In this paper, we define probabilistic measures for venture portfolio performance based on individual outlier probability for each investment and the dependence across investments. This work is inspired by loan portfolio modeling against default risk used in banking. In mathematical terms, we calculate the probability distribution of the sum of N non-homogeneous Boolean outcomes (investments becoming outliers) that are correlated through common factors such as overall market conditions and sector effects. Specifically, we implemented a latent-factor model in which each investment's success is the exceedance of a Gaussian latent variable composed of idiosyncratic returns and returns from interpretable shared factors (stock markets, industry sector indices, geography and founder type). The formulation follows a simulation approach to preserve heterogeneous deal-level success probabilities and uses empirically estimated correlation matrices. When applied to synthetic portfolios, our model reveals that expected outlier counts alone are insufficient statistics for evaluating venture portfolios. Portfolios with identical expected outcomes can exhibit drastically different levels of reliability and risk when various levels and forms of correlation are embedded. Diversification improves the probability of achieving a minimum number of outliers by reducing exposure to common shocks, but at the cost of lower upside, underscoring a fundamental tradeoff between reliability and magnitude of clustered successes. The framework provides a practical bridge between deal-level outlier probability assessment and objective-aware portfolio construction.

翻译：本文基于每项投资的个体异常概率及投资间的依赖关系，定义了风险投资组合绩效的概率测度。本研究的灵感来源于银行业针对违约风险的贷款组合建模方法。在数学表述上，我们计算了N个非齐次布尔结果（投资成为异常值）之和的概率分布，这些结果通过整体市场状况和行业效应等共同因素产生关联。具体而言，我们实现了一个潜因子模型，其中每项投资的成功被定义为高斯潜变量的超越事件，该潜变量由异质性收益和可解释的共享因子（股票市场、行业板块指数、地域及创始人类型）收益构成。该模型采用模拟方法以保持交易层面成功概率的异质性，并使用经验估计的相关性矩阵。当应用于合成投资组合时，我们的模型表明，仅依靠预期异常值数量不足以作为评估风险投资组合的充分统计量。在嵌入不同形式和程度的相关性时，具有相同预期结果的投资组合可能展现出截然不同的可靠性与风险水平。分散化投资通过降低对共同冲击的暴露程度，提高了达到最低异常值数量的概率，但代价是上行空间受限，这揭示了集群化成功的可靠性与规模之间的根本权衡。该框架为交易层面异常值概率评估与目标导向的投资组合构建提供了实用桥梁。