Expected returns, variances, and co-variances are key inputs of mean-variance portfolio selection problems. In traditional mean-variance portfolio models, the model uncertainty is excluded a priori. But in practice, these parameters are not known a priori and are usually estimated with error. Current researches incorporate the model uncertainty into the mean-variance framework but mainly focus on the uncertain means. The aim of this dissertation is to incorporate uncertain variance-covariance into mean-variance portfolio model via the concept of ambiguity and ambiguity aversion. The approaches developed in this study numerically compare the impact from return ambiguity and variance ambiguity. In particular, re-examine if uncertain variance-covariance can lead to “No-Participation in Stock Market” and/or “Home Bias” via stock indexes data.