A new estimator for calculating the optimal expected return of a self-financing portfolio is proposed, by considering the joint impact of the sample mean vector and the sample covariance matrix. A shrinkage covariance matrix is designed to substitute the sample covariance matrix in the optimization procedure, which leads to an estimate of the optimal expected return smaller than the plug-in estimate. The new estimator is also applicable for both p < n and p ≥ n. Simulation studies are conducted for two empirical data sets. The simulation results show that the new estimator is superior to the previous methods. / By the seminal work of Markowitz in 1952, modern portfolio theory studies how to maximize the portfolio expected return for a given risk, or minimize the risk for a given expected return. Since these two issues are equivalent, this thesis only focuses on the study of the optimal expected return of a self-financing portfolio for a given risk. / Finally, under certain assumptions, we extend our research in the framework of random matrix theory. / The mean-variance portfolio optimization procedure requires two crucial inputs: the theoretical mean vector and the theoretical covariance matrix of the portfolio in one period. Since the traditional plug-in method using the sample mean vector and the sample covariance matrix of the historical data incurs substantial estimation errors, this thesis explores how the sample mean vector and the sample covariance matrix behave in the optimization procedure based on the idea of conditional expectation and finds that the effect of the sample mean vector is an additive process while the effect of the sample covariance matrix is a multiplicative process. / Liu, Yan. / Adviser: Ngai Hang Chan. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 76-80). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.