The Two-stage Portfolio Model Based On Coherent Conditional Measure Of Risk

Portfolio selection is a course that investor allocate his wealth among various kinds of assets to reduce the portfolio risk given specified expected return rate. The origin and the end of financial research can be thought in a certain way as portfolio selection which domains the investor's content of management and decision of finance. It is the portfolio selection that brought the development of modern finance.This paper gives a brief introduction about the progress of portfolio and the definition of the traditional two-stage stochastic programming. Also we introduce the basic idea of Monte Carlo simulation.Chapter 2 lists the prior knowledge, mostly about the axiomatic definition of a coherent conditional measure of risk, also including the definition of CVaR and some of its characteristics widely used.Traditional two-stage stochastic programming considers the expectation as the preference criterion. However, the risk is presence while choosing the best decisions. In chapter 3, we consider an extended two-stage stochastic programming, in which there is still unresolved uncertainty after the second-stage decision is made. Then we analyze properties of the problem and derive necessary and sufficient optimality conditions.We define an abstract risk-averse two-stage problem basing on the problem in chapter 3, and it is changed into a stochastic programming which is proved to be equivalent to the formal two-stage problem. Next, we derive optimality conditions and list some characteristics for the two-stage problem. In this study, we specify conditional expectation-semideviation as the risk measure of the second phase of investment, and specify CVaR as the risk measure of the first phase of investment, so a specific risk-averse two-stage problem is modeled.In chapter 5, we give the specific portfolio model based on the model in chapter 4. The model is changed into a large scale linear programming by an auxiliary function substituting for the CVaR function and the linearity technique.Finally, in the light of the specific stock dates, we get the best weight coefficient of portfolio with matlab. Based on the results, we execute numerical tests in two aspects. The effect of expected return rate to the optimal policies is analyzed by changing expected return rate. Numerical tests also give the graph of the relationship between the curve of expected return rate/CVaR and believe degree. So investors should select expected return rate and believe degree according to their risk preferences, while making investment decisions.