A Multivariate Garch Analysis of International Value and Growth Equity Returns and Volatility

INTRODUCTION Recent advances in autoregressive conditional heteroskedastic (ARCH) and generalized autoregressive conditional heteroskedastic (GARCH) models allows to study the conditional volatility of stock markets and ascertain the predictability of future stock return volatility conditional on past volatilities and return shocks [see, for instance, Tse and Zuo (1996), Aggarwal et al. (1999), Adrangi et al. (1999) and Huang and Yang (2000)]. A few studies have even extended these to the multivariate case [see, for example, Tse (2000) and Tay and Zhu (2000)]. However, relatively few studies have applied asymmetric GARCH models to the international value and growth indexes. And even when these models are applied in a broader context (that is, along with North American and European markets) there is generally an emphasis on broad indexes. As far as the author is aware, no study to date has examined the risk-return relation between growth and value stocks separately. DATA AND SUMMARY STATISTICS The data employed in the study is drawn from Morgan Stanley Capital International (MSCI) and encompasses the period monthly returns from January 1997 to October 2007. MSCI indices are widely employed in the literature on equity market comovements and volatility on the basis of the degree of comparability and avoidance of dual listing [see, for instance, Meric and Meric (1997), Yuhn (1997), Roca (1999) and Cheung and Ho (1991)]. In this study, monthly returns of fifty international value and growth equity markets from 1994 to 2007 have been used. Even though, it has been argued that return data is preferred to the lower frequency data such as weekly and monthly returns because longer horizon returns can obscure transient responses to innovations which may last for a few days only (Elyasiani et al. 1998: 94). However, Roca (1999: 505), amongst others, has countered that ...daily data are deemed to contain 'too much noise' and is affected by the day-of-the-week effect. Another reason for using monthly data is that with daily data from many countries, the trading hours generally are in different time zones it is not possible to implement directly a portfolio strategy of buying one market at trading time, t, and selling it at the close of trading time t + 1.In addition, most of international asset pricing modes monthly data to measure the stock returns. Table 1 presents descriptive statistics for each return series for the period 1997 to 2007. Samples means, medians, maximums, minimums, standard deviations, skewness, kurtosis and the Jacque-Bera statistic and p-value are reported for the monthly returns. The highest mean returns are in Finland growth (1.492%), Austria value (1.353%), Denmark value (1.15%), France value (1.01%) and finally Italy with 1.00%. Monthly returns are also higher on average across the Asian-Australian markets (7.183%) than in the European markets (6.698%) and North American countries of Canada and USA (6.047%). As anticipated, volatility (as measured by standard deviation) is on average higher among the Asia-Australia markets (Singapore growth index 10.81% and Hong Kong value index 9.59%) in comparison with the European and North American markets. However, the highest volatility (13.1%) is exhibited by Finland growth index. A visual perspective on the volatility of returns can be gained from the plots of monthly returns for each series in Figure 1. These findings are in accordance with international analysis of equity returns and volatility by Erb et al (1996). The distributional properties of the return series generally appear to be non-normal. All of the markets have negative skewness with the exception of Finland value, Hong Kong value, Italy growth and Japan value. Positive and/or negative skewness in Asian equity returns have been documented by Huang and Yang (2000) and Tay and Zhu (2000), amongst others. The kurtosis, or degree of excess, in all markets, except Austria growth, Australia growth, Japan value and growth, Switzerland growth and United Kingdom growth have exhibited a leptokurtic distribution. …

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