Stochastic Modelling of Cash Flows in Private Equity
Abstract: An investment in a private equity is any investment made in a financial asset that is not publicly traded. As such these assets are very difficult to value and also give rise to great difficulty when it comes to quantifying risk. In a typical private equity investment the investor commits a prespecified amount of capital to a fund, this capital will be called upon as needed by the fund and eventually capital will be returned to the investor by the fund as it starts to turn a profit. In this way a private equity investment can be boiled down to consist of two cash flows, the contributions to the fund and distributions from the fund to the investor. These cash flows are usually made within a prespecified time frame but at unspecified intervals and amounts. As an investor in a fund, carrying too little liquid assets when contributions are called upon will cause trouble, but carrying significantly more than needed is also not desirable as it represents a loss in potential revenue from having less capital in more profitable investments. The goal of this thesis was to attempt to find a way to reliably model these cash flows and to find a way to represent the results in a meaningful way for the benefit of the investor by constructing value at risk like risk measures for the necessary liquid capital to carry at a given time in case contributions are called upon. It was found that the distributions could be modelled very well with the chosen stochastic processes, both as it related to predicting the average path of the cash flows and as it relates to modelling the variability of them. Contrary to this it was found that the contributions could not be modelled very well. The reason for this was found to be an observed lag in the speed of contributions at the start of the funds lifetime, this lag was not taken into account when constructing the stochastic model and hence it produced simulated cash flows not in line with those used in the calibration.
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