“Return and volatility spillovers between FTSE All-Share Index and S&P 500 Index”

This paper explores the effect of the return and volatility spillover between the Standard and Poor’s 500 index and FTSE All-Share index using the AG-DCC_ Dynamic Conditional Correlation model over the sample period from April 1995 to April 2019. It demonstrates that the Standard and Poor’s 500 return and volatility are crucial in forecasting the market’s future dynamics of the FTSE All Shares where it finds a sig- nificant spillover effect for both return and volatility from the Standard and Poor’s 500 to FTSE All Shares, while weak evidence has been found in the opposite direction, that is, an insignificant spillover effect for both return and volatility from FTSE All Shares to the Standard and Poor’s 500. In addition, the paper also finds high Dynamic Conditional Correlation (DCC) between both the Standard and Poor’s 500 and FTSE All Shares. Therefore, it finds asymmetric correlation and transmission mechanisms between the Standard and Poor’s 500 and FTSE All Shares, which means there is an asymmetric interconnectedness between two markets, so allocating assets between two markets will not benefit investor portfolios as investing in high-yielding shares do. strategic investment allocation and market positioning. Thirdly, considering volatility interconnectedness might ameliorate the calculating of conditional volatility that is important for specific financial applications like options pricing, risk valuation, optimizing portfolios, and hedging against several kinds of risk. In addition, many papers investigate returns and volatility using the popular time series models. Recent studies cover most aspects of this transmission. Umar et al. (2013) handle the relation between return and the spillover of volatility and oil prices. Malik (2021) links this relation with exchange rates, while Geng et al. (2021) measure it across global energy firms. Most studies try to measure the return and spillovers? between developed stock exchanges (efficient) and developing stock exchanges (inefficient) and vice versa to capture the transmission of global shocks. This study tries to capture the traded transmission among the developed stock exchanges.


INTRODUCTION
There are many reasons for the importance of return spillover and volatility between stock markets. Firstly, it disseminates information regarding the market's efficiency. Return prediction in an efficient market with no risk premium is difficult using the conditional lagged return in another similar marketplace. And then, the existence of a significant transmission means that there is a global trading chance that could be taken advantage of to earn abnormal returns. This is proof that the markets are inefficient. Second, the impact of spillover effects on returns and volatilities might assist with managing portfolios, especially in the areas of strategic investment allocation and market positioning. Thirdly, considering volatility interconnectedness might ameliorate the calculating of conditional volatility that is important for specific financial applications like options pricing, risk valuation, optimizing portfolios, and hedging against several kinds of risk. In addition, many papers investigate returns and volatility using the popular time series models. Recent studies cover most aspects of this transmission. Umar et al. (2013) handle the relation between return and the spillover of volatility and oil prices. Malik (2021) links this relation with exchange rates, while Geng et al. (2021) measure it across global energy firms. Most studies try to measure the return and spillovers? between developed stock exchanges (efficient) and developing stock exchanges (inefficient) and vice versa to capture the transmission of global shocks. This study tries to capture the traded transmission among the developed stock exchanges.

LITERATURE REVIEW AND HYPOTHESIS
Many researchers have studied the volatility and return spillovers and the interconnectedness between global markets. Diebold and Yilmaz (2009) examine the interconnectedness between 9 global equity markets; they measure spillovers in terms of return and volatility across these stock exchanges and find strong evidence of divergence in the dynamics of return spillovers versus volatility spillovers (asymmetric) where the return spillovers show a gradual increasing pattern, while volatility spillovers show a strong effect but with no clear pattern. With regard to the U.S. market, Diebold and Yilmaz (2012) estimate the directional and the total volatility spillovers between different US markets using a generalized vector autoregression. They employ a daily observation from 1999 to 2010 of foreign exchange, stock, commodities, and bond markets. They find a significant spillover of volatility in all 4 markets. But the strongest spillover of volatility was seen from equity exchange towards other financial markets in September 2008, just after the Lehman Brothers bankruptcy.  2019) investigate the extent and evolution of the links between energy markets using broad data, they find that in the energy markets within and across sectors effects of the volatility spillover do exist, and the nature of those markets that are exporters of volatility to other markets.
With regard to the USA, UK, and Japan, Hamao et al. (1990) show a volatility spillover from NYSE and London stock exchange to the Tokyo stock exchange. More importantly, Lin et al. (1994) try to prove that spillovers often change over time between the Tokyo stock exchange and NYSE, they find a relationship in the two directions between daytime returns and overnight returns. This paper tries to fill up an important gap in the literature by testing the volatility and return spillovers between the two biggest markets in the world, the Standard and Poor's 500 and the FTSE All Shares, because those markets are considered the main sources of transmitting the volatility and return spillovers to other global markets. To the best of the author's knowledge, nobody tried to examine the bidirectional relationship of transmitting the volatility and return spillovers between the two markets. To that end, this paper tests the return and volatility spillover effects between two markets using the Dynamic Conditional Correlation (DCC) model proposed by Engle (2002).
Following the literature, the paper expects the following hypothesis: H1: The mechanics of return and volatility transfer among the index of Standard and Poor's 500 and the index of FTSE All Shares is asymmetric (return and volatility from the Standard and Poor's 500 index to the FTSE all-shares index have considerable spillover effects). The price indices are presented in Figure 1 and Figure 2 for S&P 500 Index and FTSE All-Shares Index respectively. The two indices, as seen in the graphs, move in comparable directions and have similar long-term associations. It also indicates a significant increase at the start of 2005. The rise in oil prices aided this boom,

Regression models
To study the return and volatility spillovers between indices, this paper employs the other index's lagged returns and volatilities in the mean and variance formula of every index, the index of Standard and Poor's 500 and the index of FTSE All Shares. The methodology included the first lag of results from the Standard and Poor's 500 to highlight spillover effects in the FTSE All-share index. As a result, the following conditional mean model with spillovers from a specific market will be as follows: Monthly results using the Vector Autoregressive (VAR) process: the market performance can be measured by a parameter. In other words, a significant parameter means that the return spillover impact from index j to index i is confirmed.

Dynamic Conditional Correlation (DCC) model
The AG-DCC model, first introduced by Engle (2002), is a multivariate GARCH model that resolves computing problems and permits asymmetry.
where R t is a conditional correlation matrix that changes over time. Here is the standardized error' variance-covariance matrix.

Skewness and kurtoses
Bono et al. (2019) elucidate that skewness is a way of measuring symmetry, or rather, the absence of it. A distribution is considered to be symmetric if it appears identical to the left and right of the midpoint. In relation to normally distributed data, kurtosis is a statistical technique that determines how huge or light-tailed a set of data is. Data with a high kurtosis are more likely to contain big tails. Small tails are common in data sets with low kurtosis. Table 3 reports the two return series of both indices skewness and kurtosis with its P-value, Standard and Poor's 500's return series is skewed to the left (-0.081) with zero P-value. In addition, FTSE All Shares' return series is more skewed to the left (-0.178) with zero P-value as well. This could lead us to conclude that the return of both standard and poor's 500 and FTSE all shares indices are asymmetric. Moreover, the two series are experiencing kurtosis, it is obvious with zero P-value for both series and with a coefficient

Return normality
The Jarque-Bera test, which has acquired widespread acceptability among econometricians, is one of the most well-known tests for normalcy. The Jarque-Bera test statistic is a function of the sample's calculated skewness and kurtosis values.
The theoretical values of skewness and kurtosis under normalcy are 0 and 3, respectively. This examination assumes that the null hypothesis ensures the distribution of returns is normal, the alternative hypothesis assumes that the returns are not normally distributed. Thus, Table 4 shows

Ljung-Box Q examination of the serial correlation (Autocorrelation)
In time series analysis, autocorrelation is a popular way to assess serial dependency. Researchers construct sample autocorrelations and use Ljung and Box (1978) to examine the combined importance of these statistics to better understand the dependency structure of time series data. The volatility clustering effect is a term used in financial time series analysis to describe the need of checking serial correlations of series. The null hypothesis of this test assumes that the series of the returns are serially correlated, while the alternative hypothesis affirms the nonexistence of autocorrelation.    Return and volatility spillovers are a topic that is intensively researched and widely discussed amongst stock markets. In addition, the relationship between stock markets and exchange rates, oil prices, cryptocurrency, and bond markets was investigated. The amount of information available on the connectedness in term of returns and volatility spillovers between bond markets and cryptocurrency is currently limited, and future research projects examining these connections might be fruitful. Table 7 reports positive and highly significant estimated coefficients, which means positive and highly significant spillovers from the S&P 500 index to the FTSE All-Share index in terms of conditional mean in Panel 1 and conditional variance in Panel 2, meaning that the mechanics of return and volatility transfer among the index of Standard and Poor's 500 and the index of FTSE All-Share is asymmetric (return and volatility from the Standard and Poor's 500 index to the FTSE All-Share index have considerable spillover effects, which affirms the hypothesis that suggests the asymmetry and strong volatility and return spillovers from the Standard and Poor's 500 index to the FTSE All-Share index); this result is consistent with Maghyereh and Awartani (2012)

CONCLUSION
The positive and asymmetric spillovers of both return and volatility between the Standard & Poor's 500 index and the FTSE All-Share index are explored in this paper. Positive and asymmetric spillovers from the US market to the UK market are reported in the paper, as predicted. In addition, because the US market dominates the UK markets, the US return stock index sends conditional mean and volatility spillovers to the UK markets. These findings have significant implications for investors and portfolio managers who are investing in both markets at the same time, where diversification is of limited value. Investing in high-yielding equities, on the other hand, is given greater credit. Furthermore, the findings of this paper are important for policymakers in both markets, because market asymmetry raises the risk of insider trading and arbitrage, particularly in the UK market. Future study might offer insight on the spillovers between different asset classes inside the same market, rather than across markets. Moreover, studying connectedness is dependent on risk level, i.e. comparing low-risk and high-risk instruments.  Note: *, ** and *** indicate test statistically significant at 1 percent, 5 percent, and 10 percent, respectively.