🤖 AI Summary
This study addresses the neglect of parameter uncertainty in traditional parametric portfolio strategies, which leads to overestimated expected utility and underestimated risk. It introduces a Bayesian approach into the parametric framework by placing prior distributions on strategy coefficients, thereby constructing a Bayesian mean-variance optimization model that explicitly accounts for estimation risk. The decision rule is further refined to incorporate posterior uncertainty. Theoretical analysis reveals that utility loss is positively related to both posterior uncertainty and signal strength. Empirical results based on 242 signals and six factors from 1973 to 2023 demonstrate that the proposed method significantly improves the Sharpe ratio, reduces portfolio turnover and tail risk, and yields monotonically increasing investor welfare with risk aversion, exhibiting particularly robust performance during financial crises.
📝 Abstract
Parametric Portfolio Policies (PPP) estimate optimal portfolio weights directly as functions of observable signals by maximizing expected utility, bypassing the need to model asset returns and covariances. However, PPP ignores policy risk. We show that this is consequential, leading to an overstatement of expected utility and an understatement of portfolio risk. We develop Bayesian Parametric Portfolio Policies (BPPP), which place a prior on policy coefficients thereby correcting the decision rule. We derive a general result showing that the utility gap between PPP and BPPP is strictly positive and proportional to posterior parameter uncertainty and signal magnitude. Under a mean--variance approximation, this correction appears as an additional estimation-risk term in portfolio variance, implying that PPP overexposes when signals are strongest and when risk aversion is high. Empirically, in a high-dimensional setting with 242 signals and six factors over 1973--2023, BPPP delivers higher Sharpe ratios, substantially lower turnover, larger investor welfare, and lower tail risk, with advantages that increase monotonically in risk aversion and are strongest during crisis episodes.