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Stochastic modeling of private equity: an equilibrium based approach to fund valuation

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  • Buchner, Axel
  • Kaserer, Christoph
  • Wagner, Niklas

Abstract

In this paper, we present a new approach to measure the returns of private equity investments based on a stochastic model of the dynamics of a private equity fund. Our stochastic model of a private equity fund consists of two independent stages: the stochastic model of the capital drawdowns and the stochastic model of the capital distributions over a fund's lifetime. Capital distributions are assumed to follow lognormal distributions in our approach. A mean-reverting square-root process is applied to model the rate at which capital is drawn over time. Applying equilibrium intertemporal asset pricing consideration, we are able to derive closed-form solutions for the market value and time-weighted model returns of a private equity fund.

Suggested Citation

  • Buchner, Axel & Kaserer, Christoph & Wagner, Niklas, 2006. "Stochastic modeling of private equity: an equilibrium based approach to fund valuation," CEFS Working Paper Series 2006-02, Technische Universität München (TUM), Center for Entrepreneurial and Financial Studies (CEFS).
    • Handle: RePEc:zbw:cefswp:200602
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    References listed on IDEAS

    as
    1. Christoph Kaserer & Niklas Wagner & Ann-Kristin Achleitner, 2005. "Managing Investment Risks of Institutional Private Equity Investors — The Challenge of Illiquidity," Springer Books, in: Michael Frenkel & Markus Rudolf & Ulrich Hommel (ed.), Risk Management, edition 0, pages 259-277, Springer.
    2. Grossman, Sanford J. & Shiller, Robert J., 1982. "Consumption correlatedness and risk measurement in economies with non-traded assets and heterogeneous information," Journal of Financial Economics, Elsevier, vol. 10(2), pages 195-210, July.
    3. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
    4. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    5. Inderst, Roman & Muller, Holger M., 2004. "The effect of capital market characteristics on the value of start-up firms," Journal of Financial Economics, Elsevier, vol. 72(2), pages 319-356, May.
    6. Diller, Christian & Kaserer, Christoph, 2004. "European private equity funds: A cash flow based performance analysis," CEFS Working Paper Series 2004-01, Technische Universität München (TUM), Center for Entrepreneurial and Financial Studies (CEFS).
    7. Alexander Ljungqvist & Matthew Richardson, 2003. "The cash flow, return and risk characteristics of private equity," NBER Working Papers 9454, National Bureau of Economic Research, Inc.
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    More about this item

    Keywords

    Private Equity Funds; Stochastic Modeling; Mean-Reverting Square-Root Process; Incomplete Markets;
    All these keywords.

    JEL classification:

    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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