We study a class of genetic models in which a quantitative trait determined by several additive loci is subject to temporally fluctuating selection. Selection on the trait is assumed to be stabilizing but with an optimum that varies periodically and might be perturbed stochastically. The population mates at random, is infinitely large and has discrete generations. We pursue a statistical and numerical approach, covering a wide range of ecological and genetic parameters, to determine the potential of fluctuating environments to maintain quantitative genetic variation. Whereas, in contrast to some recent claims, this potential seems to be rather limited in the absence of recurrent mutation, fluctuating environments might, in combination with it, often generate high levels of additive genetic variation. We investigate how the genetic variation maintained depends on the ecological parameters and on the underlying genetics.