Asset Allocation by Variance Sensitivity Analysis

This article provides a solution to the curse of dimensionality associated to multivariate generalized autoregressive conditionally heteroskedastic (GARCH) estimation. We work with univariate portfolio GARCH models and show how the multivariate dimension of the portfolio allocation problem may be recovered from the univariate approach. The main tool we use is ‘‘variance sensitivity analysis,’’ the change in the portfolio variance induced by an infinitesimal change in the portfolio allocation. We suggest a computationally feasible method to find minimum variance portfolios and estimate full variance-covariance matrices. An application to real data portfolios implements our methodology and compares its performance against that of selected popular alternatives. keywords: dynamic correlations, multivariate GARCH, risk management Estimates of volatilities and correlations are used for pricing, asset allocation, hedging purposes, and risk management in general. In today’s fast changing financial world, it is essential that these measures are easy to understand and implement. Since their introduction by Engle (1982), autoregressive conditionally heteroskedastic (ARCH) models have been used extensively both in academia and by practitioners to estimate the volatility of financial variables. Many articles have been written on the subject, extending the original ARCH model in many directions. The multivariate extension, however, has been met The idea of this article came about through several discussions I had with Vladimiro Ceci and Walter Vecchiato. In fact, this article builds on an earlier draft (European Central Bank Working Paper [ECB] no. 194) coauthored with Ceci and Vecchiato, who in the meantime have gone on to other pursuits. In addition to Vladimiro Ceci and Walter Vecchiato, I would like to thank Eric Renault (the editor), an anonymous associate editor, two anonymous referees, Lutz Kilian, Luca Lotti, Neil Shephard, Kevin Sheppard, and the editorial board of the ECB Working Paper Series for useful comments and suggestions. The codes to replicate the results in the article can be downloaded from http://www.simonemanganelli.org. The views expressed in this article are those of the author and do not necessarily reflect those of the ECB. Address correspondence to Simone Manganelli, DG-Research, European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany, or e-mail: [email protected]. doi:10.1093/jjfinec/nbh015 Journal of Financial Econometrics, Vol. 2, No. 3, a Oxford University Press 2004; all rights reserved. Journal of Financial Econometrics, 2004, Vol. 2, No. 3, 370–389