Four Essays On Building Conditional Correlation Garch Models

1. Introduction

China’s economic reform, which began in the late 1970s, has been accompanied by the development of a modern financial system to allocate financial resources from savers to investors and to attract foreign capital. One important component of such a system is a vibrant and dynamic equity market. China’s current equity market consists of two stock exchanges—the Shanghai Stock Exchange (SSE) and the Shenzhen Stock Exchange (SZSE).

The Shanghai stock exchange was re-established on 26 November 1990 and was in operation on December 19 of the same year. 1 It has become the most preeminent stock market in mainland China and the world’s sixth largest stock exchange by market capitalization at U.S. $2.3 trillion as of December 2011. The Shenzhen stock exchange (SZSE) was established on 1 December 1990 and had a market capitalization of about U.S. $1 trillion in 2011. Both exchanges are subject to tight capital controls and are only partially open to foreign investors. International investors, including residents of Hong Kong, Macau and Taiwan, can participate only in the trading of B shares. 2 The Shanghai Stock Exchange composite index (SH) and Shenzhen Stock Exchange composite index (SZ) are indicators of the performance of mainland China’s stock market.

This study will examine the dynamic relationships among the two stock exchanges of mainland China, Hong Kong and the United States using daily data from 2 January 2001 to 8 February 2013. The primary purpose of the investigation is to explore the possibility of spillovers in return, as well as in conditional volatility across these four markets. The results of this investigation may have important implications regarding international investment, portfolio diversification and risk management.

The Hong Kong Stock Exchange (SEHK) is Asia’s second largest stock exchange in terms of market capitalization and the fifth largest in the world. The Hang Seng index (HK) is a weighted average of equity prices for 48 companies traded in SEHK. It represents about 60% of the capitalization of SEHK and serves as a proxy for its performance. We represent the U.S. equity market by the S&P 500 index (SP), which is based on the market capitalization of 500 leading companies publicly traded in the U.S. stock market.

Several studies have addressed the transmission of return and volatility shocks across equity markets. Earlier studies on the subject have focused on developed markets. King and Wadhwani [1] and Hamao, Masulis and Ng [2] both examine the transmission of volatility across the London, New York and Tokyo markets. Hamao, Masulis and Ng’s [2] application of the ARCH model reveals unidirectional volatility spillovers from New York to London and Tokyo and from London to Tokyo. King and Wadhwani [1] find that the correlation between markets rises following an increase in volatility. Bae and Karolyi [3] investigate spillovers in volatility between Japan and the U.S. using three asymmetric GARCH models (GARCH, PNP-GARCH and GJR-GARCH). 3 Their findings suggest bidirectional relations in volatility between the two markets. Furthermore, bad news tends to have a much larger impact on subsequent return volatility than good news. Karolyi [4] provides additional evidence on the short-run relation between stocks traded in the U.S. and Canada using four alternative models (vector autoregressive (VAR), multivariate generalized autoregressive conditional heteroscedasticity (MGARCH)-BEKK, MGARCH-CCC and the univariate GARCH model). 4

Following the Asian financial crisis of 1997, several studies have explored the possibility of contagion across Asian stock markets. Worthington and Higgs [5] investigate the transmission of stock return and volatility in three Asian developed markets (Hong Kong, Japan and Singapore), as well as six Asian emerging markets (Indonesia, Korea, Malaysia, the Philippines, Taiwan and Thailand). Broadly speaking, their results suggest that all Asian equity markets are highly integrated, though the spillovers are not homogeneous across markets.

More recently, a limited number of studies have explored the potential linkage between stock markets of mainland China and other markets. Poon and Fung [6] examine the relationships among Hong Kong’s H share, red chips and China’s Shanghai and Shenzhen composite indexes. 5 They find significant return transmissions from the red-chip market to the Shenzhen market, from the Shenzhen market to the Shanghai market and from the Shanghai market to the H-share market. They also find volatility spillovers from the red-chip market to the other markets. Joshi [7] examines the return and volatility spillovers among Hong Kong, China and four other Asian stock markets (India, Japan, Indonesia and Korea). His results suggest bidirectional return spillovers between mainland China and Indonesia and bidirectional volatility spillovers between China and each of Japan, Korea and Indonesia.

Although stock market integration has been widely studied, research on the international linkages of the Chinese stock exchanges is rather limited. Bailey [8] is one of the earliest studies on the relationship between China and international stock markets. However, the results of his investigation reveal that return on China’s B shares has little or no correlation with international equity returns. Wang and Firth [9] investigate the correlation of return and volatility between Greater China’s four stock markets (two mainland China’s exchanges, Hong Kong and Taipei) and three major international financial markets (Tokyo, London and New York stock exchanges). Their results suggest that the returns in mainland China’s two stock markets are influenced mostly by the regional developed markets (Hong Kong and Taipei). They also find that mainland China equity markets are relatively segregated. Li [10] examines the relationship among the stock markets of mainland China, Hong Kong and the U.S. His findings also indicate a unidirectional volatility spillover from Hong Kong to mainland China, but no direct linkage between mainland China and the U.S. market. Lucey and Zhang [11] investigate the role of cultural distance on the integration of financial markets. 6 Their examination of 46 stock markets suggests that country pairs tend to exhibit higher linkages if they have smaller cultural distance.

The prevailing evidence from previous studies suggests that China’s stock markets have been fairly isolated from global markets since their establishment. However, the degree of stock market integration has changed over time. Following the 1997 Asian financial crisis, the two markets have become more integrated with local emerging and developed stock markets, but the integration with Western stock markets has remained weak.

This study reexamines the short-run relationships in return and volatility among the equity markets of the U.S., Hong Kong and the two mainland China (Shanghai and Shenzhen). We use a VAR model to explore the causal relations among the returns of these four markets. To examine the possibility of volatility spillovers, we use three alternative multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) models: the BEKK model of Engle and Kroner [13], the constant conditional correlation (CCC) model of Bollerslev [14] and the dynamic conditional correlation model of Engle [15]. Our study makes three contributions to the existing literature: First, it investigates the relationship among these markets using the longest available sample period, which covers 2 January 2001 to 8 February 2013. Second, to allow for a comparison of returns and risks across markets, it adjusts the stock returns to reflect changes in the exchange rate for each country. This is a useful exercise for an international investor who is concerned with portfolio diversification. Third, it investigates the possibility of volatility spillovers using three alternative MGARCH models—the BEKK, the CCC and DCC models. Thus, it allows for a richer set of dynamics among stock returns. The BEKK model is very popular in the previous studies related to China [5,7,10]. However, it is not parsimonious, as it requires the estimation of too many parameters. The CCC and DCC models contain fewer parameters; and the DCC model allows time-varying correlations. However, no previous study has applied these two models to Chinese data.

The results of our investigation can be summarized as follows: (1) the VAR findings suggest unidirectional spillovers in returns from the U.S. to the other three markets, but a lack of spillovers between mainland China and Hong Kong; (2) evidence of unidirectional ARCH and GARCH spillovers in volatility from the U.S. to the other three markets using the BEKK model; (3) evidence from the CCC model suggesting that mainland China’s two stock markets are highly correlated, with an average correlation of 93.5%. The correlations between mainland China’s two markets and the Hong Kong market remain around 30%, while the correlations between mainland China’s two markets and the U.S. are still low, with averages of 6.4% and 7.2%, respectively. Thus, international investors can benefit from diversification by allocating their assets in China’s equity markets. (4) The patterns of the dynamic conditional correlations from the DCC model suggest an increase in correlation between China and the other stock markets since the most recent financial crisis of 2007.

The remainder of this paper is organized as follows: Section 2 addresses the empirical methodology and introduces the VAR and the three MGARCH models used in the investigation. Section 3 presents the data along with their descriptive statistics. Section 4 reports the estimation results, and Section 5 concludes.

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