Portfolio Optimization Models For Different Risk Measures Under The Safety First Criterion

With the rapid development of the stock market and the increase in national income,more and more people are turning to stock investment as a form of financial management.Investors invest in stocks with the expectation of earning higher returns at an acceptable level of risk,or taking less risk to achieve the expected returns.The portfolio is a way to diversify risk.It helps investors to determine the optimal weighting of each stock and to maximize risk avoidance or revenue generation.Therefore,the study of effective portfolio models is of great importance to investors.In 1952,Markowitz first proposed the portfolio theory,which quantifies the return and risk of investment by the mean and variance of returns,and established the mean-variance model.Then scholars introduced Value at Risk(VaR)and Conditional Value at Risk(CVaR)as risk measures.They established the mean-VaR model and mean-CVaR model to avoid the shortcoming that variance does not visually reflect the size of risk taken by investors.Later,the SFC-VaR and SFC-CVaR optimization models were developed by combining the Safety First Criterion(SFC)with the single constraint of not allowing short selling,the existence of transaction costs and restricting the minimum trading unit.Against the above background,this thesis develops portfolio models that are more consistent with the Chinese stock market under the combined constraints of multiple factors.The main contents and innovations of the thesis are as follows:1.In this thesis,we consider the impact of not allowing short selling,the existence of transaction costs and restricting the minimum trading unit on the portfolio models.Then the SFC-VaR and SFC-CVaR optimization models with combined multi-factor restrictions under normal distribution are developed.The models are solved by genetic algorithm,and the empirical results show that the multi-factor restricted portfolio models is more consistent with the Chinese stock market than the single-factor restricted portfolio models.Under certain conditions,the VaR and CVaR values of the SFC-VaR and SFC-CVaR optimization models are compared.The empirical results show that the CVaR values is always larger than the VaR values.This illustrates that CVaR takes better account of extreme situations than VaR.It can help investors to avoid risks to a greater extent.2.In this thesis,we consider the phenomenon of spikes and thick tails in stock returns and establish the SFC-VaR optimization model with multi-factor restrictions under stable distribution.The optimal model is solved by a Monte Carlo simulation-genetic algorithm.The impact of different confidence levels and expected returns on the optimal solution and VaR values of the model is analyzed.The empirical results show that investors with higher risk tolerance can set a larger confidence level.Then we compare the optimal solutions and VaR values of SFC-VaR optimization models under normal distribution and stable distribution.The empirical results show that the stable distribution can achieve the same expected return as the normal distribution with less capital invested and with a smaller value of risk.This indicates that the SFC-VaR optimization model under the stable distribution is not only more consistent with the actual stock market in China,but also more consistent with the psychological expectations of investors.The optimal portfolio and risk values obtained under this model are valuable to investors.