Portfolio Size
Cumming and Johan (2013 Chapter 17)
1
© Cumming & Johan (2013)
Portfolio Size
Chapter Objectives
•
Consider 4 main factors that influence the determinants of portfolio size in
terms of the number of entrepreneurial firms in the venture capital fund
portfolio, as well as portfolio size per fund manager per year of investment:
– The fund’s characteristics, such as type of fund, fund size and fund
management firms that operate more than one fund;
– The characteristics of the entrepreneurial firms in the venture capitalist fund
managers’ portfolio, including entrepreneurial firm development stage,
technology and location;
– The structure and characteristics of the financing transactions, including
staging, syndication and forms of finance; and
– Market conditions.
© Cumming & Johan (2013)
2
Portfolio Size
Theory
Data
Regressions
Conclusion/Summary
Issues
• How many entrepreneurial firms do VCs have in their
portfolios?
• Is efficient portfolio size affected by:
 Venture capital fund characteristics?
 Entrepreneurial firm characteristics?
 The nature of the financing transaction?
 Market Conditions?
• Nonlinearities in the predicted relationships?
• Are returns to scale increasing or decreasing?
3
© Cumming & Johan (2013)
Portfolio Size
Theory
Data
Regressions
Conclusion/Summary
Basic Conjecture
• Expansion of portfolio size eventually becomes
unprofitable as active VC investing and managerial advice
gets diluted (Kannianen and Keuschnigg, 2003,2004)
• Add another entrepreneurial firm to the VC portfolio
where the projected marginal benefits (PMB) outweigh
the projected marginal costs (PMC)
• Marginal benefits and marginal costs vary according to
 Type of entrepreneurial firm
 Type of venture capital firm
 Nature of the deal ($ amount, forms of finance, syndication, etc.)
4
© Cumming & Johan (2013)
Portfolio Size
Figure 17.1. Efficient Venture Capital Portfolio Size and Comparative Statics
Benefits /
Costs per
Firm in
Portfolio
PMC 1
PMC 0
Increase in staging frequency,
proportion of early stage
And high -tech firms; etc.
Increase in fundraising,
improvement in market
conditions; etc.
PMB 1
PMB 0
EF 1
EF 0
Number of Entrepreneurial
Firms in VC ’s Portfolio
5
© Cumming & Johan (2013)
Portfolio Size
Theory
Data
Regressions
Conclusion/Summary
Hypotheses: Venture Capital Fund Characteristics
Venture Capital
Fund Characteristics
Hypothesized Effect
on PMC
Hypothesized
Effect on PMB
Predicted Effect
# of Portfolio Firms
Government Funds,
LSVCCs
Low cost of capital
 Low PMC
---
Increase
Private Independent
Limited Partner Funds
High value added
 High PMC
Dilution VC Effort
 Low PMB
Decrease
VC Fund in VC Firm
with Many VC Funds
Effort Sharing
Across Funds
 Low PMC
Complementarities,
Co-investment
 High PMB
---
More funds
 High PMB
VC
Fund Duration
Lower Opportunity
Cost of Effort
 Low PMC
Less Dilution of
Effort, etc.
 High PMB
Increase
# VC Managers
---
High PMB
Increase
VC Fundraising
(Drawdowns)
© Cumming & Johan (2013)
Portfolio Size
Increase
Increase
6
Theory
Data
Regressions
Conclusion/Summary
Hypotheses: Entrepreneurial Firm Characteristics and Market Conditions
Entrepreneurial Firm
Characteristics
Hypothesized Effect
on PMC
Hypothesized
Effect on PMB
Predicted Effect
# of Portfolio Firms
Early Stages of
Development
Higher Effort
 High PMC
Specialization
 High PMB
Ambiguous
High-Tech
Intangible Assets,
Higher Effort
 High PMC
Economies of
Specialization
 High PMC
Ambiguous
Strong Market
Conditions
Ease in Fundraising
 Low PMC
Improved chances
of exit
 High PMB
Increase
7
© Cumming & Johan (2013)
Portfolio Size
Theory
Data
Regressions
Conclusion/Summary
Hypotheses: Financing Characteristics
Financing
Characteristics
Hypothesized Effect
on PMC
Hypothesized Effect
on PMB
Predicted Effect
# of Portfolio Firms
Staging Frequency
Intensive Monitoring
 High PMC
Dilution of VC Effort
 Low PMB
Decrease
Risk Sharing
 Low PMC
Value Added
 High PMB
Increase
$ Invested / Total
Entrepreneurial Capital
High Control Rights
 Low PMC
High Control Rights
 High PMB
Increase
Convertible Securities
High Opportunity
Costs  High PMC
Dilution of VC Effort
 Low PMB
Decrease
Syndication Frequency
8
© Cumming & Johan (2013)
Portfolio Size
Figure 17.2a. Comparative Statics and Nonlinearities
Benefits /
Costs per
Firm in
Portfolio
PMC 1
PMC 0
PMC 2
PMB (Concave)
PMB (Linear)
EF 3
EF 1
EF 4
EF 0
EF 2
Number of Entrepreneurial
Firms in VC ’s Portfolio
9
© Cumming & Johan (2013)
Portfolio Size
Figure 17.2b. Comparative
Statics and Nonlinearities
Benefits /
Costs per
Firm in
Portfolio
PMC (Convex)
PMC (Linear)
PMB
EF 3
EF 1
© Cumming & Johan (2013)
PMB
0
PMB
1
2
EF 4
EF 0
EF 2
Number of Entrepreneurial
Firms in VC ’s Portfolio
Portfolio Size
10
Figure 17.3. Nonlinearities in Hypothesis Tests
Number of
Entrepreneurial
Firms in VC ’s
Portfolio
The concave shape follows from the convex shape of the PMB curve and
the convex shape of the PMC curve (see Figures 18.2a and 18.2, respectively).
The econometric tests consider nonlinearities (both concave and convex)
in the effect of the hypothesized effects on venture capital por tfolio size.
The curvature of the slope is determined by grid search methods
various Box -Cox transformations.
on
Fundraising, Proportion of Early
Stage Entrepreneurial Firms, etc.
© Cumming & Johan (2013)
Portfolio Size
11
Theory
Data
Regressions
Conclusion/Summary
Canadian VC Data
• 1991-2000
• 214 venture capital funds
 Corporate (18)
 Government (15)
 LSVCC (29)
 Other (Institutional) Investors (48)
 Private independent Limited Partnerships (104)
• Source: Macdonald & Associates, Ltd.
• Exclude funds with (possibly) unobserved investments
12
© Cumming & Johan (2013)
Portfolio Size
Table 17.2a. Summary of the Data by Type of Venture Capital Fund
Corporate
Venture
Capital
Government
Venture
Capital
LSVCC
Private Limited
Partnership
Other Institutional
Venture Capital
Total
Total Number of Funds
18
15
29
104
48
214
2 or more Venture Capital Funds managed by the
Venture Capital Management Firm
0
3
3
14
12
32
Venture Capital Funds Raised (Drawdowns) ('000)
$70,650
$48,343
$117,273
$24,307
$110,071
$61,724
# Years Fund Investments Tracked by CVCA
4.222
5.533
4.586
4.663
4.750
4.696
Investment Duration Period (Quarters)
3.625
4.850
4.043
3.959
4.073
4.030
# Venture Capital Fund Managers
6.000
8.533
6.379
5.673
8.083
7.075
17.056
32.467
37.966
8.221
30.500
19.692
2.793
7.460
6.379
2.589
4.939
4.003
0.863
1.695
1.674
0.843
1.632
1.194
Early Stage
0.819
0.900
0.897
0.857
0.776
0.844
Life Sciences
0.066
0.200
0.229
0.198
0.088
0.167
Other High-Tech
0.597
0.393
0.427
0.510
0.428
0.479
Entrepreneur / Venture Capital Different Provinces
0.297
0.083
0.052
0.161
0.286
0.180
Staging Frequency
0.560
0.471
0.497
0.544
0.489
0.521
Syndication Frequency
0.624
0.456
0.519
0.490
0.536
0.513
Venture Capital Investments / Ent. Capital
0.526
0.509
0.409
0.481
0.630
0.511
Convertible Securities
0.237
0.201
0.272
0.262
0.200
0.243
0.296
0.268
0.360
0.268
0.334
0.297
Variable Names
Venture Capital Fund Characteristics
Entrepreneurial Firm Characteristics
Average # Portfolio Firms
Average # Portfolio Firms / # Venture Capital
Managers
Average # Portfolio Firms / # Venture Capital
Managers / # Years
Financing Transactions Characteristics
Market Conditions
MSCI Return
Note: Data over the period 1991 - 2000. Venture capital funds that invested for 1 year only in the data are excluded. Canadian Venture capitalists only. Source: Macdonald and
13
Associates, Ltd., .
© Cumming & Johan (2013)
Portfolio Size
Table 17.2b. Summary Statistics for All Types of Venture Capital Funds in the Data (214 Funds)
Variable Names
Mean
Standard Deviation
Skewness
Kurtosis
Minimum
Maximum
Venture Capital Funds Raised (Drawdowns) ('000)
$61,724
138313
5.089
34.636
150
$1,219,360
# Years Fund Investments Tracked by CVCA
4.696
2.464
0.822
2.538
2
10
Investment Duration Period (Quarters)
4.030
2.376
0.760
2.538
0.5
9.25
# Venture Capital Fund Managers
7.075
7.505
2.804
13.965
1
48
Average # Portfolio Firms
19.692
42.220
5.698
43.403
1
408
Average # Portfolio Firms / # Venture Capital Managers
4.003
6.626
3.966
22.686
0.091
48.4
Average # Portfolio Firms / # Venture Capital Managers / # Years
1.194
1.936
5.651
47.929
0.026
20
Early Stage
0.844
0.207
-1.731
5.801
0
1
Life Sciences
0.167
0.271
2.104
6.460
0
1
Other High-Tech
0.479
0.338
0.063
1.734
0
1
Entrepreneur / Venture Capital Different Provinces
0.180
0.277
1.749
5.112
0
1
Staging Frequency
0.521
0.211
-0.434
2.789
0
0.933
Syndication Frequency
0.513
0.313
0.028
1.827
0
1
Venture Capital Investments / Ent. Capital
0.511
0.275
0.293
1.948
0.047
1
Convertible Securities
0.243
0.194
0.828
3.500
0
1
0.297
0.198
1.628
7.315
-0.067
1.192
Venture Capital Firm Characteristics
Entrepreneurial Firm Characteristics
Financing Transactions Characteristics
Market Conditions
MSCI Return
Note: Data over the period 1991 - 2000. Venture capital funds that invested for 1 year only in the data are excluded. Canadian Venture capitalists only. Source: Macdonald
14
and Associates, Ltd., .
© Cumming & Johan (2013)
Portfolio Size
Table 17.2c. Summary Statistics for Private Limited Partnership Funds Only (104 Funds)
Variable Names
Mean
Standard Deviation
Skewness
Kurtosis
Minimum
Maximum
Venture Capital Funds Raised (Drawdowns) ('000)
24306.5
29385.7
1.969
6.645
600
149316
# Years Fund Investments Tracked by CVCA
4.663
2.400
0.808
2.489
2
10
Investment Duration Period (Quarters)
3.959
2.297
0.758
2.564
0.75
9.25
# Venture Capital Fund Managers
5.673
4.788
1.261
3.840
1
19
Average # Portfolio Firms
8.221
6.987
2.152
9.167
1
42
Average # Portfolio Firms / # Venture Capital Managers
2.589
3.385
3.244
16.187
0.200
23
Average # Portfolio Firms / # Venture Capital Managers / # Years
0.843
0.877
1.680
5.519
0.048
4
Early Stage
0.857
0.213
-1.843
5.948
0.071
1
Life Sciences
0.198
0.321
1.626
4.224
0
1
Other High-Tech
0.510
0.364
-0.074
1.582
0
1
Entrepreneur / Venture Capital Different Provinces
0.161
0.236
1.638
5.152
0
1
Staging Frequency
0.544
0.236
-0.686
2.819
0
0.933
Syndication Frequency
0.490
0.293
-0.041
1.998
0
1
Venture Capital Investments / Ent. Capital
0.481
0.283
0.485
2.032
0.047
1
Convertible Securities
0.262
0.192
0.750
3.072
0
0.875
0.268
0.180
1.218
5.000
-0.067
0.944
Venture Capital Firm Characteristics
Entrepreneurial Firm Characteristics
Financing Transactions Characteristics
Market Conditions
MSCI Return
Note: Data over the period 1991 - 2000. Venture capital funds that invested for 1 year only in the data are excluded. Canadian Venture capitalists only. Source: Macdonald
15
and Associates, Ltd., .
© Cumming & Johan (2013)
Portfolio Size
Table 17.3. Difference Tests
All 214 Funds
Average #
Portfolio
Firms
Difference Test
Average # Portfolio
Firms / # Venture
Capital Managers /
Years
Difference Test
Average #
Portfolio
Firms
Limited Partnership Venture Capital Fund
8.221
Corporate Venture Capital Fund
17.056
0.863
---
Limited Partnership Venture Capital Fund
8.221
0.843
---
-7.483***
-19.515***
0.843
104 Limited Partnerships Only
-0.102
-2.805***
---
LSVCC Fund
37.966
1.674
---
Limited Partnership Venture Capital Fund
8.221
0.843
---
Government Venture Capital Fund
32.467
-14.247***
-2.566**
1.695
---
22.311
8.365
1.107
6.843
Investment duration period > 4 years
24.730
0.985
10.333
Investment duration period < 4 Years
10.727
# Managers >7
35.246
# Managers <7
12.290
Early Stage >.75
20.067
Early Stage <.75
18.429
Life Sciences >.5
10.045
Life Sciences <.5
20.797
Other High-Tech >.5
15.626
Other High-Tech <.5
23.191
Venture Capital / Entrepreneur Different Province > .15
10.452
Venture Capital / Entrepreneur Different Province < .15
24.475
Staging Frequency >.5
21.575
Staging Frequency <.5
17.584
Syndication Frequency >.5
15.783
Syndication Frequency <.5
23.528
Venture Capital Investments / Entrepreneurial Capital >.5
21.970
Venture Capital Investments / Entrepreneurial Capital <.5
17.730
Convertible Securities >.5
9.333
Convertible Securities <.5
20.643
MSCI > .25
19.775
MSCI < .25
19.585
© Cumming & Johan (2013)
0.242
36.749***
14.880***
1.428
-2.780***
1.565
22.060***
0.530
1.211
-5.915***
0.331
1.318
-8.938***
1.063
0.485
0.688
-1.268
-4.701***
0.862
-9.065***
0.700
-3.758***
1.514
-5.588***
1.277
3.127***
1.335
1.014
8.265
9.250
7.154
7.474
9.164
7.833
7.390
0.314
8.700
0.308
6.980
0.574
-1.598
0.623
-3.100***
0.275
-5.330***
0.895
1.265
0.638
1.413
0.858
0.061
0.841
-4.268***
0.794
-0.541
0.893
-2.336**
0.633
-1.956*
0.964
4.406***
0.609
-3.046***
1.176
-1.406
0.588
-2.706***
1.062
-2.590***
1.099
2.212**
0.676
0.568
8.170
1.795*
-0.517
1.043
8.762
1.186
0.216
8.469***
8.554
0.919
-13.839***
12.185
1.059
1.226
6.884
1.679
4.740***
13.136***
8.652
1.565
---
0.889
9.288
1.456
4.470***
11.085***
8.034
1.306
-19.352***
16.400
8.048
1.180
---
1.166
6.831
1.136
-12.790***
-6.313***
4.553
1.510
1.465
6.956
10.611
1.446
---
---
17.790
1.166
-----
---
Venture Capital Mgmt. Firm with 1 Fund
50.155
1.214
---
Difference Test
---
-----
Venture Capital Mgmt. Firm with 2 or More Funds
Venture Capital Fund with More than $50,000,000
Drawdowns
Venture Capital Fund with Less than $50,000,000
Drawdowns
-5.044***
Difference Test
---
Average # Portfolio
Firms / # Venture
Capital Managers /
Years
1.083
0.753
0.818
-4.816***
9.415
Portfolio Size
0.761
0.922
-0.879
16
Theory
Data
Regressions
Conclusion/Summary
Variables
• Dependent Variable:
 Number of firms in VC fund portfolio
• Independent Variables:
 VC Fund Characteristics
 Fund type, # funds in VC firm, duration, # VC Managers, fundraising
(drawdowns)
 Entrepreneurial Firm Characteristics
 Development stages, life sciences, other high-tech
 Financing Characteristics
 Frequency of use of Convertible Pref Equity, Staging, Syndication, $
Invested / Firm Capital
 Market Conditions
 TSX Index
17
© Cumming & Johan (2013)
Portfolio Size
Theory
Data
Regressions
Conclusion/Summary
Regressions
• (1) All funds together
 with dummy variables for the type of fund)
• (2) Private Independent Funds Only
 Different types of funds face different restrictive covenants;
different objectives
• (3) For Portfolio Size and Portfolio Size / Manager / Year
18
© Cumming & Johan (2013)
Portfolio Size
Theory
Data
Regressions
Conclusion/Summary
Box-Cox Transformation
• Grid search over various values of  to
allow for both concavity and convexity
 x 1
when   0 ;

B ( x,  )   
log( x) when   0.

• Transformation applies to independent
variables, not the dependent variable
19
© Cumming & Johan (2013)
Portfolio Size
Theory
Data
Regressions
Conclusion/Summary
Heteroscedastic Box-Cox
• Box – Cox grid-search specification as per last slide
• Also consider Var ( )  ( 2 )[ w2 ](  )
where w=fund duration
possibility of truncated observations in the data
• Likelihood dominance tests  superior
• High Adjusted R2 (>.88)
20
© Cumming & Johan (2013)
Portfolio Size
Table 17.5. Regressions with All Types of Venture Capital Funds in the Same Sample (continues on next slide)
PANEL A. Dependent Variable: # of Entrepreneurial Firms in Venture Capital Fund Portfolio (continues on next slide)
(1) Box-Cox
(2) Linear
(3) Box-Cox
(4) Box-Cox
(5) Box-Cox
(6) Box-Cox
Independent
Variables
Coefficient
t-statistic
Slope
Elasticity
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Constant
21.997
4.415***
21.997
0.579
147.656
2.365**
-10.119
-2.891***
-2.547
-0.588
-11.137
-2.700***
1.442
0.510
Corporate Venture
Capital
-5.027
-2.885***
-5.027
-0.010
0.847
0.094
-7.521
-3.694***
-6.307
-3.087***
-7.016
-3.429***
-5.058
-2.875***
Government Venture
Capital
1.141
0.639
1.141
0.003
0.610
0.061
6.614
3.203***
5.547
2.659***
6.461
3.120***
5.809
3.232***
LSVCC
1.910
1.196
1.910
0.007
1.887
0.224
3.504
2.056**
4.760
2.707***
5.699
3.238***
7.811
5.210***
Private Independent
Venture Capital
-10.757
-8.669***
-10.757
-0.136
-9.110
-1.416
-6.489
-4.708***
-7.870
-5.593***
-5.694
-4.092***
-6.469
-5.355***
2 or more Venture
Capital Funds in the
Venture Capital
Mgmt.Firm
-13.920
-15.435***
-13.920
-0.163
-6.379
-1.351
-15.670
-15.114***
-13.295
-12.637***
-15.406
14.731***
-14.615
-15.997***
Venture Capital
Funds Raised
(Drawdowns) ('000)
0.164
4.397***
0.0002
0.4872
0.0002
7.698***
0.338
3.857***
0.346
3.697***
0.329
3.682***
0.145
4.050***
Venture Capital
Fund Duration
-2.482
-3.985***
-0.870
-0.137
0.265
0.225
-2.633
-3.273***
0.370
0.466
-1.698
-2.037**
-2.067
-3.370***
# Venture Capital
Fund Managers
7.954
20.253***
2.210
0.515
1.818
5.748***
8.297
16.847***
8.468
16.346***
8.441
16.377***
8.313
19.372***
Venture Capital
Fund Characteristics
21
© Cumming & Johan (2013)
Portfolio Size
Table 17.5. Regressions with All Types of Venture Capital Funds in the Same Sample (Continued)
PANEL A. Dependent Variable: # of Entrepreneurial Firms in Venture Capital Fund Portfolio (Continued)
(1) Box-Cox
Independent
Variables
(2) Linear
(3) Box-Cox
(4) Box-Cox
(5) Box-Cox
(6) Box-Cox
Coefficient
t-statistic
Slope
Elasticity
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Early Stage
17.833
5.305***
12.438
0.605
15.613
1.344
---
---
---
---
---
---
---
---
Life Sciences
---
---
---
---
---
---
---
---
0.431
0.176
---
---
2.271
1.089
Other High-Tech
---
---
---
---
---
---
-19.152
-9.454***
---
---
-16.129
-7.230***
---
---
Entrepreneur /
Venture Capital
Different Provinces
-23.242
-11.909***
-21.121
-0.655
-16.779
-2.000**
-26.509
-11.432***
-27.626
-11.770***
-27.880
11.940***
-23.206
-11.756***
Staging Frequency
-33.607
-9.741***
-25.932
-1.062
-26.072
-2.093**
---
---
-40.845
-10.002***
---
---
---
---
Syndication
Frequency
-32.113
-11.494***
-25.159
-1.004
-30.731
-2.952***
---
---
---
---
---
---
-25.178
-12.816***
Venture Capital
Investments / Ent.
Capital
-24.588
-6.717***
-19.441
-0.764
-22.264
-1.706*
---
---
0.502
0.164
5.165
1.783*
---
---
Convertible
Securities
-13.253
-4.556***
-11.679
-0.382
-10.028
-0.851
---
---
---
---
-14.257
-4.224***
-12.909
-4.443***
-10.956
-2.632***
-9.535
-0.318
-8.607
-0.697
3.357
0.711
-7.190
-1.497
1.253
0.264
-5.120
-1.243
0.413
21.405***
---
---
---
---
0.346
15.498***
0.340
14.543***
0.344
14.710***
0.414
19.778***
Entrepreneurial Firm
Characteristics
Financing
Transactions
Characteristics
Market Conditions
MSCI Return
Returns to Scale
λ
Adjusted R2
0.891
0.443
0.869
0.870
0.869
0.887
# Observations
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22
Table 17.5. Regressions with All Types of Venture Capital Funds in the Same Sample (continues on next slide)
PANEL B. Dependent Variable: # of Entrepreneurial Firms in Venture Capital Fund Portfolio / # Venture Capital Fund Managers / Investment Years
(1) Box-Cox
(2) Linear
(3) Box-Cox
(4) Box-Cox
(5) Box-Cox
(6) Box-Cox
Independent
Variables
Coefficient
t-statistic
Slope
Elasticity
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Constant
2.917
2.860***
2.917
2.241
8.099
2.502**
0.631
1.160
1.095
1.364
0.305
0.460
1.487
2.802***
Corporate Venture
Capital
-0.471
-1.030
-0.471
-0.030
-0.376
-0.799
-0.513
-1.055
-0.519
-1.093
-0.455
-0.941
-0.426
-0.913
Government
Venture Capital
0.081
0.158
0.081
0.004
0.064
0.120
0.393
0.738
0.360
0.683
0.438
0.826
0.230
0.445
LSVCC
-0.206
-0.485
-0.206
-0.021
-0.212
-0.480
0.031
0.072
0.137
0.317
0.215
0.494
0.006
0.013
Private Independent
Venture Capital
-0.515
-1.590
-0.516
-0.193
-0.529
-1.563
-0.266
-0.799
-0.258
-0.781
-0.187
-0.562
-0.458
-1.420
2 or more Venture
Capital Funds in the
Venture Capital
Mgmt. Firm
-0.160
-0.667
-0.160
-0.052
-0.194
-0.787
-0.357
-1.436
-0.223
-0.894
-0.278
-1.104
-0.172
-0.709
Venture Capital
Funds Raised
(Drawdowns) ('000)
0.006
0.535
0.0003
0.426
0.0002
4.628***
0.005
0.488
0.013
0.531
0.005
0.435
0.002
0.395
Venture Capital
Fund
Characteristics
23
© Cumming & Johan (2013)
Portfolio Size
Table 17.5. Regressions with All Types of Venture Capital Funds in the Same Sample (continued)
PANEL B. Dependent Variable: # of Entrepreneurial Firms in Venture Capital Fund Portfolio / # Venture Capital Fund Managers / Investment Years (continued)
(1) Box-Cox
Independent
Variables
(2) Linear
(3) Box-Cox
(4) Box-Cox
(5) Box-Cox
(6) Box-Cox
Coefficient
t-statistic
Slope
Elasticity
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Early Stage
0.648
0.895
0.508
0.720
0.487
0.790
---
---
---
---
---
---
---
---
Life Sciences
---
---
---
---
---
---
---
---
0.379
0.723
---
---
0.537
1.115
Other High-Tech
---
---
---
---
---
---
-1.060
-2.445**
---
---
-0.727
-1.574
---
---
Entrepreneur /
Venture Capital
Different Provinces
-0.739
-1.517
-0.692
-0.627
-0.646
-1.459
-0.791
-1.554
-0.817
-1.565
-0.861
-1.691*
-0.741
-1.552
Staging Frequency
-2.088
-2.687***
-1.769
-2.068
-1.616
-2.495**
---
---
-2.429
-2.914***
---
---
---
---
Syndication
Frequency
-2.476
-3.927***
-2.102
-2.443
-2.147
-3.956***
---
---
---
---
---
---
-1.952
-4.130***
Venture Capital
Investments / Ent.
Capital
-1.578
-1.949*
-1.340
-1.556
-1.267
-1.810*
---
---
0.441
0.686
0.844
1.419
---
---
Convertible
Securities
-0.383
-0.572
-0.352
-0.336
-0.405
-0.648
---
---
---
---
-0.765
-1.117
-0.619
-0.954
1.764
2.494**
1.591
1.586
1.801
2.854***
2.662
3.574***
1.643
2.191**
2.513
3.349***
2.258
3.284***
0.605
2.549**
---
---
---
---
0.624
2.408**
0.499
2.037**
0.624
2.147**
0.724
2.307**
Entrepreneurial
Firm Characteristics
Financing
Transactions
Characteristics
Market Conditions
MSCI Return
Returns to Scale
λ
Adjusted R2
0.316
0.257
0.229
0.259
0.242
0.287
# Observations
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Portfolio Size
24
Theory
Data
Regressions
Conclusion/Summary
Summary of Some Key Results (refer also to Ch. 18)
•
Empirical support for Kannianen and Keuschnigg (2003,2004):
 expansion of portfolio size eventually becomes unprofitable as active
VC investing and managerial advice gets diluted
•
VCs have fewer firms in their portfolios when marginal costs are greater
and monitoring and value added active assistance is more intensive
 Greater frequency of staging and syndication
 Private independent VCs
•
VCs have more firms in their portfolios when marginal costs are lower and
marginal benefits are greater
 VC fund in VC firm with 2 or more VC funds
 More VC managers
 Convertible securities (for private independent funds)
25
© Cumming & Johan (2013)
Portfolio Size
Theory
Data
Regressions
Conclusion/Summary
Summary of Key Results (Con’t)
• Specialization and complementarities are important
 Life Sciences, Other High-Tech, Early Stage Firms
 Subsample of private independent funds only: different results
• Differences in the results across different types of VC
funds




Private independent funds have smaller portfolios
Value added investors
Concave function for full sample (λ =0.4)
Less concave function for subsample of private independent funds
 Less pronounced diminishing returns to scale (λ =0.8)
26
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Portfolio Size
Theory
Data
Regressions
Conclusion/Summary
Conclusions
• Importance of context: type of entrepreneurial firm,
type of venture capital firm, and nature of the
financial contract
• Risk-taking and capital structure affect optimal
portfolio size
• Future research
 Differences across countries?
 Impact on entrepreneurial firm innovation?
27
© Cumming & Johan (2013)
Portfolio Size