)

Ln(Fund Size) Square Term 0.002 -0.003 -0.004

(0.866) (0.873) (0.842)

Ln(Fund Size/N of Partners): Comparable VCs Median Adjusted) 0.026 0.046

(0.891) (0.840)

Ln[Fund Size/(N of Partners/N of Parallel Funds)]: Comparable VCs Median Adjusted 0.006 0.010

(0.836) (0.776)

N 1757 1399 1399 1399 1399

Adjusted R2 2.56 3.12 3.12 3.12 3.12

Quartile 4 (Lowest Valuation)

Ln(Fund Size) -0.166 -0.276 -0.342*

(0.163) (0.137) (0.067)

Ln(Fund Size) Square Term 0.018 0.027 0.036*

(0.186) (0.183) (0.076)

Ln(Fund Size/N of Partners): Comparable VCs Median Adjusted) 0.223 0.134

(0.398) (0.665)

Ln[Fund Size/(N of Partners/N of Parallel Funds)]: Comparable VCs Median Adjusted -0.004 -0.037

(0.942) (0.510)

N 1723 1354 1354 1354 1354

Pseudo R2 4.25 4.58 4.54 4.72 4.74 30


Conclusions (1 of 3)


DataEmpirical Tests

Conclusions

Valuations:• The most reputable VCs pay lower price, ceteris paribus. • We find a convex relationship between fund size and firm valuation and a

significantly positive correlation between limited attention and valuation. – However, the positive correlation between fund size square term and valuation disappears when we

control for limited attention with the exception of the group of less reputable VCs.

• These findings suggest that, in general, fund size is positively correlated with negotiation power and thus reduces pre-money valuation. However, human capital is overstretched when funds grow larger and the diluted attention reduces VCs’ outside option, which weakens their negotiation power and thus increases pre-money valuation. At the same time, the agency problem may also kick in, especially for the less reputable VCs who presumably have weaker inside governance mechanisms.

31




DataEmpirical Tests

Conclusions

Performance• We find a concave relationship between fund size and the probability of successful

exits. • We further show that the negative correlation between fund size square term and the

probability of successful exits are particularly strong and significant when the pre-money valuation is high.

• Our findings show that the price of private equity investments are not just determined by the quality of the ventures or entrepreneurs, or the supply and demand of capital, but also influenced by various characteristics of the VCs investing in the ventures.

– There is a tradeoff between being affiliated with the most reputable VCs and the valuation that ventures can get.

– Large VC funds may provide entrepreneurs with larger investment and higher prices, however, as a trade-off, the probability of successful exits is lower.

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DataEmpirical Tests

Conclusions

• Our findings also suggest that there is scale diseconomy in the venture capital industry,

• Further, we show that the scale diseconomy is at least partially due to the constraints from human capital.

• VCs often do not increase human capital in proportion to the growth in fund size, which reduces VCs’ outside options. Their bargaining power is thus reduced and they pay a higher price for investments of similar quality.

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© cumming & johan (2013) fund size cumming and johan (2013 chapter 18) 1

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