Persistent Blessings of Luck: Theory and an Application to Venture Capital

Financial economists have long debated whether or not investment managers differ in the skills they have. While studies of individual stocks, mutual funds, and other fund classes generally find that investors do not consistently outperform passive benchmarks after-fee and out-performance is not persistent, an important exception is the private equity (PE) sector, especially concerning venture capital (VC) funds fund (Kaplan and Schoar, 2005). Such a phenomenon manifests itself not only at the fund level, but also at the investment level (Nanda, Samila, and Sorenson, 2019) and the individual partner level (Ewens and Rhodes-Kropf, 2015). It is taken as evidence that VC managers have differential abilities, with the more skilled managers consistently outperforming the others.

We challenge practitioners and academics to re-evaluate this seemingly foregone conclusion. After all, the lack of persistence in returns in the mutual fund industry was initially taken to imply that fund managers do not have skills, and it is only after the turn of the century that studies, notably Berk and Green (2004), point out that capital flows to outperforming funds and reduce their future returns. Managers may very well have skills that reflect in more skilled ones managing larger funds. The PE industry not only entail endogenous capital flows from LPs to GPs, but also feature endogenous matching between funds and entrepreneurs. We argue that performance persistence and entrepreneur funding choices do not necessarily imply heterogeneity in managerial skills. Pure luck can lead to persistent outperformance of some funds.

To illustrate, consider a simple multiple-period economy in which an endowment fund invests in two VC funds, A and B. Each VC screens projects, chooses the way he nurtures project, and decides on unobservable effort to increase the probability of success. There are two different types of projects, innovative and conventional. Innovative projects are of high quality and generate higher expected probability but are of limited supply. A and B are similar in skill and initially are assigned the same contract that incentivizes their effort by promising better contracts in future. If A is lucky in the current fund and successfully nurtures a project, A then finds it easier to raise the next fund with better contract terms. With a past success record, investors are less sensitive to fund short-term performance. A is consequently more tolerant towards initial failure and experimentation. Different from other asset classes, in PE industry the deal is endogenous, and the innovative nature of startups makes his fund more attractive to entrepreneurs with high-quality innovative projects. This is to say, even with identical skill, funds with good past performance would have a better access of deal flows, and thus deliver a higher performance in the future. This positive reinforcement can lead to persistence in differential performance, both before- and after-fee, across managers even when they do not differ in skills. Figure 1 summarizes the example.

Two-Fund example
Figure 1. Two-fund Example

To drive the point home, we present a dynamic model of venture investment with endogenous fund heterogeneity and deal flow that produces performance persistence without innate skill difference. Investors work with multiple funds and use tiered contracts to manage moral hazard dynamically. Recent successful funds receive continuation contracts that encourage greater innovation, and subsequently finance innovative entrepreneurs through assortative matching. Initial luck thus exerts an enduring impact on performance by altering managers' future investment opportunities.

Our model generates implications broadly consistent with empirical findings, such as short-term performance persistence, outperforming funds' appeal to innovative entrepreneurs even with worse terms, and the link between failure-tolerance and innovation. For example, our model predicts intermediate-term performance persistence but long-term mean-reversion that extant theories cannot produce but are observed empirically in Nanda, Samila, and Sorenson, (2019). The authors there provide evidence that the deal flow and the “access channel” (a form of endogenous manager heterogeneity captured in our model) explain the majority of persistence. Our model offers many testable predictions, and further empirical studies to carefully distinguish between luck and innate skills are called for.

Note that the endogenous deal flow channel we studied and the innate skill channel are not mutually exclusive. In fact, endogenous deal flow augments skill differences in managers, and thus contributes to performance persistence. Our model starts with fund managers without differential skills to underscore the point that sheer transient luck can induce the apparent fund heterogeneity, in contrast to innate-skill-based explanations. While alternative channels, such as managerial scale or the ability to commit personal capital after recent successes, can also predict gross-performance persistence, they do not explain net-of-fee performance persistence. 

Our study is not intended to be merely a theoretical exercise, but it has several practical implications for investors, venture capitalists, and entrepreneurs. First, limited partners investing in multiple VC firms should take advantage of the inter-contract incentives in managing agency rent and motivating effort from managers; investors without the power to offer contract hierarchy should still invest in funds based on past performance. Second, fund managers need to go beyond presenting a simple track record of past returns to demonstrate superior skill and value to investors and entrepreneurs. This is consistent with limited partners' recent focus on more detailed information about funds such as their internal organization, culture, deal sourcing, etc. (Korteweg and Sorensen, 2017). Third, entrepreneurs choosing which VC to work with should focus not only on the funds' status and past success, but also on the exact advantages of the funds or characteristics past successes endogenously generate.

Finally, the economic insights uncovered in the paper should apply more broadly to situations in which a lucky outcome gives a manager an advantage that is self-reinforcing and perpetuating. For example, an initial IPO success makes the entrepreneur more likely to become a future relationship investor and provide network support for the VC's future funds. In essence, our theory formalizes and extends the notion of the “Matthew effect,” originally introduced in the book of Matthew 25:29 to describe “the rich get richer and the poor get poorer.” Here, whoever becomes rich initially at random enjoys the persistent blessings of luck.

Berk, J.B. and Green, R.C., 2004. Mutual fund flows and performance in rational markets. Journal of political economy112(6), pp.1269-1295.
Kaplan, S.N. and Schoar, A., 2005. Private equity performance: Returns, persistence, and capital flows. The journal of finance60(4), pp.1791-1823.
Korteweg, A. and Sorensen, M., 2017. Skill and luck in private equity performance. Journal of Financial Economics124(3), pp.535-562.
Nanda, R., Samila, S. and Sorenson, O., Forthcoming. The persistent effect of initial success: Evidence from venture capital .The Journal of Financial Economics.

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