The photophysical properties of a multicomponent rotaxane bearing a β-cyclodextrin ring covalently connected to an axle comprising an azobenzene photoisomerisable moiety and a naphthalimide-type fluorescent stopper are investigated by a combined experimental and computational study. The absorption and fluorescence spectra, and particularly the induced circular dichroism (ICD) signal, are determined. The latter shows a sign relation that cannot be rationalised in terms of the simple general rules commonly employed to analyse the ICD spectra of achiral guests encircled by chiral hosts. To assist the interpretation of experimental results, DFT and time-dependent (TD) DFT calculations are performed to explore the availability of low-energy conformations and to model their spectroscopic response. Molecular dynamics simulations performed in water show the interconversion of a number of conformers, the contribution of which to the ICD signal is in agreement with the observation.