We investigate a framework for robo-advisors to estimate non-expert clients' risk aversion using adaptive binary-choice questionnaires. We model risk aversion using cost functions and spectral risk measures in a static setting. We prove the finite-sample identifiability and, for properly designed questions, obtain a convergence rate of $\sqrt{N}$ up to a logarithmic factor, where $N$ is the number of questions. We introduce the notion of distinguishing power and demonstrate, through simulated experiments, that designing questions by maximizing distinguishing power achieves satisfactory accuracy in learning risk aversion with fewer than 50 questions. We also provide a preliminary investigation of an infinite-horizon setting with an additional discount factor for dynamic risk aversion, establishing qualitative identifiability in this case.