Multi-period Sparse Portfolio Optimization Model And Empirical Research Based On Risk Measuremen

With the formation and development of global financial markets,investment and financial management has become a popular topic in the daily life of residents.Investors invest money and determine the proportion of different assets to be invested,expecting to minimize risks or maximize returns.In the process of financing and investment operations,various factors make the actual return deviate,and financial risk management has gained widespread attention.In order to reduce the difficulty of management and transaction costs,this paper takes the multi-period sparse portfolio problem as the research object and explores the optimal portfolio strategy based on different risk measures.Firstly,the classical mean-variance model provides a quantitative solution for single-period investment activities and lays the foundation for asset portfolio research.Using the mean of returns to measure returns,the variance of returns reflects the magnitude of volatility risk,but the model has many limitations.Sparse portfolio studies along the variance first are able to obtain a very small number of non-zero weight vectors,effectively overcoming the shortcomings of the mean-variance model’s unstable output values.Further consider that the variance is symmetric in nature,expressing the degree of deviation from the mean,making it difficult to distinguish between upward and downward market scenarios.In practice,financial asset return data is characterized by "spikes and tails",and the use of conditional value at risk(CVa R),a measure of tail risk,as a reference indicator can better describe the extent of losses.Secondly,holding too many asset positions will increase the management difficulty and transaction cost for investors,combining the idea of sparse optimization with portfolio modelling.Using the Fused Lasso method,the paradigm is applied to the weight vector and the difference between adjacent period vectors respectively.A limited number of investments can be selected from a large pool of assets,helping to reduce transaction costs and increase period-end returns.The model is solved by the alternating directional multiplier method(ADMM)and its modified form,which combines the Augmented Lagrange Multiplier Method with the pairwise decomposition method to optimize the number of iteration steps and time.Improving the speed and efficiency of the solution while ensuring convergence.Thirdly,the asset composition and allocation within the portfolio are not fixed,and it is more practical to construct an optimization model with multi-period inter-stage dynamic decision making.For the empirical analysis,the Fama and French database and the A-share market return data are used to verify the validity.Conclusions are drawn by comparing the analysis with other models using various specific indicators.The optimized model in this paper can achieve lower sparsity and risk,and reduce the number of changes and transaction costs.A very small number of the many underlying assets are selected for allocation,providing reference suggestions for the problem of obtaining a sparse asset portfolio with high-dimensional data.With the comprehensive reform of the stock registration system and the continuous development and improvement of China’s capital securities market,the study of the portfolio optimization allocation problem has important practical significance and theoretical value.In view of the situation of China’s securities market,corresponding suggestions are put forward.