Portfolio optimization and long-term dependence

Abstract

Whilst emphasis has been given to short-term dependence of financial returns, longterm dependence remains overlooked. Despite financial literature provides evidence of long-term's memory existence, serial-independence assumption prevails.This document's long-term dependence assessment relies on rescaled range analysis (R/S), a popular and robust methodology designed for Geophysics but extensively used in financial literature. Results correspond to most of the previous evidence of significant long-term dependence, particularly for small and illiquid markets, where persistence is its most common kind. Persistence conveys that the range of possible future values of the variable will be wider than the range of purely random and independent variables.Ahead of R/S financial literature, authors estimate an adjusted Hurst exponent in order to properly estimate the covariance matrix at higher investment horizons, avoiding the traditional -independence reliant-square-root-of-time rule.Ignoring long-term dependence within the mean-variance portfolio optimization results in concealed risk taking; conversely, by adjusting for long-term dependence the weight of high (low) persistence risk factors decreases (increases) as the investment horizon widens. This alleviates some well-known shortcomings of conventional portfolio optimization for long-term investors (e.g. central banks, pension funds and sovereign wealth managers), such as excessive risk taking in long-term portfolios, extreme weights, home bias, and reluctance to hold foreign currency-denominated assets.Keywords: Portfolio optimization, Hurst exponent, long-term dependence, biased random walk, rescaled range analysis. JEL Classification: G11, G32, G20, C14. † We are grateful to Marco Ruíz, Jack Bohn and Daniel Vela, who provided valuable comments and suggestions. Research assistance, comments and suggestions from Karen Leiton and Francisco Vivas are acknowledged and appreciated. As usual, the opinions and statements are the sole responsibility of the authors.