In our recent paper The Flattening of the Private Equity J-Curve we discussed developments that could be leading to the weakening, or even the demise, of the J-curve. In this paper we present quantitative analysis to explore some of the qualitative concepts discussed in the previous paper, as well as document changes in capital calls over the past decade. The fund management scenarios discussed in the previous paper and examined here are: 
In addition to the two fund-management scenarios listed above, we will also investigate the impact of the shortening of the fundraising cycle, which has led to an accelerated capital call sequence over the current fund’s investment period. We will use two methodologies to examine these issues: simulation and comparing actual fund data of 2010-19 vintage buyout funds. Simulation offers the opportunity to isolate the impact of each variable, while the actual fund data allows us to determine whether the impacts are significant enough to be observed in real-world data. As the simulations will show, each of the three fund management scenarios has the potential to lead to higher reported Internal Rates of Returns (IRRs). The actual fund data will also show that there has been a noticeable shift to calling capital earlier in a fund’s life, which may have contributed to the observed increase in reported IRRs in the early years of later vintage funds.
Historically, most private equity funds have employed a five-year investment period. In that time, a fund manager can add new platform investments to their portfolio, which usually absorb the bulk of the investment capital of the fund. Often, a manager reserves some capital for additional investment in the existing portfolio companies to support activities after the end of the investment period. Commonly, funds have a threshold of 75% of invested capital prior to raising and closing on their subsequent fund. Although most fund managers have an active investment pipeline at the initiation of their fund, they do not have perfect knowledge of which deals will close or when. Thus, while fund managers may have some ability to predict their expected near-term capital calls, they are unlikely to be able to forecast precisely the capital calls across their entire investment period. With this background, we examined the following fund management scenarios:
To deal with the uncertainty of the capital call sequence, we made several initial assumptions for the simulations, shown in Figure 1.
Figure 1. Simulation assumptions
These assumptions are for the Standard Fund scenario; we used them to generate a capital call sequence as well as a valuation sequence. From those two sequences, we then calculated Internal Rates of Returns (IRRs). To generate similar sequences for the Warehoused Investments scenario, we deleted the last two quarterly capital calls in the investment period and added them to the initial quarterly capital call. For the Credit Line Usage scenario, the only change from the Standard Fund scenario was cutting the time to first valuation increase from one year to two quarters, as the use of a capital call shortens the time between the call and the first valuation increase. Imbedded in this approach is the assumption that the credit line is used consistently for two quarters throughout the investment period of the fund. For the Accelerated Investment scenario, the only change from the Standard Fund scenario was cutting the investment period from five years to four, which thereby increased the quarterly capital calls proportionally. Figure 2 shows the capital calls by quarter for each of the four scenarios relative to the date of the initial capital call.
Figure 2. Cumulative capital calls under various fund management scenarios
As expected, the Warehoused Investments scenario has the highest initial capital call ($1,010,000) followed by the Accelerated Investment scenario ($450,000). Note that the capital call sequence for both the Standard Fund and Credit Line Usage scenarios are identical as they are presented relative to the date of their initial capital call. A point of interest is that the Accelerated Investment scenario capital calls ($7,300,000) did not reach that of the other scenarios ($7,400,000), owing to lower fees after the termination of its investment period. Figure 3 presents the associated valuation sequences.
Figure 3. Fund valuations under various fund management scenarios
As with the capital call sequence, the Warehoused Investments scenario starts off with the highest valuation ($960,000) but is surpassed by the Accelerated Investment scenario mid-way through the investment period. Despite that, the Warehoused Investment scenario does conclude with the highest final valuation ($8,739,624). Finally, Figure 4 below presents the IRRs calculated from the capital calls and valuations sequences.
Figure 4. Internal rate of return under various fund management scenarios
Although some of the differences in the capital call and valuations sequences appeared to be relatively minor, when we combined the two sequences and calculated the respective IRRs from them, the differences became much more apparent. In general, there is significant divergence in the IRRs between the four fund management scenarios. Specifically:
It is worth noting that all three scenarios have significantly higher IRRs throughout the remainder of the investment period than the Standard Fund scenario. Of the three strategies, the Accelerated Investment scenario had the highest final IRR compared with the Standard Fund scenario. This is owing to the earlier deployment of capital, which allowed the called capital to compound at the valuation increase over longer periods. Even the IRR differential between the Standard Fund scenario and the Credit Line Usage scenario could have significant implications. It is likely that the differential is large enough that it could move a fund’s performance up at least one quartile relative to its peers.
Simulations allow for the isolation of variables and can offer insight into the underlying dynamics of myriad phenomena. Ultimately, however, the true test of theoretical propositions is whether they are strong enough to manifest themselves in real world data. For this analysis, we used the Private i dataset and analytical tools available from Burgiss. Certainly, one of the challenges with using real-world data is that it is often very difficult to isolate the impact of single variables. And, as a fund’s life usually extends over ten years, a further challenge is that the variables of interest may not remain constant over such a long period. However, based on the results from the simulations, as well our extensive experience in managing private equity investment portfolios, the expected impact on capital calls under the three non-standard scenarios is shown in Figure 5.
Figure 5. Expected impact on capital calls
It is worth noting that an important difference between the simulation analysis and the fund analysis is the measurement of time. In the simulation analysis, the quarters and years were relative to the initiation of the first capital call, that is, relative to the beginning of a fund’s actual life. In the Private i dataset the timeline is based on vintage and calendar years. A fund that made its first call in October 2019 would be deemed a 2019 vintage year fund. However, that fund’s Year 1 capital calls would only constitute one quarter’s worth of actual capital calls. As few funds will make their first capital call on January 1st, this issue will impact all funds in the dataset to a varying degree. For this analysis, the timeline differential probably has the greatest influence on the Credit Line Usage scenario. Although the first capital call would determine a fund’s vintage year, the classification of subsequent calls could depend on a fund managers’ decision to carry a capital from one calendar year to the next. This is the logic for the “Dependent on Manager” entries in Figure 5.
To perform this quantitative analysis we used the Burgiss Private i database and downloaded capital call and IRR information for all buyout funds across all geographies with vintages from 2010 to 2019. We then grouped the data into two based on their vintage. The sample sizes for the two groups are presented in Figure 6 below:
Figure 6. Number of funds in samples
As the 2010-14 sample consists of mature funds, there is no decrease in the number of funds over time. However, there is a significant fall in the size of the 2015-19 sample, especially in the last two years. This is an endemic issue in private equity research in that the length of a fund’s life can make it very difficult to draw relevant comparisons between contemporaneous funds and historical ones. However, this analysis is partly mitigated by its focus on the early years of a fund’s life. As the first step in analysis, we examined the Year 1 capital calls for both samples, as shown in Figure 7:
Figure 7. Year 1 capital call distributions
Median capital calls increased from 19.5% for the 2010-14 sample to 22.7% for the 2015-19 sample. The difference between the two is highly statistically significant. Additionally, it is clear that the entire distribution shifted upwards from the beginning to the end of the decade. As shown in Figure 6, this could be consistent with all three scenarios. However, the granularity of the data does not allow us to distinguish the individual contribution of each scenario. Figure 8 suggests the higher level of capital calls correlates positively with a substantial improvement in IRR. The median IRR for the 2010-2014 sample was -12.0%, compared with -9.2% for the 2015-19 sample. Also, as with the capital calls, the entire distribution shifts upwards.
Figure 8. Year 1 IRR distributions
In Figure 9 we present the time series of the median annual capital calls over the traditional fund investment period of five years. Capital calls for the 2015-19 sample are significantly above the earlier fund vintages for the first three years and then slightly below for the remaining two years. As funds are limited to calling approximately 100% of commitments over the life of a fund, higher early capital calls will translate into lower later capital calls. Further, the median cumulative capital called in Year 5 for the 2010-14 sample is 55.8% (not shown in graph), compared with 65.3% for the 2015-19 sample. Thus, it does appear that fund managers are calling capital more quickly than they have previously.
Figure 9. Median capital calls
The median IRRs for the two samples (shown in Figure 10 below) follow a similar pattern. The capital calls in the 2015-19 sample have significantly higher IRRs until Years 4 and 5. However, as noted in Figure 6, the number of funds in the 2015-19 sample drops off considerably in the last two years. And if the practices we have been discussing are becoming increasingly common, the loss of the later funds in the 2015-19 sample could be responsible for the inversion in the graph. As mentioned above, the data does not allow us to distinguish between the three hypothesized fund management scenarios. Nevertheless, later vintage funds are clearly engaging in activities that generate consistently higher IRRs.
Figure 10. Median IRRs
Both the simulations and actual fund data results support the supposition that fund managers are employing techniques that result in capital being called in ways that can increase the IRRs of their funds. Although that in itself may be interesting information, there are some important implications for managing a private equity portfolio:
The simulations offered us the ability to isolate the individual scenarios and thereby examine their potential impacts on capital calls and IRRs. In the fund results data we were able to observe significant differences in the behavior of funds over the last decade of private equity fund vintages, but we were not able to distinguish the exact sources of those differences. Fund managers are likely using a combination of the various scenarios and it’s possible that the degree to which they use them may vary over time, further complicating definitive analysis. Although it is important to understand the changing nature of capital calls and their implications, it is also necessary to develop and maintain strong communication channels with fund managers in order to mitigate the issues discussed as well as to optimize the management of a private equity portfolio.
 In the previous paper, we also considered the trend toward timelier portfolio company valuation adjustments. As this paper focuses on capital calls, we did not create a distinct model that incorporates that aspect; rather it will be imbedded in the assumptions for each of the scenarios as discussed later.
 These comments apply to general private equity funds, which are distinct from venture capital funds. Dependent on the stage, a venture capital fund can have a dramatically different investment and capital call sequence.
 That this generates the classic private equity J-curve pattern provides some confidence that the simulation accurately replicates a realistic private equity fund cash flow series.
 As previously mentioned, different types of funds can have markedly divergent capital call sequences. To minimize issues associated with that we focused solely on buyout funds, which represent the largest subset, both by number and capital raised, of funds. Also, we selected the starting vintage of 2010 to avoid the potentially distorting impacts of the global financial crisis.
 The samples were created to provide an equal number of vintage years as well as an approximately comparable number of funds in Year 1.
 It is not unusual for funds to have recycling provisions, which can allow them to slightly exceed calling 100% of committed capital.