A Model Of Portfolio Selection Based On The Conditional Value-at-Risk And Safety-first Theory

As an important part of modern financial investment,the main research of portfolio theory is how to allocate the limited wealth to different assets in order to achieve minimum risk in fixed income or achieving the maximum income at a certain risk.In 1952,Markowitz put forward to mean-variance model of portfolio selection.He first applied mathematical statistical methods to the study of the portfolio selection,which opened the research prelude on modern finance.Experienced the bull market in 2014 and the bear market in 2015,most of the investors found that they would lost revenue surplus in bull market because of strict control of risk.On the other hand,they maybe suffer losses in bear mark because of not coping with the downside risk if they only thinking of the traditional portfolio theory.Basing on it,this paper tries to focus on the constraint of downside risk and study on portfolio aiming at ensuring assets safe firstly.This study inspired by the Safety First Portfolio Optimization Model and it considered a very similar decision model:investors select portfolio investment through maximize the probability of total return over the end of a fixed benchmark rate of return.Then considered introduction of mean-CVaR model basing on the security-first model and found the optimal solution.This paper research on the three aspects on the basis of previous study.Firstly,the article explores the measure of downside risk under normal and optimal decision under the Safety First Thought.Then establish a portfolio model based on CVaR and safety first thought.Secondly,the article continues to explore expansion model not allowing short selling,making it more in line with stock market investment behavior with us.Finally,I compare the model in this paper with the model of Zhao Mingqing.In the three-part research,we first explore theoretically optimal solution of the model,then use the actual stock price data to calculate an example.The fourth part,the fifth part and the sixth part are the core content of the article,and it also reflects the innovation of this paper.In the discussion of the theoretical solution of the model,we discuss the solutions of portfolios model in the article.We found that the optimal solution is the cut point of straight line of investment objective function and the mean-CVaR efficient frontier.The fifth part,by extending model we solved the problem of not allowing short selling.Though the comparison of study in the sixth part,we found that the model in this paper are equal to the model of Zhao Mingqing under the assumption of joint multivariate normal distribution of assets returns.