Security Selection Diversity Issues

In the early 50's Markowitz advanced portfolio theory. From that time on, finance stepped into the stage of quantificational analysis, which can be regarded as the beginning of financial mathematics. Then it has been greatly developed by the work done by Sharp, Miller, Merton, Scholes and Black et al in the field of financial mathematics. Now financial mathematics has been an extensive application subject that has abundant contents, profound theories. A large quantity of theoreticians and practioners are now making theory innovations and practice testing in the field of financial mathematics. It is very important to develop and perfect financial mathematics.A further study on the portfolio selection and efficient subset for portfolio selection, that is the problems that securities should be selected in the given securities set and the investment proportion of every securities, is made in this thesis. These are two problems that are connected with each other.The innovations of this thesis embody the following two aspects.For the problem of portfolio selection, a new multi-factor model for portfolio investment decision is established and the properties and solving method are also studied. This model is based on the multi-factor model given by Ma Yongkai and Tang Xiaowo who simplify Markowitz's model for portfolio investment with the help of Ross' arbitrage pricing theory. Compared with the Markowitz's mean-variance model, the new model has the following merits: 1. The operation times in calculating the optimal portfolio is fewer. 2. The investment controllability is strong. The model can control not only the expectation return rate, but also the value of factor risk. Compared with Ma Yongkai and Tang Xiaowo's multi-factor model for portfolio investment decision, the merits of the new model are that not only the value of factor risk but also the expectation return rate is taken intoconsideration. And the properties and results of the model are more extensive,comprehensive and profound.For the problem of efficient subset for portfolio selection, firstly, a searching method, one-by-one-judging method, for efficient subset for portfolio selection is established and applied to a real example. Secondly, efficient subset for multi-factor portfolio selection is studied. These two problems, which have not been studied by now, have a close relationship with efficient subset for portfolio selection provided by Shi Shuzhong and Yang lie. The first problem studies that how to decide the securities which should to be invested in from the given securities set by calculating the historical price-data and filtering one by one the calculating results. The study to the second problem shows that efficient subset for multi-factor portfolio selection can abbreviate operation times in solving efficient subset for portfolio selection, and a theoretic explanation on the result that only minority securities is selected in securities investment is given out.