Application Of High-dimensional Elliptical Factor Model In Investment Portfolio

Along with the development of financial markets,financial data dimension becomes very large.High-dimensional factor model has attracted wide attention in the era of big data,However,the traditional factor model estimation method usually need to assume that the data has finite fourth moment,this assumption ignores the influence of the heavy tail,and the actual characteristics of the financial market data are not consistent.Therefore,when the traditional factor model is applied to the portfolio,the return per unit risk of the constructed portfolio may be low,which is contrary to the original intention of our investment.How to estimate portfolio using factor model is always attracting scholars’ attention.Due to the heavy tail characteristic of stock data,the robust two-step estimation method of high-dimensional elliptical approximation factor model(RTS)is applied to the portfolio.The portfolio constructed has strong robustness because it takes into account the characteristic of the heavy tail of returns,with a high Sharpe ratio and low sensitivity to outliers.Monte Carlo simulation is carried out on the constructed portfolio,the study found that the investment portfolio constructed by RTS method is better than that constructed by PCA method,the extra return under unit risk tends to the theoretical real value,and the variance of the estimate is small,even when cross-sectional correlation and sequence correlation are set,the constructed portfolio is relatively robust,the superiority of the RTS approach grows as the number of assets and the time dimension increases.At the end of the paper,the high-dimensional elliptical approximation factor model is applied in the actual stock panel data.The results show that compared with the traditional factor model,the elliptical factor model can construct more robust portfolio.In the empirical analysis,the return rate of the portfolio is much higher than that of the traditional factor model,both pre-epidemic and post-epidemic.Therefore,it can be inferred that RTS method can be used as a substitute of traditional PCA method in real life.