Quadratic hedging strategies for private equity fund payment streams

Abstract

To better understand the relation between public markets and private equity, we consider quadratic hedging strategies to replicate the typical payment stream pattern associated with private equity funds by traded factors. Our methodology is inspired by the risk-minimization framework developed in financial mathematics and applies the componentwise L₂ Boosting machine learning technique to empirically identify feasible replication strategies. The application to US venture capital fund data further draws on a stability selection procedure to enhance model sparsity. Interestingly a natural connection to the famous Kaplan and Schoar (2005) public market equivalent approach can be established.