Active portfolio management has developed substantially since the formulation of the Capital Asset Pricing Model (CAPM). While the original methodology of portfolio optimization has been lauded, it is essentially an academic exercise, with practitioners eschewing the suggested weightings. There are myriad reasons for this: nonstationarity of data, insufficiency of modeling parameters, sensitivity of optimization to small perturbations, and assumption of uniform investor utility all indicate potential failures in the model. We present historical market data to exhibit the pitfalls outlined above. From this analysis, we proceed to examine robust portfolio construction methods. One in particular is provided by Goldfarb and Iyengar. We adapt their methodology to a cross sectional model for returns and examine the performance we achieve.