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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. --

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Bibliographic Info

Paper provided by Center for Entrepreneurial and Financial Studies (CEFS), Technische Universität München in its series CEFS Working Paper Series with number 2006-02.

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Date of creation: 2006
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Handle: RePEc:zbw:cefswp:200602

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Related research

Keywords: Private Equity Funds; Stochastic Modeling; Mean-Reverting Square-Root Process; Incomplete Markets;

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  1. 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.
  2. Kaserer, Christoph & Wagner, Niklas & Achleitner, Ann-Kristin, 2003. "Managing investment risks of institutional private equity investors: The challenge of illiquidity," CEFS Working Paper Series 2003-01, Center for Entrepreneurial and Financial Studies (CEFS), Technische Universität München.
  3. 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.
  4. 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.
  5. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  6. Diller, Christian & Kaserer, Christoph, 2004. "European private equity funds: A cash flow based performance analysis," CEFS Working Paper Series 2004-01, Center for Entrepreneurial and Financial Studies (CEFS), Technische Universität München.
  7. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
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