Study On Decision Making Models For Portfolio Selection

The main wish of investor is to obtain maximum profits for themselves. Since invest return is tightly associated with the risk, the common sense principle is that the investors should diversify his portfolio, i.e. he should invest his funds in a spread of low and high risk securities in such a way that the total expected return for all his investments is maximized and at the same time the investment risk is minimized. Portfolio theory has been an important part of modern finance theory. It's central problem is how to allocate and utilize capital assets under risk.The work of Markowitz in portfolio selection has been most influential for the development of modern finance and its application in practice, where he applied variance to measure invest risk and constructed the mean-variance model.As the research on risk measure deepens on, it has been found that there are some flaws which cannot be avoided when using variance. In order to overcome these shortcomings, a lot of research has been done in theoretical field. But up to the present, these problems have not been solved satisfactorily. In this dissertation, we study portfolio selection by employing stochastic dominance, risk-value theory and optimization theory. The main results of the work can be summarized as follows:1. While the original Markowitz model forms a quadratic programming problem, following Sharpe(1971) and Stone(1973), many attempts has been made to linearize the portfolio optimization problems. Konno & Yamazaki(1991) presented and analyzed the complete portfolio optimization model based on the risk measure —the so-called mean-absolute deviation(MAD) model. The mean-semi-absolute devia- tion(MSAD) is a half of the mean absolute deviation. Hence, the corresponding MSAD model is equivalent to the MAD model. We propose an extension to the MSAD model to account for downside risk aversion of an investor, it doesn't require any specific type of return distributions, and it is easily transformed into a linear programming model for discreat stochastic variables. Consistency of the proposed extension model with the second degree stochastic dominance is proved. We found that the new model perform better than the MSAD model when the required return rate of the investor is relatively low.2. Based on the generalized disappointment models that were proposed by Jia and l)yer(2001), we presents a new asymmetric risk function. It applies upper absolute deviation to revise the lower semivariance, not only focuse on return dispersion below the expected mean return, but also use the return dispersion above the expected mean return that contains promising profits. Under the new risk measure, the computation recipes of the portfolio are provided, and an emprirical study using data from Shanghai stock market is given in order to describe its application.Our computational results show that the proposed model may led to fewer losses than the MV model and mean-semivariance model when the market was going down.3. The original Markowitz model based on the assumption of a perfect fractionability of the investments in such a way that the portfolio fraction for each security could be represented by a real variable. A quadratic integer programming portfolio optimization model with minimum transaction lots is developed through designing a asymmetric risk measurement based on generalized disappointment models proposed by Jia&Dyer. Further, a novel and available humoral immune algorithm is proposed to solve the model according to humoral immune theory. The key of the algorithm to construct an excellent antibody set-updating operator to collect and update good solutions from the search process while establishing several kinds of immune operations to improve diversity of population and strengthen the capacity of global, local, and parallel searching, as well as search optimal solutions from different directions. Practical application shows that the algorithm can search the optimal investment decision-making scheme of the model rapidly and effectively. Simulation and comparison illustrates the reasonability and availability of the model and the algorithm.4. Based on Jia&Dyer's risk-value framework, we proposes an asymmetric risk measure model. The measure of risk is a weighted sum of below-target deviations and above-target deviations, where downside risk is supplemented with the "upper partial moment",we also setup the quadratic programming portfolio optimization model with this new measure; Consistency of the proposed optimal portfolio model with the third degree stochastic dominance is proved; and finally an empirical study using data from Shanghai stock market is given in order to describe its application. Our computational results show that the new model may led to fewer losses than thetarget semi-variance model when the market was going down.5. We carry out the empirical numerical study on recently developed several linear programming portfolio optimization models using data from Shanghai stock market. These models are: MSAD, Minimax(Young 1999), /? (Cai, 2000), Deviation from the Quantile(Ruszczynski& Vanderbei, 2003) and MV, respectively .We compares the global minimum risk portfolios of the different models. Our experiments suggests that the MAD model yield the better performance for investors based on monthly rebalancing strategies in the out-of-sample testing, while the Minimax model of Young tends to perform poor in the period examined.Our method is the deepening of the present theoretical study on security investment risk, and our model is not restricted in symmetric distribution. This will surely make a new contribution for further research on portfolio selection.