An empirical study on effect of estimation risk on portfolio risk.

Abstract

This study explores effect of estimation risk on an admissible efficient set and an optimal portfolio based on a Bayesian framework assuming diffuse prior and informative conjugate prior distribution functions. Based on the U.S. sectorial index, the result indicated that, when estimation risk is taken into account, the admissible efficient set is not changed. Therefore, three conclusions can be drawn. First, true portfolio returns can be represented by weighted average sample returns given that samples are drawn from high frequency data with a long average period. However, historical sample average is not an efficient estimator for true parameters. Second, portfolio risk or variance, when estimation risk is built into a decision, is affected by a scale factor. Therefore, a Bayesian admissible efficient set will always lies to the right of the traditional admissible efficient set due to higher risk from estimation. Third, portfolio decisions based on a traditional approach, ignoring estimation risk, would lead to a suboptimal portfolio due to utility loss caused by underestimation of risk. Empirical results show that annualized Bayesian portfolio risk is larger than that of a traditional portfolio by approximately 40 to 80 basis points for a weekly index return interval and approximately 100 to 220 basis points for a monthly index return interval. Moreover, the annualized average excess portfolio return from Bayes-Stein shrinkage portfolio is higher than those of traditional, passive, and naïve portfolio by 36, 384, and 144 basis points, respectively.