Portfolio Selection And Capital Asset Pricing

The Semi-variance Theory amends the bugs of the traditional finance theories from the view of risk measurement. The traditional theory uses the variance to measure the investment risk and considers all the upside and downside offset from the target return as risks which overstates the risk and falls away from the people's comprehension of the risk. Furthermore, by using this method to make investment decisions, we might lose the opportunity to get the excessive return. Markowitz brought forward the mean-variance portfolio selection theory in which he used the variance to measure the risk in 1952. From that time on, this risk measuring method has been criticized by many scholars. Since the semi-variance measurement is consistent with the comprehension of the risk and it can help the investors to grasp the excessive return, this measurement is considered as a more reasonable risk measuring method. However, considering the complexity in the mathematic forms, more efforts are needed to be made on the semi-variance theory.This paper gives a definition of the semi-co-variance from the aspect of risk diversifica- tion and discusses the condition of the portfolio risk dispersion. The paper concludes that when the semi-co-variance between two single assets is zero, the risk of the combination can be dispersed furthest. Also it concludes that smaller the semi-co-variance, better the condition of the dispersion risk.This paper puts forward a semi-variance portfolio selection model which includes forecast variables of the investors. As a result, it overcomes the shortcomings of Hoggan's semi-variance selection model which relies merely on the historical data. This paper uses MC and QMC methods to count the portfolio's risk, at the same time, it uses the improved gradient projection arithmetic to optimize the portfolio. The empirical test finds that the arithmetic can get more precise portfolio and the arithmetic is more efficient when thc number of the single asset in the portfolio is less than 10. This paper also compares the efficient frontiers obtained from the mean-variance portfolio selection model among the Hoggan's semi-variance selection model and the mc and qmc model in the chapter 2, and finds that the mean-variance model has the highest precision, also the other three models have the phenomena of degeneration. But comparing the later three models, we can find that the precision of the two models put forward in the chapter 2 is higher than that of Hoggan's model. At the same return, the risk of mc and qmc model in the chapter 2 is less than that of Hoggan's model.From the point of operation, this paper puts forward three indexes the elastic coefficient of the expectation return, the elastic coefficient of the variance and the elastic coefficient of the correlation——to measure the influence of the forecast variable of single asset on the portfolio selection. In reality, the investors can improve the specific single asset's forecast by comparing the three elastic indexes. If they can do so, they can remarkably improved the performance of the optimized portfolio.Based on the semi-variance portfolio selection theory, this paper discusses the asset pricing under the semi-variance framework. When we use the semi-variance to measure the risk, or when the target return rate and the risk-free rate are equal, we find the two-funds separation theorem comes into existence definitely. However, when the target rate and the risk-free rate are not equal, the tow-funds separation theorem is not always true. In this paper, the author gets the asset pricing formulation, whose beta differs from the one in CAPM.Using the direct and the indirect methods, this paper tests the semi-variance asset pricing model in China stock markets. This paper finds that when we use this pricing model to forecast the price, the error is less than that of CAPM. The cross-section analysis indicates that the semi-variance beta has more power of interpreting the return of the single asset than the CAPM beta.