A Model for the Dynamics of Private Equity Funds

Abstract

A private equity fund is a particular investment vehicle whose dynamics depend on three primary elements: the capital committed by the investors and drawn down into investments by the fund manager; the performance of the investments; and the dividends and proceeds distributed to the investors. Each of the three elements, which correspond to the three essential phases of the private equity fund lifecycle, are modelled by a separate diffusion process. As an illiquid investment, a private equity fund also requires a specific treatment for its reported net asset value that does not necessarily represent a market value but merely represents an accounting value. Thus a fourth random variable representing the initial net asset value of the fund is introduced. This random variable deals with the uncertainties and errors in the net asset values that are reported by the fund manager. Overall, conditional on the drawdowns, distributions and initial net asset value, the model reduces to an inverse gamma process.

Keywords: Private equity fund, lognormal process, Cox-Ingersoll-Ross (CIR) process, inverse gamma process

JEL Classification: G12, G13, G24