Molecular dynamics simulations are used to investigate structural and dynamical properties of liquid mixtures of water and ethanol over the entire range of compositions from neat liquid water to neat liquid ethanol. Particular emphasis is given to the time relaxation of the anisotropic collective polarizability and the low-frequency part of the depolarized Raman spectra. While the dynamics was carried out using simulations with standard force fields for water and ethanol, the post-analysis was performed employing the chemical potential equalization (CPE) method. For comparison purposes, the CPE results are compared to those obtained with the traditional interaction-induced model. Both methods are able to capture the basic shape and position of the Raman bands. Polarizability response in time and frequency domains is disentangled in permanent, interaction-induced and induced-permanent (cross) terms. Our findings suggest that the polarizability relaxation of water is more sensitive to environmental fluctuations. Once water signal remains covered by the ethanol contribution even in water-rich concentrations, some water polarizability features were unveiled and correlated with H-bond dynamics. The permanent term, representative of the reorientational dynamics, captures the short-time oscillations and responds for a part of the total relaxation, while the long-range interaction-induced contribution is responsible for great part of the total polarizability relaxation.