An ideal portfolio is a utopia and most investors are content with rewards that protect the initial investment with a high probability. Portfolio managers are faced with the problem of selecting the stocks and finding their corresponding weights, so that they make the investors' investment grow in an efficient manner. Henry Markowitz provided a standard approach to solving the stock allocation problem, which is now commonly referred to as

\emph{Mean-Variance Optimization}. While being a very popular methodology, several authors have shown that the \emph{Mean-Variance} framework has poor \emph{out-of-sample} performance. In particular, DeMiguel et al. (2009a) showed that equally weighted portfolios, on average, outperform optimized portfolios. After that study, DeMiguel et al. (2009b) proposed a new framework for \emph{minimum-variance} portfolios that improves the out-of-sample performance of the portfolios by putting constraint on the stocks weights. In this project, we study three portfolio allocation topics: how to conduct portfolio allocation when there is a natural grouping structure among the stocks, when there is a possibility of grouping across the stocks, and how to conduct portfolio allocation when the stocks have different length of return histories. We propose a general framework that exploits similarity between the stocks and improves out-of-sample performance of portfolios in terms of Sharpe and Sortino ratios. We also propose a modified framework for the imputation of stock returns.