Portfolio Optimization Problem Based On Regression Model

Risk is understood as the uncertainty between expected returns and actual returns.With the rapid development of financial markets,financial market risks are also emerging,and portfolio investment is an effective way to diversify risks.At present,the commonly used portfolio investment models are Mean-Variance model,Mean-VaR model and Mean-ES model,and the calculation process of these three models is very complicated,resulting in inaccurate calculation results.In this paper,these three models are transformed into several regression problems,and the empirical analysis shows that the Mean-ES model based on expectile regression can better distribute the tail risk.This article is divided into five parts.First,the first chapter expounds the research background of financial risk and portfolio investment,and introduces the research status of risk measurement and portfolio investment.The second chapter gives several basic mathematical definitions,outlines the concepts of risk measurement and consistent risk measurement,and introduces several commonly used risk measurement methods: variance risk measurement,VaR and ES,and finally discusses several risk measures.The calculation methods and their respective advantages and disadvantages.The third chapter expounds the concept of expectile and the relationship between expectile and quantiles.It introduces several commonly used portfolio investment models: mean-variance model,Mean-VaR model and Mean-ES model.These models are transformed into mean regression model,quantile regression model and expectile regression model,and the corresponding derivation and calculation process of model optimization is given.After the conversion to the regression problem,the complexity of the model is greatly reduced,and the accuracy of the model estimation is also improved.Finally,the fourth chapter and the fifth chapter are the empirical and conclusion parts,respectively calculate the investment weights of the three model portfolios,and estimate the volatility of the combined rate of return series based on the GARCH(1,1)model,and calculate the corresponding in-sample risk metrics and out-of-sample risk predictions,the analysis concludes that the Mean-ES model based on expectile regression greatly reduces the computational complexity of the original model and has a significant effect on the tail-end risk of stock and fund portfolios.