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Most studies view transaction costs and constraints separate in the mean-variance framework. As such, I evaluate the benefits of holding and turnover constraints in the presence of transaction costs on Swedish Asset Returns. In theory, the benefits should be limited when transaction costs are included in the portfolio rebalancing problem. By using the model developed by Mitchell and Braun (2003), my results indicate that there are benefits of holding constraints in the mean-variance optimization. The main issue with the long-only portfolio is its lack of diversification. The strategy allocates the majority of the investment in 15 out of 100 assets. By imposing holding constraints, the portfolio becomes more diversified while reducing turnover volume and increasing Sharpe ratio. I find that the homogenous 1/N holding constraint increases monthly Sharpe ratio performance by 50 percent over the entire sample. However, the results are not consistent over all samples and not statistically significant. Further, turnover constraints only marginally increase performance, which more likely originates from the increase in diversification.

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.