Asymmetric effects and long memory in dynamic volatility relationships between stock returns and exchange rates

Abstract

We use univariate and multivariate GARCH-type models to investigate the properties of conditional volatilities of stock returns and exchange rates, as well as their empirical relationships. Taking three European stock markets and two popular US dollar exchange rates as case study, our results show strong evidence of asymmetry and long memory in the conditional variances of all the series considered. In multivariate settings we find that bilateral relationships between stock and foreign exchange markets are highly significant for France and Germany. Moreover, both the univariate FIAPARCH and bivariate CCC-FIAPARCH models provide more accurate in-sample estimates and out-of-sample forecasts than the other competing GARCH-based specifications in almost all cases. Finally, there is evidence to support the suitability of the FIAPARCH model in forecasting portfolio's market risk exposure and the existence of diversification benefits between stock and foreign exchange markets.

Introduction

Modeling stock market volatility has been an important focus of the empirical finance literature over the past three decades. Among the proposed models, GARCH-family processes are the most popular specifications, given their ability to capture stylized facts of financial time-series such as volatility clustering and persistence (Engle, 1982, Bollerslev, 1986). While the standard GARCH model seems to be suitable for modeling and forecasting volatility dynamics, recent studies pay more attention to alternative specifications allowing for asymmetric reactions to shocks and long memory because the latter are the other important distributional features of financial variables. For instance, Baillie et al. (1996) proposed the fractionally integrated GARCH (FIGARCH) model which explicitly accommodates long memory characteristics in the conditional variance process. Such a model fits best to series that exhibit long temporal dependence and slowly decaying autocorrelation functions. Using an asymmetric power ARCH approach, Tse (1998) extends the FIGARCH process to the FIAPARCH process in order to jointly capture asymmetry and long memory features in conditional volatility.

Several new extensions of the traditional FIGARCH have recently been developed. Baillie and Morana (2009) propose the adaptive FIGARCH model (A-FIGARCH), which accommodates both long memory and structural change in the conditional variance process. Their simulation experiments as well as empirical application to stock market data provide evidence that the A-FIGARCH model outperforms the standard FIGARCH model when structural change is present. Christensen et al. (2010) suggest that the FIEGARCH-in-mean model generates more accurate estimates and forecasts than the standard GARCH-type specifications. Kiliç (2011) extends the FIGARCH model to a smooth transition FIGARCH (ST-FIGARCH) model to account for long memory and nonlinear (smooth regime switching) dynamics in the conditional variance. Applying this model to study the volatility dynamics of exchange rate and stock market returns, the author finds that it has greater forecasting ability than the standard FIGARCH model.

The FIGARCH and FIAPARCH processes have been applied to stock market returns by various studies (see, e.g., Beine et al., 2002, Kang et al., 2009). For example, Degiannakis (2004) uses the FIAPARCH model to examine the main characteristics of conditional volatility in three European stock markets and documents that extended ARCH processes generate more accurate volatility forecasts of stock returns. Kasman et al. (2009) investigate the long memory propriety of stock market returns in eight Central and Eastern European countries. Their results provide evidence of dual long memory in both the conditional mean and variance for considered markets. More recently, Kang et al. (2010) test whether long memory is present in Chinese stock market returns and find that the FIGARCH (1,d,1) model has superior performance compared to the GARCH and IGARCH models.

Empirical literature using multivariate FIGARCH and FIAPARCH frameworks is somewhat less extensive. Brunetti and Gilbert (2000) adopt a bivariate ECM-FIGARCH model to study the volatility of crude oil future contracts traded on the New York Mercantile Exchange (NYMEX) and London International Petroleum Exchange (IPE). They find that the two markets are fractionally cointegrated. Conrad et al., 2011a, Conrad et al., 2011b estimate univariate and multivariate versions of the FIAPARCH model for stock market returns in eight countries and find that this multivariate setting is applicable once power, leverage and long memory effects are taken into consideration. Further, their multivariate FIAPARCH specification provides higher forecast accuracy than other models such as APARCH and IAPARCH.

This paper also uses the GARCH-class models to address three important research questions. First, the persistence, long memory and asymmetric effects in the conditional volatility of daily returns on stock market indices and exchange rates are evaluated by three univariate volatility models, namely the GARCH, FIGARCH and FIAPARCH models. Second, the multivariate versions of these models are estimated to examine the empirical relationships between stock returns and exchange rate movements. Most of previous papers considering this question have not taken asymmetry and long memory characteristics into account (Kanas, 2000, Yang and Doong, 2004, Aloui, 2007, Mun, 2007). Finally, forecasting performance is compared across different competing models in order to know whether volatility models accommodating asymmetries and long memory perform better than the others. Empirical results from our bivariate analysis are of great interest to investors as they can be used to build optimal portfolio designs and hedging strategies between stock and foreign exchange markets following for example the approach suggested by, among others, Arouri et al. (2011).

The remainder of this paper is organized as follows. Section 2 presents the theoretical background explaining the potential linkages between stock and foreign exchange markets. Section 3 discusses the GARCH-type models. Section 4 describes the sample data and their statistical characteristics. Section 5 discusses the estimation results of univariate and multivariate GARCH models and their implications for portfolio's risk management. Section 6 provides some concluding remarks.