Bayesian unsmoothing for private market investments: a probabilistic approach to risk estimation

Martin Jehli

Abstract

Investors in alternative asset classes rely on performance metrics that are distorted by return smoothing biases, leading to misrepresentation of risk and suboptimal portfolio allocations. Despite the availability of unsmoothing techniques, existing methods may not fully capture the underlying risk dynamics, particularly in private markets. We introduce a Bayesian unsmoothing approach that models smoothing parameters probabilistically and mitigates some limitations of traditional methods. Using Monte Carlo simulations and real-world private market indexes, we compare frequentist and Bayesian implementations of common unsmoothing algorithms. Our findings demonstrate that probabilistic models can reduce volatility bias and provide a more accurate assessment of tail risk, particularly for simpler algorithms such as the Fisher–Geltner–Webb procedure. As a direct result, probabilistically modeling the smoothing parameter can result in more conservative ex ante risk estimates and asset allocations. Our approach, therefore, offers a practical method for enhancing transparent risk measurement and strengthening robust risk modeling for illiquid asset classes.