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

30 Pages Posted: 17 Nov 2020 Last revised: 6 Feb 2022

See all articles by Henry Lahr

Henry Lahr

The Open University - Business School; University of Cambridge - Centre for Business Research (CBR)

Date Written: January 30, 2022

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

Suggested Citation

Lahr, Henry, Fat tails in private equity fund returns: The smooth double Pareto distribution (January 30, 2022). Available at SSRN: https://ssrn.com/abstract=3702903 or http://dx.doi.org/10.2139/ssrn.3702903

Henry Lahr (Contact Author)

The Open University - Business School ( email )

Milton Keynes, MK6 7AA
United Kingdom

University of Cambridge - Centre for Business Research (CBR) ( email )

Top Floor, Judge Business School Building
Trumpington Street
Cambridge, CB2 1AG
United Kingdom

HOME PAGE: http://www.cbr.cam.ac.uk

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