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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 En investering i private equity r en investering i en tillg ng som inte r b rsnoterade P grund av detta r s dana tillg ngar v ldigt sv ra att v rdera och medf r ven store sv righeter n r det kommer till att kvantifiera risk I en typisk private equity investering so ing r en investerare i ett l fte att under en viss f rbest md tidsperiod bidra med en fixt m ngd kapital till en private equity fond Detta kapital kommer att gradvis kallas p av fonden vid behov f r att sedan mot slutet av fondens livstid ge utdelning n r private equity fonden b rjar g ra en vinst P detta viset kan en private equity investering brytas ner i tv kassafl den kontributioner in i fonden och distributioner ut ur fonden Dessa kassafl den sker under en f rbest md tidsperiod men ej f rbest mda belopp Som en investerare i denna typen av fond r d rf r en risk att b ra f r lite likvid kapital n r kontributioner blir kallade p men ven oattraktivt att b re p f r mycket de detta representerar f rlorar potentiell avkastning M let i denna uppsatts r att hitta ett s tt att p att tillf rlitligt vis modellera dessa kassafl den och representera resultaten p ett meningsfullt s tt fr n perspektivet av en investerare F r att uppn detta skapades value-at-risk liknande m tt f r m ngden likvid kapital som kr vs under en tidsperiod f r att s kra sig mot p kallade kontributioner Slutsatsen blev att distributioner kunde modelleras v l b de n r det kom till att efterlikna den genomsnittliga v gen av kassafl den och ven f r att modellera risken I kontrast till detta s kunde inte kontributioner modelleras mot tillr ckligt h g s kerhet f r att anv ndes i det mnade syftena Anledningen till detta var en eftersl pning i hastigheten som kontributioner kallades med som inte t gs i beaktande av den till mpade matematiska modellen

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Stochastic Modelling of Cash Flows in Private Equity / Stokastisk modellering av kassaflöden i private equity

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