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.
We consider the problem of evaluating the quality of startup companies. This can be quite challenging due to the rarity of successful startup companies and the complexity of factors which impact such success. In this work we collect data on tens of thousands of startup companies, their performance, the backgrounds of their founders, and their investors. We develop a novel model for the success of a startup company based on the first passage time of a Brownian motion. The drift and diffusion of the Brownian motion associated with a startup company are a function of features based its sector, founders, and initial investors. All features are calculated using our massive dataset. Using a Bayesian approach, we are able to obtain quantitative insights about the features of successful startup companies from our model. To test the performance of our model, we use it to build a portfolio of companies where the goal is to maximize the probability of having at least one company achieve an exit (IPO or acquisition) , which we refer to as winning. This picking winners framework is very general and can be used to model many problems with low probability, high reward outcomes, such as pharmaceutical companies choosing drugs to develop or studios selecting movies to produce . We frame the construction of a picking winners portfolio as a combinatorial optimization problem and show that a greedy solution has strong performance guarantees . We apply the picking winners framework to the problem of choosing a portfolio of startup companies. Using our model for the exit probabilities, 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.
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