The article presents problems related the to long - only optimized (with the help of the Markowitz model) portfolio diversification with L2 regularization. The backtesting for stocks selected from some subset of S&P 500 index for the 2002 - 2019 year interval with Markowitz portfolio optimization with L2 regularization was performed. The expected return was varied from 0.1 to 0.25, the regularization parameter was varied in the range 0.05 - 0.15. The results of backtesting are shown. The geometrical average of annual return for year interval 2002 - 2019, was about 0.13 - 0.14 in all the parameter range. It has been exposed, that the mean annual portfolio return for this year range actually nearly not depends on the expected return and the regularization parameter, if they are changes in aforementioned range, but the minima and the maxima of the annual portfolio return, i.e. the variance of the annual portfolio return, moreover, shows more pronounced dependency on these parameters of the optimized portfolio. The data of the backtesting seems to show the heteroscedasticity of a stock market.