Quantile approximations in auto-regressive portfolio models

Abstract

This paper develops an analytical approximation for the distribution function of a terminal value of a periodic series of buy-and-hold investments placed over a fixed time horizon for the case when log-returns of assets follow a p -th order vector auto-regressive process. The derivation is based on a first order Taylor conditioned approximation with a suitably chosen conditioning variable. The results indicate a remarkably good fit between the approximating procedure and simulations based on realistic parameters.