Fat tails in private equity fund returns: The smooth double Pareto distribution

Abstract

Whether fat tails exist in the distribution of venture capital and private equity returns affects how investors view the attractiveness of such investments, especially if means or variances are potentially infinite. Using fund performance data, I propose and test a smooth double Pareto distribution to explain the observed stationary distribution of funds’ valuation multiples. This distribution emerges from a random growth model with a lognormally distributed diffusion process and lognormally distributed initial valuation of funds. This model endogenously generates power-law tails in the cross-section. The resulting smooth double Pareto distribution fits the data better than competing lognormal or ordinary double Pareto models. Fat tails are particularly pronounced in seed-stage, early-stage and generalist venture capital funds and suggest returns with infinite variance if investments are held for the lifetime of the fund. The smooth double Pareto distribution has wide applicability to growth processes with a random initial value or size.

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