  We study the fluctuations of the autocorrelation and autoresponse functions
and, in particular, their variances and co-variance. In a first general part of
the Article, we show the equivalence of the variance of the response function
with the second-order susceptibility of a composite operator, and we derive an
equilibrium fluctuation-dissipation theorem beyond-linear order relating it to
the other variances. In a second part of the paper we apply the formalism to
the study to non-disordered ferromagnets, in equilibrium or in the coarsening
kinetics following a critical or sub-critical quench. We show numerically that
the variances and the non-linear susceptibility obey scaling with respect to
the coherence length $\xi$ in equilibrium, and with respect to the growing
length $L(t)$ after a quench, similarly to what is known for the
autocorrelation and the autoresponse functions.
