Does measurability of cardinal $\kappa$ imply measurability of $2^\kappa$?

A cardinal $ \kappa$ is real-valued measurable if there is a $ \kappa$ -additive probability measure on $ 2^\kappa$ which vanishes on singletons. The existence of measurable $ \kappa$ is independent of ZFC.

Question: if $ \kappa$ is assumed to be real-valued measurable, does it necessarily follow that $ 2^\kappa$ is real-valued measurable?