The Rational Investor is a Bayesian

Sammanfattning: The concept of portfolio optimization has been widely studied in the academy and implemented in the financial markets since its introduction by Markowitz 70 years ago. The problem of the mean-variance optimization framework caused by input uncertainty has been one of the foci in the previous research. In this study, several models (linear shrinkage and Black-Litterman) based on Bayesian approaches are studied to improve the estimation of inputs. Moreover, a new framework based on robust optimization is presented to mitigate the input uncertainty further.  An out-of-sample test is specially designed, and the results show that Bayesian models in this study can improve the optimization results in terms of higher Sharpe ratios (the quotient between portfolio returns and their risks). Both covariance matrix estimators based on the linear shrinkage method contain less error and provide better optimization results, i.e. higher Sharpe ratios. The Black-Litterman model with a proper choice of inputs can significantly improve the portfolio return. The new framework based on the combination of shrinkage estimators, Black-Litterman, and robust optimization presents a better way for portfolio optimization than the classical framework of mean-variance optimization.