Modeling the Cash Flow Dynamics of Private Equity Funds: Theory and Empirical Evidence

Abstract

This article presents a novel continuous-time approach to modeling the typical cash flow dynamics of private equity funds. The model consists of two independent components. First is a mean-reverting square-root process applied to model the rate at which capital is drawn over time. Second is the stream of capital distributions, which is assumed to follow an arithmetic Brownian motion with a time-dependent drift component that incorporates the typical time-pattern of the repayments of private equity funds. The empirical analysis shows that the model can easily be calibrated to real-world fund data by the method of conditional least squares and nicely fits historical data. The authors use a data set of mature European private equity funds provided by Thomson Venture Economics. Their model explains up to 99.6% of the variation in average cumulated net fund cash flows and provides a good approximation of the empirical distribution of private equity fund cash flows over a typical fund’s lifetime. Overall, the empirical results indicate that the model is of economic relevance in an effort to accurately model the cash flow dynamics of private equity funds.