Universal portfolios generated by rational functions

Kee Seng Kuang,Choon Peng Tan,Yann Ling Goh,L.E Teoh,W.S Ng

doi:10.1051/itmconf/20213602004

Abstract

The f -divergence of Csiszar is defined for a non-negative convex function on the positive axis. A pseudo f -divergence can be defined for a convex function not satisfying the usual requirements. A rational function where both the numerator and the denominator are non-integer polynomials will be used to generate universal portfolios. Five stock-price data sets from the local stock exchange are selected for the empirical study. Empirical results are obtained by running the generated portfolios on these data sets. The empirical results demonstrate that it is possible for the investors to increase their wealth by using the portfolios in investment.

Highlights

Cover and Ordentlich [1] introduced a general method to generate universal portfolio by weighting the current and past relatives in a stock portfolio utilizing the moments of a probability distribution with emphasis on the Dirichlet distribution
The CoverOrdentlich universal portfolio requires a substantial amount of computer memory and implementation time
Empirical studies show that the performance of finite-order portfolios can match the performance of the CoverOrdentlich universal portfolios

Summary

Introduction

Cover and Ordentlich [1] introduced a general method to generate universal portfolio by weighting the current and past relatives in a stock portfolio utilizing the moments of a probability distribution with emphasis on the Dirichlet distribution. The CoverOrdentlich universal portfolio requires a substantial amount of computer memory and implementation time To surpass this difficult, Tan [2] proposed the finite-order universal portfolio to save computer memory and implementation time. Empirical studies show that the performance of finite-order portfolios can match the performance of the CoverOrdentlich universal portfolios. Tan and Kuang [4] studied method to generate universal portfolios by f-divergence and Bregman divergences. The f-divergence is generated by a non-negative convex function f(t) on the positive axis. Tan and Kuang [5] proposed the use of f-divergence which is defined for two types of convex functions to generate universal portfolios. The universal portfolio generated by f-divergence using second type of convex functions defined above will be derived. The empirical result will be compared with the well-known Helmbold’s Universal Portfolio

Definition

Main results

Proposition 2

Empirical results