Hi. Here are some suggestions that might be helpful for the research with the title “Proximal Gradient Method in Mean-variance Portfolio Selection”.
1. The sample period is too short. Should take longer period but need to check whether there is “Regime Switching” or “Structural Break” during the sample period.
2. The Financial Data usually have stylized fact of non-normal, fat-tail, serial correlation, heteroscedasticity, Non IID and etc. , which will seriously affect the performance of Mean-Variance Optimization.

To solve the above problems.

(a) Use the sample autocorrelation function (ACF) of the returns to check for serial correlation and sample autocorrelation function (ACF) of the squared returns to check for heteroscedasticity.
(b) Filter it using AR-GARCH or AR-EGARCH or AR-TGARCH.
(c) Having filtered the model residuals from each return series, standardize the residuals by the corresponding conditional standard deviation. These standardized residuals represent the underlying zero-mean, unit-variance, IID.
(d) Then only proceed to mean-variance optimization.
Hopefully my suggestions are helpful for the research.
Regards,
Tong Gee Kok