A pigment-comprising formulation for coating substrates, comprising: (i) an aqueous dispersion of at least one water-insoluble polymer P which has phosphonate groups, as a binder, said polymer P having a glass transition temperature Tg in the range of −60° to 80° C., (ii) at least one inorganic pigment, (iii) optionally, one or more inorganic fillers, and (iv) at least one auxiliary, wherein water-insoluble polymer P is obtained by free-radical aqueous emulsion polymerization of ethylenically unsaturated monomers comprising: 90 to 99.9% by weight of at least one monomer a, which is selected from the group consisting of vinylaromatic monomers, the esters of acrylic acid with C1-C12-alkanols, the vinyl esters of aliphatic C1-C12-monocarboxylic acids, ethylene and vinylchloride, and 0.1 to 10% by weight of at least one phosphonate group containing monomer.