Evaluation of multivariate GARCH models in an optimal asset allocation framework

Abstract

JEL classification: C58 G11 G15 G17 G32 A B S T R A C TThis paper analyses plethora of advanced multivariate econometric models, which forecast the mean and variance-covariance of the asset returns to create optimal asset allocation models. Most existing studies use a limited number of Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models. In this study, we provide an in-depth knowledge of large asset modeling and optimization strategies for solving a portfolio selection problem involving the dynamic conditional correlation models (DCC). Specifically, we use symmetric GARCH models and an asymmetric version of it (GJR-GARCH). Several studies have also tried to examine the effectiveness of using parametric copula in estimating portfolio risk measures but their results have been inconclusive. We are interested in evaluating if Copula-GARCH could be an optimal model for assessing the performance of a portfolio. This study, therefore, implemented various Copula-GARCH based models using the static and dynamic estimation of the correlation. By employing different model specifications, we are able to explore the empirical applicability of the multivariate GARCH models when estimating large conditional covariance matrices. In constructing the optimal portfolios, we evaluate the minimum variance, mean-variance, maximising Sharpe ratio, mean-CVaR, and maximization of Sortino ratio. We compare the out-of-sample performance for each of the models based on the risk-adjusted performance for a portfolio with and without short sales, consisting eight stocks and four bond indices of 10 years maturity, in the United States (US), Kong. Our results suggest that the dynamic models are more capable of delivering better performance gains than the static models. These models reduce portfolio risk and improve the realized return in the out-of-sample period. This paper concludes that by adding copula functions to the model, it does not give a better performance model when compared to the dynamic correlation model.

The Implementation of Asset Allocation Approaches: Theory and Evidence

“…The results showed that the portfolios containing INE outperformed the other portfolios including the Brent and WTI. As compared with previous studies [14][15][16][17][18][19][20][21][22][23], they found only one effective portfolio, whereas this study obtained a set of effective portfolios, the efficient frontier. In addition, as contrasted with studies using the same optimization strategy as in this study, such as the minimum variance of portfolio [21][22][23], those studies focused on which model (respectively, variance forecast) among several models (respectively, variance forecasts) could get the best portfolio performance [21,22].…”

“…As compared with previous studies [14][15][16][17][18][19][20][21][22][23], they found only one effective portfolio, whereas this study obtained a set of effective portfolios, the efficient frontier. In addition, as contrasted with studies using the same optimization strategy as in this study, such as the minimum variance of portfolio [21][22][23], those studies focused on which model (respectively, variance forecast) among several models (respectively, variance forecasts) could get the best portfolio performance [21,22]. In contrast, Lv, Yang and Fang [23] focused on whether the INE crude oil futures could better aid investors' multi-asset allocation on petrochemical-related stocks compared to the Brent and WTI.…”

“…Stochastic programs aim at "maximizing a specific utility function constraint to initial wealth balance" [14], "minimizing the square deviations of the distribution" [16], "maximizing the expected terminal wealth subtracted by the variance of terminal wealth" [17], and "maximizing the expected terminal wealth" [18]. The stochastic programs may also include "maximizing portfolio's return subtracted by the variance of portfolio's return" [19], "minimizing total factors risk" [20], "maximizing Sharpe ratio" [21], "maximizing Sortino ratio" [21], and "minimum variance of portfolio" [21][22][23]. For example, Aziz, Vrontos, and Hasim [21] explored, among 26 multivariate dynamic conditional correlation (DCC) generalized autoregressive conditional heteroskedasticity (GARCH) models, which model can get the best optimal portfolio for each of five different optimization strategies.…”

“…The stochastic programs may also include "maximizing portfolio's return subtracted by the variance of portfolio's return" [19], "minimizing total factors risk" [20], "maximizing Sharpe ratio" [21], "maximizing Sortino ratio" [21], and "minimum variance of portfolio" [21][22][23]. For example, Aziz, Vrontos, and Hasim [21] explored, among 26 multivariate dynamic conditional correlation (DCC) generalized autoregressive conditional heteroskedasticity (GARCH) models, which model can get the best optimal portfolio for each of five different optimization strategies. The five optimization strategies are the minimum variance, mean-variance, maximizing Sharpe ratio, mean-CVaR, and maximizing Sortino ratio.…”

Safe-Haven Currencies as Defensive Assets in Global Stocks Portfolios: A Reassessment of the Empirical Evidence (1999–2022)

“…Notes 1 When using monthly data, volatility tends to dissipate with respect to empirical analyses relying on higher frequency observations. The use of the monthly frequency, however, is not unusual in this empirical literature (see, e.g., Filis et al 2011;Guesmi and Fattoum 2014;Grisse and Nitschka 2015;Chan et al 2018;Abdul Aziz et al 2019;Batten et al 2021;Robiyanto et al 2021;Tronzano 2022). In empirical analyses relying on monthly data, the sample needs to be sufficiently long in order to get reliable statistical inferences.…”