Modeling Equity Returns Using a Simple ARCH Model

Studies by Willie (1984, 1986, 1987) and Carter (1991), among others, have proposed models of equity returns for actuarial work. In particular, Carter proposes a random walk model for Australian equity returns. The aim of this paper is to examine the use of a simple ARCH model for equity returns and to compare the performance of such a model with a model that is commonly used by actuaries! the random walk model of returns. The model is fitted using Australian data for equity returns on the Australian All Ordinaries Index for the period January 1970 to December 1992. The relative performance of the model is assessed using simulation studies.