Commitment Planning for Drawdown Vehicles in a Stochastic Setting

We address the problem of how to best manage a limited partner’s capital commitments to various vintages of private equity funds in order to achieve a desired target level of exposure. We adopt and extend the Yale modeling framework by accounting for dynamical noise on the fund returns with both systematic and idiosyncratic components assumed independent across vintages. Adequate models for the fund returns, including volatility, and for a general partner’s procedure for capital calls and distributions are assumed to be known. The management problem is quantitatively expressed as choosing a capital commitment strategy that minimizes the mean-squared difference between the actual and target exposure, averaged both over the noise and a specified horizon of time. We computationally address this problem in three ways: choosing the entire capital commitment strategy non-adaptively at the start, optimizing a heuristic control strategy, and employing stochastic dynamical programming.