Estimating Public Market Exposure of Private Capital Funds Using Bayesian Inference

The market exposure (beta) of private capital to the public market is important for a variety of reasons, including asset allocation and risk estimation. However, estimating beta is challenging. The root cause of this difficulty is the illiquid and private nature of the asset class. This, in turn, leads to data issues, namely limited access to high-quality, granular data. It also leads to statistical problems caused by valuations that are smoothed (leading to returns that are autocorrelated) and valuations that are imprecise (leading to noisy per-fund returns).

This paper uses a high-quality dataset of per-fund cash flows and valuations (the Burgiss Manager Universe) to fit Bayesian hierarchical models to per-fund returns. These provide precise estimates of per-fund betas for buyout and venture capital funds. In addition, given the size of our dataset, the authors are able to estimate how beta changes with the age of a fund, thereby resolving some puzzles regarding previous estimates of beta based on pooled data.