A heteroscedastic volatility model with Fama and French risk factors for portfolio returns in Japan

Abstract: This thesis has used the Fama and French five-factor model (FF5M) and proposed an alternative model. The proposed model is named the Fama and French five-factor heteroscedastic student's model (FF5HSM). The model utilises an ARMA model for the returns with the FF5M factors incorporated and a GARCH(1,1) model for the volatility. The FF5HSM uses returns data from the FF5M's portfolio construction for the Japanese stock market and the five risk factors. The portfolio's capture different levels of market capitalisation, and the factors capture market risk. The ARMA modelling is used to address the autocorrelation present in the data. To deal with the heteroscedasticity in daily returns of stocks, a GARCH(1,1) model has been used. The order of the GARCH-model has been concluded to be reasonable in academic literature for this type of data. Another finding in earlier research is that asset returns do not follow the assumption of normality that a regular regression model assumes. Therefore, the skewed student's t-distribution has been assumed for the error terms. The result of the data indicates that the FF5HSM has a better in-sample fit than the FF5M. The FF5HSM addresses heteroscedasticity and autocorrelation in the data and minimises them depending on the portfolio. Regardingforecasting, both the FF5HSM and the FF5M are accurate models depending on what portfolio the model is applied on.