Bayesian Inference for Return Distributions With Informative and Non-Informative Priors

Returns volatility is a prominent characteristic of the financial market. Previous research has extensively discussed the estimation of volatility parameters. However, the influence of prior distribution in Bayesian models on estimation accuracy, especially in the context of return distributions, has not been extensively studied. The paper focuses on the process of forming the posterior distribution in Bayesian inference models for return distributions, considering the role of both informative and non-informative priors. The analysis was carried out by comparing two cases, first, when the prior distribution is informative (Inverse Gamma), and second, when the prior distribution is non-informative. The obtained results of the study indicate that, in both cases, the variance posterior distribution follows the Inverse Gamma distribution, while parameters differ depending on the type of prior distribution. The current study develops Bayesian estimation of return distribution parameters and supports investment risk analysis and portfolio management.