Portfolio optimisation

Abstract

Every investor knows that there is a tradeoff between risk and reward: to obtain greater expected returns on investments, one must be willing to take on greater risk. In solving the Portfolio Selection problem, we aim to use quantitative measures of risk and reward to obtain a balance between these two factors that suits the individual investor. No one combination of securities is optimal for all investors. The best portfolio for any one investor depends on his or her own tolerance for risk. Each investment instrument has its own expected return, and its own propensity for these returns to fluctuate from time to time. However, the returns from different instruments are not in general independent. These joint tendencies are quantified by the covariance. In this thesis, we had use three mathematical programming: linear, quadratic and stochastic programming to formulate the portfolio selection problem. For the three cited programs the necessarily theoretical overview is given. Then some general conclusion and drawbacks for the models built are discussed. The quadratic programming investment models or as it is better known the mean and variance problem is extensively discussed, particularly the sensitivity of the problem to changes in the mean of individual assets. The implementation part consists of solving most of the mentioned models throughout the text and see whether the analytic results are confirmed by the computational results.