It is generally thought that active galactic nucleus (AGN) optical variability is produced, at least in part, by reprocessing of central X-rays by a surrounding accretion disc, resulting in wavelength-dependent lags between bands. Any good model of AGN optical variability should explain not only these lags, but also the overall pattern of variability as quantified by the power spectral density (PSD). Here, we present $\sim$daily g'-band monitoring of the low-mass AGN NGC 4395 over 3 yr. Together with previous Transiting Exoplanet Survey Satellite (TESS) and Gran Telescopio Canarias (GTC)/HiPERCAM observations, we produce an optical PSD covering an unprecedented frequency range of ~seven decades allowing excellent determination of PSD parameters. The PSD is well fitted by a bending power law with low-frequency slope $\alpha _{L} = 1.0 \pm 0.2$, high-frequency slope $2.1^{+0.2}_{-0.4}$, and bend time-scale $3.0^{+6.6}_{-1.7}\,$ d. This time-scale is close to that derived previously from a damped random walk (DRW) model fitted to just the TESS observations, although $\alpha _{L}$ is too steep to be consistent with a DRW. We compare the observed PSD with one made from light curves synthesized assuming reprocessing of X-rays, as observed by XMM-Newton and Swift, in a disc defined by the observed lags. The simulated PSD is also well described by a bending power law but with a bend two decades higher in frequency. We conclude that the large-amplitude optical variations seen on long time-scales are not due to disc reprocessing but require a second source of variability whose origin is unknown but could be propagating disc accretion rate variations.