Abstract
The problem of portfolio optimization has been widely studied in the past decades. The standard framework of Modern Portfolio Theory provides a theoretically optimal solution in the ideal situation in which the investor only cares about the mean and the variance and knows the true value of the input parameters. However, the sensitivity of this mathematical technique to estimation errors in the parameters leads to disappointing results when applied out-of-sample. Moreover, the non-normality of financial returns casts doubts on the adequacy of the mean-variance utility approach itself. Therefore, an increasing body of literature focuses on the two issues of parameter uncertainty and downside risk preferences. Despite the efforts by many scholars, both issues remain open as of today. This thesis consists of an introductory chapter that delineates the problem and briefly summarizes the existing literature, and of three separate papers that provide novel insights and solutions. The first paper presents a strategy to limit extreme positions due to estimation errors when the investor can take advantage of return predictability. The second paper shows that the popularity of the mean-variance approach is rationally justified in light of the greater parameter uncertainty that afflicts downside risk measures. The last paper proposes an approach to reduce the impact of estimation errors in the semicovariance matrix when performing mean-semivariance or minimum semivariance optimization. In addition to introducing new optimization strategies, these three papers highlight the relationship between the two issues analyzed, and also provide various methodological contributions.