<p>In this thesis, portfolio optimisation is used to evaluate if a specific sample of portfolios have</p><p>a higher risk level or lower expected return, compared to what may be obtained through</p><p>optimisation. It also compares the return of optimised portfolios with the return of the original</p><p>portfolios. The risk analysis software Aegis Portfolio Manager developed by Barra is used for</p><p>the optimisations. With the expected return and risk level used in this thesis, all portfolios can</p><p>obtain a higher expected return and a lower risk. Over a six-month period, the optimised</p><p>portfolios do not consistently outperform the original portfolios and therefore it seems as</p><p>though the optimisation do not improve the return of the portfolios. This might be due to the</p><p>uncertainty of the expected returns used in this thesis.</p>

In this thesis, portfolio optimisation is used to evaluate if a specific sample of portfolios have a higher risk level or lower expected return, compared to what may be obtained through optimisation. It also compares the return of optimised portfolios with the return of the original portfolios. The risk analysis software Aegis Portfolio Manager developed by Barra is used for the optimisations. With the expected return and risk level used in this thesis, all portfolios can obtain a higher expected return and a lower risk. Over a six-month period, the optimised portfolios do not consistently outperform the original portfolios and therefore it seems as though the optimisation do not improve the return of the portfolios. This might be due to the uncertainty of the expected returns used in this thesis.

>Magister Scientiae - MSc / In this thesis, we discuss methods for optimising the expected rate of return of a portfolio with minimal risk. As part of the work we look at the Modern Portfolio Theory which tries to maximise the portfolio's expected rate of return for a cer- tain amount of risk. We also use Quadratic Programming to optimise portfolios. Generally it is recognised that portfolios with a high expected return, carry higher risk. The Modern Portfolio Theory assists when choosing portfolios with the lowest possible risk. There is a nite number of assets in a portfolio and we therefore want to allocate them in such a way that we're able to optimise the expected rate of return with minimal risk. We also use the Markowian approach to allocate these assets. The Capital Asset Pricing Model is also used, which will help us to reduce our e cient portfolio to a single portfolio. Furthermore we use the Black-Litterman model to try and optimise our portfolio with a view to understanding the current market conditions, as well as considering how the market will perform in the future. An additional tool we'll use is Value at Risk. This enables us to manage the market risk. To this end, we follow the three basic approaches from Jorion [Value at Risk. USA: McGraw-Hills, 2001]. The Value at Risk tool has become essential in calcu- lating a portfolio's risk over the last decade. It works by monitoring algorithms in order to nd the worst possible scenarios within the portfolio. We perform several numerical experiments in MATLAB and Microsoft Excel and these are presented in the thesis with the relevant descriptions.