Estimating parameters of the CAPM under generalised asymmetric student-t distribution—The case of the Warsaw Stock Exchange sectoral indices

Abstract

This paper analyses selected sub-indices listed on the Warsaw Stock Exchange (WSE) covering seven sectors: construction, IT, media, real estate, fuel, food, and telecommunications, from 3 January 2006 to 29 May 2020. We use daily, weekly, monthly, and quarterly data, resulting in 3600 daily, 751 weekly, 172 monthly, and 56 quarterly observations. The WIG index quotations were used to approximate the market portfolio and the Poland 10Y government bond yields for the risk-free rate. We have estimated the parameter β in CAPM regression using three different stochastic assumptions for the error term. The basic stochastic framework of the model utilises the generalised asymmetric student-t distribution (GAST). We have also estimated the parameter β based on the symmetric version of the GAST distribution and on the Gaussian one. These models can be treated as a special case of the basic framework. The estimates of the β parameter are influenced by the assumptions made about the error term. The data indicates that except for WIG-Paliwa, the Gaussian error term leads to larger β estimates than other non-Gaussian specifications. The inference about the shape parameters is not very certain, and the data does not strongly support the two-piece mechanism that enforces the asymmetry of the error term distribution. Furthermore, the estimates of the β parameter depend strongly on the frequency of the analysed series.