Estimation of Dynamic Conditional Correlations of Shariah-Compliant Stock Indices through the Application of Multivariate GARCH Approach

Abstract

A major issue in both Islamic finance and conventional finance is whether the shocks to the volatilities in the asset returns are substitutes or complements in terms of taking risk. An understanding of how volatilities of and correlations between asset returns change over time including their directions (positive or negative) and size (stronger or weaker) is of crucial importance for both the domestic and international investors with a view to diversifying their portfolios for hedging against unforeseen risks. This study is the first attempt to advance the frontier of knowledge particularly in the fast growing field of Islamic Finance through the application of the recently -developed Dynamic Multivariate GARCH approach. We analyze the daily returns of five Shariah-compliant stock indices (such as, FTSE Shariah China Index, FTSE Shariah India Index, FTSE Sharia USA index, FTSE Malaysia EMAS Shariah Index and Dow Jones Shariah Index) covering the period from 26 October 2007 to 9 March 2011. Our study is focused on investigating the following empirical questions: (i) Are the time-varying volatility parameters of these five Shariah-compliant stock indices significant and decaying? (ii) Are these dynamic parameters mean-reverting? (iii) Are these dynamic conditional volatilities of Shariah indices and dynamic conditional correlations between Shariah indices changing? Our findings based on the maximum likelihood estimates of dynamic conditional volatilities and dynamic conditional correlations tend to suggest: (i) the time-varying conditional volatility parameters of all these Shariah-compliant stock indices are highly significant with most of their estimates very close to unity implying a gradual decay in volatility (assuming both the Gaussian and 't' distributions). Of the two distributions, however, the t-distribution appears to be more appropriate in capturing the fat-tailed nature of the distributions of asset returns (ii) a test of 'no mean-reversion of volatility parameters' of all these Shariah indices is rejected in all cases with the results showing a slow but significant mean reverting volatility of all Shariah indices excepting FTSE Shariah China index which decays faster than others after any shock to its volatility and finally (iii) dynamic conditional volatilities and conditional correlations of all these Shariah indices are not constant but are changing and time-varying. There is relatively low and even at times negative dynamic conditional correlation between FTSE Shariah China index and FTSE Shariah USA index with strong policy implications for the domestic and international investors in their portfolio diversification for hedging against unforeseen risks