*The Independence of Indexed Volatilities DOI: http://dx.doi.org/10.5772/intechopen.90240*

shocks. The latter proposition is about how institutional demand increases for all assets are positively correlated with index, especially demand for commodity storage.

The results for [14] illustrated those volatilities in futures markets do spillover into other commodities. Further, there is a trade-off between investors due to relative performance fluctuates. The latter phenomenon is consistent with what is illustrated by VIX volatility index [14]. In addition, the model information is 'asymmetric and investors have the same beliefs'.

In [15], excess co-movements of commodity prices in developed (118 variables from Australia, Canada, France, Germany, Japan, the UK and the U.S.) and emerging markets (six variables from China, Brazil, Brazil, Taiwan, Mexico, etc.) were investigated. They argue that prior studies illustrate that financialization in the commodities markets lead to excess price volatility. One possible reason for that is that commodities especially of currency nature such as gold are characterised by spikes in prices. Central to their investigation is that (i) co-movements imply that 'demands and supplies are affected by unobserved forecast of the economic variable' and (ii) portfolio management strategies are affected by co-movements. The latter phenomenon resonates with this study. The variables that [15] are (i) the U.S. index of industrial production, (ii) consumer price index (CPI), (iii) effective \$US exchange rate, (iv) three-month Treasury bill interest rate, (v) M1 monetary measure and (vi) S&P500 stock index.

One thing which is evident in [15] is that they are dealing with a large database which has numerous variables. And in order to probably account for those variables, you need a model that accounted for such variables. For the commodity prices, they used wheat, copper, silver, soybeans, raw sugar, cotton, crude oil and live cattle. Further, arbitrariness and computational difficulties should be minimised. One of the ways of how to avoid arbitrariness and computational difficulties is to use principal component analysis (PCA) and stepwise regression, although stepwise is time consuming when one uses many variables. In their analysis [15] focused on filtering commodity returns using large approximate factors models. And for that [15] used (i) static factor model and (ii) ARCH-LM for illustrating spillovers and (iii) SUR model to test whether residuals are unrelated.

The preliminary analysis of [15] the skewness of all commodities except of wheat is negatively skewed. Thus, wheat should have high volatilities than the rest of the commodities. And the Jarque-Berra test confirms non-normality for all commodities. The latter illustration is consistent with other studies on commodities. The correlation matrix shows that all commodities are correlated with one another except with live cattle. That is, live cattle in when compared with the seven commodities might offer diversification benefits. The results of returns show that crude oil and copper are costly correlated with variables of emerging markets. Monetary measures have more influence in emerging markets than developed countries. When they test for excess co-movement of commodity returns, results exemplify that commodity co-movements are common and influencing across all markets. Moreover, those co-movements are sampling dependent. In [15], it stated that given that the speculation is rife in commodity markets, some co-movements might be driven by speculation. The OLS model confirms the presence of endogeneity.

### **2.3 Equities**

The Black Monday of October 1987, the U.S. born global financial crisis of 2008 and 2009, as well as the European debt crisis that occurred in late 2009 are known as the some of the few financial crisis in the past three decades that have resulted in the volatility of financial markets and further resulted in wide spread international

crisis. These are known as co-movements of financial markets defined as volatility spillovers from one market to another. Volatility spillover studies have come to the vanguard as they are largely associated with risks that have implications on (i) optimal portfolio construction, (ii) financial stability and (iii) implementation of policies that may render harmful shock transmissions in financial markets. Recent studies that address the issue of volatility dynamics indicate that volatility spillover effects among countries or financial markets are time varying, most importantly during times of crisis. This has particularly significant consequences for investors and policy makers. Consequently, understanding the changing aspects of volatility spillovers is imperative.

2005–2010. The study employs a multivariate VAR-EGARCH framework and finds that Nigeria is the dominant in volatility transmission to Ghana, Kenya and South Africa and while it is not a receiver of volatility from these markets. The study however finds that the domestic volatility indices of these markets are the highest coefficients for all these markets, which implies that domestic shocks may impact

In [2], it was positioned that a more effective way of better understanding efficient asset pricing, volatility forecasting, efficient cross-market allocation and hedging decisions along with optimal international portfolio strategies is through understanding the stock market dynamics and volatility spillover effects of listed asset sectors individually in particular markets. Several literatures have focused on volatility spillovers in financial markets on a global, regional and country level. This section particularly focuses on volatility spillovers among equity stocks in financial markets. Cross-market volatility linkages in global developed equity markets attracted much attention in research. An earlier study of [18] studied the return volatility dynamics and transmission among the G-7 countries' equity markets using both the GARCH and VAR models. They find that while in these markets, domestic market shocks are the largest single source of domestic volatility variation for other markets, (apart from the U.K. and U.S.) shocks to foreign markets account for a significant portion of domestic market volatility. The study provides empirical evidence of volatility spillover effects in the equity markets of these industrialised countries. The results also indicate that volatility spillovers in these equity markets

for this period had significant changes due to the global financial crises.

of shock transmission and reception during turbulent times.

**2.4 Listed real estate**

investigated.

**135**

that are net transmitters of risk and others are net receivers of risk in global financial markets. The study particularly analyses the global financial shifts of volatility spillovers by employing the [20] forecast-error variance decomposition and incorporating a Markov switching framework which considers economic regime changes, into the generalised vector autoregressive (VAR) model. The study uses the following daily stock market volatility indices as proxies of market risk; the VIX (S&P 500 volatility, U.S.), VFTSE (FTSE 100 volatility, U.K). VCAC (CAC 40 volatility, France), VDAX (DAX 30 volatility, Germany). VAEX (AEX 25 volatility Netherlands), VSMI (SMI 20 volatility, Switzerland), VHSI (HIS 50 volatility, Hong Kong) and JNIV (Nikkei 225 volatility, Japan) for the period 2001 to 2017. The results of the study support the theory of shock transmissions and volatility spillovers by finding that all markets are more intense and are at the frequent risk

Studies such as [19] find that during tranquil times there are particular countries

The co-movement of real estate stocks and financial markets has been studied extensively. Previous literature has documented the theory that low correlation of an asset with other capital markets, international and domestic portfolios provides the opportunity for risk reduction and diversification in an investment [21]. In [22], the local, regional and global linkage of securitized real estate and stock markets and possible integration in nine developed markets from the three regions of North America (the U.S.), Europe (Germany, France, Netherlands and the U.K.) and Asia-Pacific (Japan, Hong Kong, Singapore and Australia) in the period 1990–2011 were

The study employs the spillover index of [20] that produces variance decompositions that are insensitive to variable ordering by allowing correlated shocks and historically observed distribution of the errors to account for the shocks. The spill-

over index is further based on a multivariate VAR that can capture market

these markets more than external shocks.

*The Independence of Indexed Volatilities DOI: http://dx.doi.org/10.5772/intechopen.90240*

In [16], both implied and realised volatility linkages were analysed through a rolling correlation analysis across global equity markets. This covers the U.S., European, German, Japanese, and Swiss markets during the sample period of 1999 to 2009. Implied volatility indices provide information regarding future uncertain expectations of stock price movements. Using the VAR method, the study indicates that both unconditional and conditional correlations for implied and realised volatility exhibit large fluctuations during that sample period. These results coincide with market fluctuations that occurred during the period of the global financial crises.

The consensus emerging from literature on asset co-movements is that asset markets are linked internationally, and volatility is transmitted from one market to another. Earlier studies of market linkages were habitually focused on developed countries however due to the financial liberalisation and trade openness of emerging economies, research has also focused on investigating cross-border links in emerging economies from developed countries. Emerging markets have increasingly played an important role in financial markets and were not spared from the impact of the global financial crisis. A better understanding of how emerging markets respond to exogenous shocks can assist investors and portfolio managers better understand if there are any diversification possibilities.

On another standpoint [2], volatility spillover effects were identified on a sectorial basis (industrial and financial sectors) from the U.S. as a developed country to BRICS nations as emerging markets using a VAR(1)-GARCH (1,1) framework. In the industrial sector, overall results indicate that the volatility transmission from the U.S. predominantly affects Brazil, Russia and India, while in the financial sector; it predominantly affects Brazil and Russia. In [17], the volatility impact is also indicated from developed markets by looking at regional spillovers across transitioning emerging markets and frontier equity markets, particularly in the Middle East and Africa together with the U.S. as the developed market. The study examines the stock markets of Saudi Arabia, UAE, South Africa and Israel from the period of 1994 to 2010 using a multi-timescale analysis using a wavelet-based time and frequency distributions compositions. The study finds that the Middle Eastern countries were more susceptible to the U.S. subprime crisis as compared to South Africa, however indication of short-term shocks that produced additional vulnerability in the South African equity market prior to the global financial crisis are noted, which could have potentially been due to investor sentiment.

Despite the increased studies of volatility spillover analyses from developed to emerging markets, there continues to be limited cross-market studies that are undertaken in equity markets of emerging nations. The possible integration of emerging markets continues to be of great concern as theory suggests that expected returns might be expected to reduce, following a greater integration of emerging markets in the world economy. Ref. [8] contributes to the empirical literature of volatility spillover dynamics between equity markets by examining the returns and volatility dynamics of Ghana, Kenya, Nigeria and South Africa for the period
