The Smooth Double Pareto Distribution: A Model of Private Equity Fund Returns

Abstract

Whether returns of venture capital and private equity investments exhibit fat tails, particularly in the upper tail, affects how entrepreneurs and investors view the attractiveness of such investments. Using fund performance data, we propose and test a random growth model with a random initial valuation of funds to explain the observed distribution of funds’ residual-value and payout multiples. This model endogenously generates power-law tails in the cross-section from a log-normally distributed diffusion process and log-normally distributed birth valuation. We find that the resulting smooth double Pareto distribution fits the data better than competing log-normal or double Pareto models and generally performs well, apart from a small region around a valuation multiple of one. The divergence of the fitted distribution from the empirical one can be explained by an excess number of funds without distributions to investors – funds that may not have made or revalued any investments yet.

Keywords: Size Distribution, Income Distribution, Pareto Law, Power-Law Distribution, Fat Tails, Private Equity, Venture Capital, Financial Returns

JEL Classification: C46, D31, G24, G32, L11, R12