A Comparative Study of Bayesian Portfolio Optimization: Evidence from U.S. Large-Cap AI-Related Stocks
Abstract
This paper conducts a comparative analysis of portfolio optimization methods, focusing on Bayesian approaches, applied to U.S. AI-related stocks (2020–2025). While the classical Markowitz model relies on fixed estimates of return and risk, the Bayesian framework incorporates parameter uncertainty through priors on expected returns, soft portfolio concentration constraints, and weights parameterized via Dirichlet or softmax transformations. Posterior inference is conducted using Hamiltonian Monte Carlo with the No-U-Turn Sampler (NUTS), allowing more adaptive and probabilistically informed decision-making. Portfolio performance is evaluated using risk-adjusted returns, measured by the Sharpe ratio, and supplemented with conditional volatility and beta dynamics via the conditional CAPM and DCC-GARCH framework. In the reported experiment, the Markowitz model achieved the highest Sharpe ratio (0.049 in-sample; 0.089 out-of-sample), but this result is limited by the narrow stock universe, daily frequency, zero risk-free rate assumption, and the exclusion of transaction costs. Advanced Bayesian models showed improved risk-adjusted performance relative to early Bayesian specifications, reaching up to 0.038 in-sample and 0.084 out-of-sample Sharpe ratios, while simultaneously reducing conditional volatility and market beta.
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