Ji-Woong Chung, Berk A. Sensoy, Léa Stern, and Michael S. Weisbach
Pay for performance from future fund flows: The case of private equity
Review of Financial Studies | Volume 25, Issue 11 (Jun 2014), 3259–3304

The incentives of private equity general partners to create value for their investors (limited partners) are often questioned by investors, industry observers, and academics alike. Critics argue that pay-for-performance incentives from the carried interest profit share (typically 20%) are muted when funds fall short of their hurdle rates, and because fixed fees alone represent a substantial source of income for many private equity groups.

In this paper, we point out that the direct incentives from carried interest are only part of the total pay-for-performance incentives that general partners have. The other part is the indirect, market-based incentives that arise from the fact that general partners' ability to raise capital for new funds in the future, and so to earn income from managing that capital, depends on the performance of their current funds.

To better understand general partners' motivations, it is essential to have a complete picture of their total pay for performance incentives, which is the sum of the direct effect of current performance on earnings from carried interest, and the indirect effect of current performance on earnings from managing future funds.

An additional contribution of our work is that our general framework for quantifying these effects can be extended to other asset management settings in which future fund raising or flows depend on current performance.

Modeling indirect pay-for-performance

Our goal is to quantify the indirect effect and compare its magnitude to the direct effect. To do so, we present a rational learning model based on Berk-Green (JPE 2004) that formalizes the logic by which good performance in the current fund could lead to higher future incomes for general partners through an effect on expected future fund-raising. In our model, the ability of a general partner to generate abnormal returns is unknown to market participants. However, a general partner builds his reputation as the market updates its assessment of his ability based on the observed returns. Ultimately, investors will decide whether the observed returns are sufficient for the general partner to raise another fund, and if so how much capital will be allocated.

The key ingredients of the learning model are these. The general partner has some unknown ability θ to generate (abnormal) returns. Investors have a prior θ0, drawn from a normal distribution with mean θ and precision τ. Fund returns ri are distributed normally, with mean θ (the general partner's true ability) and precision s. After the market observes the returns, it updates its assessment of the general partner's ability  theta_i= frac{ tau cdot theta_0 + s cdot sum_{i} r_i}{ tau + i cdot s};/var/tmp/iawltxhtml/mathcache//udisplaymathc20701dec03989a55e91aadfcb294d2f.svg In the model, both the probability that the general partner is able to raise another fund p( θi ) and the size of that fund if one is raised, f( θi ), are both increasing functions of the current estimate of ability, θi. The expected size of the next fund is therefore equal to p( θi ) · f( θi ).

The rational learning framework thus predicts that both the likelihood of raising a follow-on fund and the size of the follow-on if it is raised increase with current performance. If we assume that a general partner runs a total of N+1 funds, his total lifetime revenues are TR = k( ri ) · f( θ0 ) + k( r2 ) · p( θ1 ) · f( θ1 ) + ... + k( rN + 1 ) · ∏ [ p( θi ) · f( θN ) ]

In the above equation, k( r ) is the general partner's revenue as a percentage of fund size as a function of performance r. In order to estimate how a general partner's lifetime compensation varies with the performance of his current fund, we differentiate the above equation with respect to r. The resulting explicit formula for indirect pay-for-performance from future fundraising provides estimates of how general partners' lifetime income varies with their current performance. Indirect pay-for-performance is a function of

Predictions of the learning model

The model provides us with several cross-sectional predictions about the magnitude of the sensitivity of future fundraising to current performance that have not been previously tested in the private equity literature, and that in our framework translate directly into cross-sectional differences in indirect pay for performance incentives.

The first prediction is that for a given assessment of a general partner's ability to generate returns, the more `scalable' abilities are, the more investors are willing to put money into a following fund. To the extent that buyout funds are more scalable than venture capital funds (Metrick-Yasuda (RFS 2010)), future fundraising-performance sensitivity should be greater for buyout funds than for venture capital funds. Intuitively, if a general partner of a buyout partnership is shown to be talented at increasing value by buying out companies, he can potentially employ the same skills to buy out larger companies and increase their value, and hence make effective use of a larger pool of capital. In contrast, if a venture capitalist has demonstrated that she is talented at investing in startup companies, she is not able to increase fund size as much because the size of startup investments is not scalable (and because, given the time-consuming value-added nature of the private equity investing process, it is not feasible simply to increase the number of investments).

The model also predicts that as a partnership ages, so its ability is known with more precision, performance in a given fund should have less incremental impact on the market's overall assessment of the partnership's ability. This means that future fundraising should be more sensitive to performance for younger partnerships than for older ones.

Finally, the model predicts that for a given performance, a manager is more likely to raise a subsequent fund if the prior assessment of his ability is better. It implies that later sequence funds should be more likely to raise a follow-on fund because the average assessment of ability will be higher in later sequence funds than in earlier ones, for the simple reason of their survival.

Main results

Using a sample of buyout, venture capital, and real estate private equity funds from Preqin from 1993–2010, we find support for all of these predictions. In particular, the data support the rational learning framework over a simple return chasing story for future fundraising, which predicts if anything the opposite relations with respect to partnership age.

The tests provide estimates of the sensitivities of the probability of raising a future fund, and its size if one is raised, to performance in the current fund. We combine these estimates with sample summary statistics on the fraction of funds that raise a future fund, and the size of that fund if one is raised, and with Metrick-Yasuda (RFS 2001)'s estimates of general partner revenue per dollar of fund size. We use these three pieces of information to compute indirect pay for performance from future fundraising according to the formula derived from the learning model. We compute indirect pay for performance under various sets of assumptions.

Our results show that for a first time buyout (venture capital) fund of average size, whose managers can run a maximum of three more funds in the future, a one-percentage-point improvement in net return to limited partners in the current fund relative to the sample average return will increase the present value of his expected total lifetime income by over $4 million ($0.31 million). When the maximum number of future funds is five, these figures increase to $7.8 million and $0.35 million for buyout funds and venture funds, respectively.

To gauge the significance of these figures, we then compare the magnitude of this indirect pay for performance to the direct pay for performance from carried interest, under the assumption that the current fund is in the money so the general partner receives, at a carried interest of 20%, an incremental $0.25 for every incremental $1.00 returned to fund investors. While this assumption reflects reality for the typical fund in our data, it means that our estimates of the importance of indirect pay for performance is understated because some funds never earn any carried interest.

The following figure summarizes these calculations. The figure shows the ratio of indirect to direct pay for performance, for different types of funds and as a function of the sequence number of the current fund, which is the position of the current fund in the partnership's overall sequence of funds.

There are three main takeaways from the figure. First, indirect pay for performance is sizeable and of the same order of magnitude as direct pay for performance from carried interest. For all funds taken together, the ratio of indirect to direct pay for performance is 0.7. Second, indirect pay for performance is much stronger for buyout funds than for venture capital funds, with real estate in between. Indeed, the ratios of indirect to direct pay for performance for first time buyout, venture and real estate funds are 2.3, 0.4 and 2, respectively. This result is in accordance with our prediction as buyout funds are much more scalable by nature than venture capital funds. Third, indirect pay for performance becomes weaker as a partnership ages and manages more funds. This is again consistent with the model's prediction that current performance has less impact on the market's overall assessment of ability as a partnership ages. The magnitude is reduced by more than half for a fifth-fund buyout partnership compared to a new partnership, and for venture capital there is essentially no indirect pay for performance beyond the fourth fund. Our results are all consistent with the learning framework, and suggest that learning about ability is a key driver of indirect pay for performance in private equity.

1: Ratio of indirect to direct pay for performance, for different types of funds and sequence numbers
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The figure shows that indirect compensation was sizable compared to direct compensation, higher for buyout than for VC funds, and higher early in the partnership.

Implications of our results

These results have several implications. One is that total pay for performance in private equity is much larger and much more heterogeneous than suggested by the carried interest alone (the focus of much academic work and practitioner interest). This is suggestive of greater alignment of general partner interests with investors' interests than discussions of the carried interest alone would suggest. At the same time, the results imply that total pay for performance goes down as a partnership ages. In particular, in contrast to theories such as Gibbons-Murphy (JPE 1992), in private equity we do not see explicit incentives from contractual carried interest rise (enough) to offset the decline in market-based, indirect pay for performance. Whether it is optimal for private equity compensation contracts to look the way they do in light of the market-based incentives we document is an important question for future research.


12-tsunami
Hokusai (1760-1849): Great Waves of Kanagawa, Japan, 1829.. This is one of the most-recognized Japanese art pieces in the world. It is made with a woodblock print technique called ukiyo-e. Hokusai broke away from the traditional ukiyo-e subjects, such as courtesans, actors, used landscapes, and daily-life social situations. This ukiyo-e print shows a Tsunami wave off the coast of Kanagawa, with Mount Fuji in the background. (The nuclear reactor is probably behind the mountain.) Copies of this print are in many Western collections, such as the Met and the Chicago Art Institute.

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