Quantile three-factor model with heteroskedasticity, skewness, and leptokurtosis

Abstract

The Fama-French three-factor model advances the capital asset pricing model by expanding size risk and value risk factors to market risk factors. A quantile Fama-French three-factor model with GARCH-type dynamics, leptokurtosis, and skewness via asymmetric Student t errors is proposed to overcome the limitations of the existing ones. One can investigate how the daily volatility and market risk factors act under different market conditions represented by quantile levels via the proposed model. Bayesian adaptive Markov chain Monte Carlo methods are used to estimate model parameters in the proposed model over various quantile levels. This study assesses the Bayesian inference performance via simulation studies in which the designated models are misspecified and considers some daily stock returns from NASDAQ to help further select the best model via the posterior odds ratio. It is clear that the various market conditions and the GARCH effect should be incorporated into the model. Findings show that the estimation of the size factor turns insignificant for lower quantiles - i.e., when the market is in a panic, investors ignore the size effect of a company's assets.