We utilize ridge regression to create a novel set of characteristics-based "ridge factors". We propose Bayesian Average Stochastic Discount Factors (SDFs) based on these ridge factors, addressing model uncertainty in line with asset pricing theory. This approach shrinks the relative contribution of low-variance principal portfolios, avoiding model selection and presumption of a "true model". Our results demonstrate that ridge factor principal portfolios can achieve greater sparsity while maintaining prediction accuracy. Additionally, our Bayesian average SDF produces a higher Sharpe ratio for the tangency portfolio compared to other models.

Efficient portfolio is a portfolio that yields maximum expected return given a level of risk or has minimum level of risk given a level of expected return.However,the optimal portfolios seem not being as efficient as intended.Especially during financial crisis period.optimal portfolio is not an optimal investment as it does not yield maximum return given a specific level of risk,vice and versa.One possible explanion for an unimpressive performance of the seemingly efficient portfolio is incorrectness in parameter estimates called"estimation risk in parameter estimates".Five different estimating strategies are employed to explore ex post portfolio performance when estimation risk is incorporated.These strategies are traditional mean-variance(EV),Adjusted Beta(AB) approach,Capital Asset Pricing Model(CAPM),Single Index Model(SIM), and Single Index Model incorporating shrikage Bayesian factor namely Bayesian Single Index Model(BSIM).Among the five alternative strategies,shrinkage estimators incorporating the single index model outperforms other traditional portfolio selection strategies.Allowing for asset mispricing and applying Bayesian shrinkage adjusted factor to each asset's alpha,a single factor namely excess market return is adequate in alleviating estimation uncertainty. JEL：G320