We report the results of quasi-simultaneous optical and near-IR (NIR) photometry of the low-mass X-ray binary, 4U 1957+115. Our observations cover the B, V, R, I, J, H and K-bands and additional time series NIR photometry. We measure a spectral energy distribution (SED), which can be modelled using a standard multitemperature accretion disc, where the disc temperature and radius follow a power-law relation. Standard accretion disc theory predicts the power-law exponent to be -3/4, and this yields, perhaps surprisingly, acceptable fits to our SED. Given that the source is a persistent X-ray source, it is however likely that the accretion disc temperature distribution is produced by X-ray heating, regardless of its radial dependence. Furthermore, we find no evidence for any emission from the secondary star at any wavelength. However, adding a secondary component to our model allows us to derive a 99 per cent lower limit of 14 or 15 kpc based on Monte Carlo simulations and using either an evolved K2 or G2V secondary star, respectively. In >60 per cent of cases, the distance is >80 kpc. Such large distances favour models with a massive (>15 M_&sun;) black hole primary. Our quasi-simultaneous J- and V- band time series photometry, together with the SED, reveals that the optical/NIR emission must originate in the same region, i.e. the accretion disc. The likely extreme mass ratio supports suggestions that the accretion disc must be precessing which, depending on the length of the precession period, could play a major part in explaining the variety of optical light-curve shapes obtained over the last two decades.