This master thesis considers and evaluates a few different risk models for stock portfolios, including an ordinary sample covariance matrix, factor models and an approach inspired from random matrix theory. The risk models are evaluated by simulating minimum variance portfolios and employing a cross-validation. The Bloomberg+ transaction cost model is investigated and used to optimize portfolios of stocks, with respect to a trade off between the active risk of the portfolio and transaction costs. Further a few different simulations are performed while using the optimizer to rebalance long-only portfolios. The optimization problem is solved using an active-set algorithm. A couple of approaches are shown that may be used to visually try to decide a value for the risk aversion parameter λ in the objective function of the optimization problem. The thesis concludes that there is a practical difference between the different risk models that are evaluated. The ordinary sample covariance matrix is shown to not perform as well as the other models. It also shows that more frequent rebalancing is preferable to less frequent. Further the thesis goes on to show a peculiar behavior of the optimization problem, which is that the optimizer does not rebalance all the way to 0 in simulations, even if enough time is provided, unless it is explicitly required by the constraints.