Functionalized copolymers hydrophobicized with silicones, in the form of aqueous dispersions or water-redispersible powders are prepared by copolymerizing a) from 60 to 99.89% by weight of one or more monomers selected from the group consisting of vinyl esters of optionally branched C1-15 alkylcarboxylic acids, methacrylates and acrylates of C1-15 alcohols, vinylaromatics, olefins, dienes, and vinyl halides, b) from 0.01 to 30% by weight of one or more silicones with from 10 to 1,000 SiO(CnH2n+1)2 repeat units where n is from 1 to 6, and where from 90 to 100% by weight of the silicones b) contain at least one but not more than two polymerizable groups, c) from 0.05 to 5.0% by weight of one or more hydrolyzable silane monomers selected from the group consisting of ethylenically unsaturated hydrolyzable silicon compounds, and hydrolyzable epoxysilanes, aminosilanes and mercaptosilanes, and d) from 0.05 to 5.0% by weight of one or more monomers selected from the group consisting of ethylenically unsaturated epoxy compounds. The copolymers may be used as binders for paints and coatings with high wet abrasion resistance.