Motivated by the psychological factor of time-varying risk-return relationship, we study a linear varying coefficient ARCH-M model with a latent variable in this paper. Due to the unobservable property of latent variable, a corrected likelihood method is employed for parametric estimation. Estimators are proved to be consistent and asymptotically normal under certain regularity conditions. A simple Z-statistic is also established for testing latent variable effect. Simulation results confirm that our estimators and test perform well. We also apply our model to examine whether the risk-return relationship depends on investor sentiment in American Market and some explainable results are obtained.