Optimal Portfolio Based On CVaR And Its Application In The Security Market Of China

The portfolio theory investigates how to select and allocate assets. The target of a portfolio is to make the return of the portfolio maximized in a given risk level that the investors can accept or to make the risk of the portfolio minimized in a given level of return. In the construction of a portfolio, the risk measure is crucial and different risk measures will result in a different portfolio. CVaR has a lot of advantages over other risk measures; it is a coherent risk measure. However, it would encounter the difficulties of computation. When constructing this type of portfolio, many authors assume the asset return follows certain kind of distribution in advance, some authors even assume the return follows the normal distribution. In fact, in this case, the risk measure of CVaR is equivalent to the risk measure of variance. The thesis will directly use sample to construct a mean-CVaR portfolio by considering the properties of CVaR as well as the related portfolio theory. This is a method based on statistical estimation, which entirely relies on the information of sample, regardless of which distribution the asset returns follow. Meanwhile, the thesis uses the historical data of stock market of China to construct an optimal CVaR-type portfolio and then observes and analyzes its running over the market. It comes to the conclusion that the distributions of almost all the returns of assets are not normal, in the case of the same requirement of return, the mean-CVaR portfolio has less risk compare with mean-variance portfolio, and it indicates that the optimal portfolio can diversify risk and the portfolio theory based on CVaR is valid in some extent in the security market of China.