Picking Winners: A Framework For Venture Capital Investment

We consider the problem of selecting a portfolio of items of fixed cardinality where the goal is to have at least one item achieve a high return, which we refer to as winning. This framework is very general and can be used to model a variety of problems, such as pharmaceutical companies choosing drugs to develop, studios selecting movies to produce, or our focus in this work, which is venture capital firms picking startup companies in which to invest. We first frame the construction of a portfolio as a combinatorial optimization problem with objective function given by the probability of having at least one item in the selected portfolio win. We show that a greedy solution to this problem has strong performance guarantees, even under arbitrary correlations between the items. We apply the picking winners framework to the problem of choosing a portfolio of startups to invest in. This is a relevant problem due to recent policy changes in the United States which have greatly expanded the market for startup investment. We develop a novel model for the success of a startup company based on Brownian motion first passage times. We fit this model to a large amount of data on startup company founders, investors, and performance. Our model provides some qualitative insights to the features of successful startup companies. Using our model we are able to construct out of sample portfolios which achieve exit rates as high as 60%, which is nearly double that of top venture capital firms.