Table 8: Results Tobit Regressions
This table displays the results from Tobit regressions. The dependent variable is the logarithm of fund size, where fund size is the amount in millions of USD that is committed to the fund. The dependent variable is censored at 0. The variables Net IRRt-1 and Net IRRt-2 are lagged realised Net IRRs of a private equity firm’s previous fund and the fund before that. The variables Net IRR2t-1 and Net IRR2t-2 are the squared terms of the lagged Net IRRs. Sizet-1 is the amount of capital under management in the fund before the current one. Sequence represents the sequence number of the fund. All regressions include year fixed effects.
(1) (2) (3) (4)
Log(Size) Log(Size) Log(Size) Log(Size)
Net IRRt-1 0.006*** 0.007 0.004
(0.002) (0.004) (0.005)
Net IRRt-2 0.003 0.016**
(0.002) (0.007)
Net IRR2t-1 0.000 0.000
(0.000) (0.000)
Net IRR2t-2 -0.000***
(0.000)
Log(Sizet-1) 0.685*** 0.644*** 0.684*** 0.650***
(0.020) (0.024) (0.019) (0.026)
Log(Sequence) 0.163*** 0.199*** 0.144*** 0.202***
(0.049) (0.067) (0.049) (0.065)
_cons 1.521*** 1.676*** 2.037*** 1.368***
(0.095) (0.126) (0.118) (0.175)
Firm fixed effects No No No No
Year fixed effects Yes Yes Yes Yes
Pseudo R2 0.301 0.245 0.301 0.254
Obs. 1064 771 1064 738
Standard errors are in parenthesis and they are corrected for heteroskedasticity and clustered by year.
*** Significant at the 1 percent level.
** Significant at the 5 percent level.
* Significant at the 10 percent level.
As mentioned in chapter 3, some researchers, including Phalippou (2008), showed that net IRR contains certain flaws when it is used as a performance measure in the private equity context. To check whether the results are robust to the choice of performance measure, a robustness check has been performed with two different proxies for performance: the Kaplan-Schoar Public Market Equivalent (KS PME) and the net multiple. The results can be found in Table 9. When KS PME is used as a performance measure, the results are slightly different regarding the two main variables of interest. The coefficients on the variable “Number of Deals” is again always positive but now only significant in regression 4. The coefficient in regression 4 can be interpreted in the following way: a one unit increase in the number of deals leads to an increase in the change in the KS PME between subsequent funds from the same private equity firm of 0.8. The coefficients on the variable “Investment per Deal” are again always positive but now also significant in models 2, 3 and 4. The positive significant coefficients in those models imply that an increase in the investment per deal (by 1 million) is
associated with an increase in the KS PME of 0.1. An explanation for this positive relation between deal size and performance may be that doing large (specialised) deals leads to access to better networks and the fund possess a lot of specialised knowledge that helps them to select the best investments (Gejadze et al., 2017; Norton & Tenenbaum, 1993). Their
extensive knowledge also results in them having a better understanding of industry dynamics and so they are able to act upon market signals faster (Gompers et al., 2008). That large deals positively influence performance may also be due to the fact that larger investments are often more efficiently priced (Lopez-de-Silanes et al., 2015). It is important to note however that due to limitations regarding data on the KS PME variable, the number of observations is a lot smaller for the regressions using KS PME compared to the ones that use net IRR or the net multiple. This makes the results with KS PME as the dependent variable less reliable. The results with the net multiple as the dependent variable are similar to those where net IRR had been used. The coefficients on the variable “Number of Deals” are positive and highly significant across all four regressions. The coefficient on “Number of Deals” in model 5 indicates that a one unit increase in the number of deals leads to an increase in net multiple of 0.005. When the change in net multiple between subsequent funds is used the conclusions are again similar to those from the regressions that use the change in net IRR as the dependent variable. The coefficient on “Number of Deals’ in column 8 for example indicates that a one unit increase in the number of deals leads to an increase in the change in net multiple between subsequent funds from the same private equity firm of 0.010. The variable “Investment per Deal” is also always positive and only significant in regression 8. From column 5 we can conclude that an increase in deal size by 1 million (USD) is associated with an increase in the net multiple by 0.001. The results regarding the control variables are similar across all
regressions, regardless of the proxy for fund performance. “Log(Size)” is negatively associated with fund performance. Lagged performance is positive when the dependent variable is KS PME or net multiple but becomes negative when the dependent variable is the change in KS PME or the change in net multiple. The coefficients on the industry specialist dummy are again positive across all regressions. Also in these regressions the adjusted R2 increases a lot when firm fixed effects are included in the model. This confirms the believe that performance differs a lot across different private equity firms. Overall, the results from Table 9 show that the previous results are robust to the choice of performance measure. We can again conclude that the number of deals that a fund does positively influences a fund’s performance and that the deal size (investment per deal) does not have a significant impact.
Table 9: The Effect of Number of Deals and Deal Size on Fund Performance using Different Performance Measures
The dependent variable in regressions 1 and 2 is the Schoar Public Market Equivalent and in regressions 3 and 4 the change in the Kaplan-Schoar Public Market Equivalent between subsequent funds. The dependent variable in regressions 5 and 6 is the net multiple and in regressions 7 and 8 the change in net multiple between subsequent funds. Number of deals is the amount of deals the fund engaged in. Investment per deal is the average amount in millions of USD that the fund invests per deal. Size is the amount in millions of USD that is committed to the fund. KS PMEt-1
and Net Multiplet-1 represent the performance of the previous fund. Sequence represents the sequence number of the fund. Industry Specialist is a dummy variable equal to 1 when the fund is considered specialised in the industry of the buyout and 0 otherwise. Columns 1, 3, 5 and 7 include only year fixed effects. Columns 2, 4, 6 and 8 include both firm fixed effects and year fixed effects.
(1) (2) (3) (4) (5) (6) (7) (8)
KS PME KS PME KS PME KS PME Net
Multiple Net
Multiple Net
Multiple Net
Multiple
Number of Deals 0.003 0.001 0.003 0.008** 0.005*** 0.003** 0.009*** 0.010***
(0.003) (0.002) (0.003) (0.003) (0.002) (0.002) (0.003) (0.003)
Investment per Deal 0.001 0.001*** 0.001* 0.001*** 0.001 0.000 0.001 0.001**
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.000)
Log(Size) -0.064 0.032 -0.092 -0.109 -0.111* -0.237*** -0.148* -0.353***
(0.076) (0.084) (0.078) (0.068) (0.065) (0.083) (0.076) (0.097)
KS PMEt-1 0.347*** 0.075 -0.694*** -1.154***
(0.084) (0.123) (0.077) (0.073)
Log(Sequence) 0.130** -0.140 0.061 -1.040*** 0.038 -0.282** -0.056 -0.299*
(0.061) (0.307) (0.068) (0.165) (0.057) (0.110) (0.072) (0.167)
Industry Specialist 0.015 0.004 0.028 0.000 0.011 0.006 0.031 0.031*
(0.016) (0.005) (0.020) (0.005) (0.013) (0.008) (0.022) (0.016)
Net Multiplet-1 0.189*** -0.054 -0.586*** -0.692***
(0.024) (0.033) (0.064) (0.075)
_cons 0.824* 1.013 1.137*** 3.481*** 1.907*** 3.914*** 1.658*** 3.708***
Firm fixed effects No Yes No Yes No Yes No Yes
Year fixed effects Yes Yes Yes Yes Yes Yes Yes Yes
(0.461) (0.891) (0.403) (0.465) (0.293) (0.621) (0.336) (0.767)
R-squared 0.409 0.887 0.603 0.961 0.196 0.556 0.243 0.500
Adjusted R-squared 0.405 0.883 0.600 0.960 0.195 0.549 0.242 0.492
Obs. 4829 4827 3955 3954 26398 26391 24986 24981
Standard errors are in parenthesis and they are corrected for heteroskedasticity and clustered by year.
*** Significant at the 1 percent level.
** Significant at the 5 percent level.
* Significant at the 10 percent level.
Another robustness check is performed where the sample is dividend in different subsamples based on the geographical focus of the buyout fund. The results can be found in Table 10. For this analysis buyout funds are included that either focus on the U.S. or on Europe. The
regulations for private equity firms can differ substantially between countries/continents.
Seretakis (2013) concludes that the legal environment regarding private equity transactions and firms is a lot more restrictive in Europe compared to in the U.S. So by doing regressions for both subsamples separately, it can be tested whether the results are robust to the
geographical focus of the buyout fund. From Table 10 it can be concluded that the positive effect of increasing the number of deals on performance is only significant for buyout funds that focus on the U.S. The coefficients on the variable “Number of Deals” for the sample that focuses on the U.S. are positive and highly significant, whereas the coefficients for the
sample that focuses on Europe are not significant anymore. Besides that, all other conclusions remain the same for both subsamples: the effect of deal size is positive but not significant, size has a negative impact on performance, past performance is positive when we use net IRR but becomes negative when change in net IRR is used, sequence does not have a significant impact on performance and the coefficients on the industry specialist dummy variable are positive although not significant across all regressions.
Table 10: The Effect of Number of Deals and Deal Size on Fund Performance per Geographical Region Regressions 1 and 2 are performed on a subsample of buyout funds with a geographical focus on the U.S.
Regressions 3 and 4 are performed on a subsample of buyout funds with a geographical focus on Europe. The dependent variable in regressions 1 and 3 is net IRR and in regressions 2 and 4 the change in net IRR between subsequent funds. Number of deals is the amount of deals the fund engaged in. Investment per deal is the average amount in millions of USD that the fund invests per deal. Size is the amount in millions of USD that is committed to the fund. Net IRRt-1 is the performance of the previous fund. Sequence represents the sequence number of the fund. Industry Specialist is a dummy variable equal to 1 when the fund is considered specialised in the industry of the buyout and 0 otherwise. All regressions include year fixed effects.
(1) (2) (3) (4)
U.S. U.S. Europe Europe
Net IRR Net IRR Net IRR Net IRR
Number of Deals 0.063*** 0.125*** 0.032 0.068
(0.023) (0.039) (0.038) (0.057)
Investment per Deal 0.003 0.010 0.004 -0.006
(0.006) (0.009) (0.014) (0.019)
Log(Size) -1.289* -2.229** -1.253 -0.737
(0.753) (0.906) (0.757) (0.962)
Net IRRt-1 0.185*** -0.623*** 0.150*** -0.684***
(0.047) (0.085) (0.039) (0.086)
Log(Sequence) -0.164 -1.800 1.706 0.660
(0.986) (1.369) (1.074) (1.476)
Industry Specialist 0.085 0.745 0.363 0.480
(0.333) (0.496) (0.397) (0.662)
_cons 19.649*** 21.462*** 17.661*** 11.537*
(3.836) (5.682) (4.873) (6.720)
Firm fixed effects No No No No
Year fixed effects Yes Yes Yes Yes
R-squared 0.161 0.264 0.241 0.488
Adjusted R-squared 0.159 0.262 0.238 0.486
Obs. 17051 16431 7948 7272
Standard errors are in parenthesis and they are corrected for heteroskedasticity and clustered by year.
*** Significant at the 1 percent level.
** Significant at the 5 percent level.
* Significant at the 10 percent level.