Commitment Pacing: Targeting a Fixed Valuation
If you were to take over the management of a private capital portfolio at a large pension fund and were tasked with maintaining a valuation of about $1B, how would you approach it? At what rate should you commit capital to best achieve this goal? It turns out that this question can be formulated in a number of different ways, each leading to an algorithm that dictates the pace at which commitments should be made:
Constant Commitment –Assumes the investment manager would make commitments of a constant size every quarter.
Expectation Pacing –Combines the expected valuation curve of funds in such a way as to achieve the target, using an algorithm that tries to make the expected valuation of the portfolio equal to the target valuation.
Stochastic Pacing – Takes into account the uncertainty in future valuations, and employs an algorithm that minimizes the expected deviation from the target valuation.
Dynamic Pacing – This is a dynamic approach which, when making the current decision, takes into account that all future decisions will be made optimally; it minimizes the expected deviation from the target valuation, further assuming that after the current commitment all future ones are made in the same optimal way.
In this paper we define each of these formulations rigorously, construct optimal algorithms, and quantify their performance.
Expected Valuations and Standard Deviations of Buyout Funds as Function of Fund Age
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