Viscosity modifier for lubricating oils, additive composition for lubricating oils, and lubricating oil compositions

[Problem] To provide a viscosity modifier for lubricating oils and an additive composition for lubricating oils for obtaining a lubricating oil composition having exceptional storage stability at low temperatures and exceptional viscosity characteristics at low temperatures. [Solution] This viscosity modifier for lubricating oils includes a resin (α), wherein the resin (α) satisfies specific requirements and includes a grafted olefin polymer [R1] that is configured from a main chain and a side chain and that satisfies the following requirements (i) and (ii). (i) The main chain comprises a copolymer of ethylene and at least one α-olefin selected from C3-12 α-olefins, and structural units derived from the ethylene are within the range of 74-86 mol%. (ii) The side chain comprises a copolymer of ethylene and at least one α-olefin selected from C3-12 α-olefins, and structural units derived from the ethylene are within the range of 30-65 mol%.