Investments in private equity have become an increasingly significant portion of institutional portfolios as investors seek diversification benefits relative to traditional stock and bond investments. Despite the increasing importance of the private equity asset class, we have only a limited understanding of the economics of private equity funds-the typical vehicle through which private equity investments are made. Particularly, three questions are mostly unresolved in the current private equity literature: (i) What is the value of a private equity fund and how does it develop overtime? (ii) How does a fund's expected return and systematic risk changeover time? (iii) How does illiquidity affect fund values and expected returns?
These questions are difficult to evaluate without models that explicitly tie these variables of interest to the cash flow dynamics of private equity funds. In this paper we provide such a model and use it to develop answers to the above-mentioned questions. Private equity funds differ from other managed funds because of their particular bounded life cycle. When the fund starts, the investors make an initial capital commitment. The fund manager then gradually draws down the committed capital into investments.
Finally, returns and proceeds are distributed as the investments are realized and the fund is eventually liquidated as the final investment horizon is reached. Modeling private equity funds therefore requires two stages: modeling capital drawdowns and modeling capital repayments (or capital distributions) of the funds. This paper develops anew continuous-time approach modeling these two components.
Specifically, a mean-reverting square-root process is applied to model the rate at which capital is drawn overtime. Capital distributions are assumed to follow an arithmetic Brownian Motion with a time-dependent drift component that incorporates the typical time-pattern of the repayments of private equity funds.
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Private Equity Funds: Valuation, Systematic Risk and Illiquidity
