Risk Management and Portfolio Budgeting Based on ARMA-GARCH Non-Gaussian Multivariate Model

Abstract

In this work, we propose an ARMA(1,1)-GARCH(1,1) model with standard classical tempered stable (CTS) innovations for historical daily returns of 29 selected stocks. The non-Gaussian nature of the innovations captures the fat-tail property observed in data. The dependency between different assets is modeled by a student’s t copula. We fit the data and estimate the parameters of the model and perform statistical goodness-of-fit tests for fitted parameters. Based on the multivariate model consisting of standard CTS marginals and student’s t copula, we construct ARMA-GARCH Monte-Carlo paths for daily returns of each single stock. Daily VaR is computed for an equally weighted portfolio, and for a time span of 250 trading days, the model is being backtested. It is shown that in comparison with the Gaussian model, the proposed CTS-t copula offers more realistic estimation for the portfolio risk. Moreover we study the portfolio selection problem. We compute the marginal VaR and Component VaR of single stocks for the VaR optimized portfolio. We consider an active portfolio budgeting method, where we change the portfolio composition according to marginal VaR measurements. We show that the resulting portfolio converges to the VaR minimized portfolio in the 29 dimensional space of portfolio weight vectors. We perform a return to VaR ratio, performance test, to realize the ”costs” of this risk reduction action in terms of potential return suppression. Little transaction costs due to limited and relatively small position modification in portfolio, presents an efficient management scenario for pension funds and other investment organization, where relative changes in investment positions are restricted.