**2.4 Listed real estate**

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 investigated.

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

fluctuation of more than two countries concurrently rather than bivariate models. Liow [22] finds evidence of the following: (i) time-varying return co-movement and volatility spillovers in all markets and positive association with the global financial crisis (ii) a bi-directional and regime-dependant relationship of crossvolatility spillover effects, (iii) synchronisation between co-movements of volatility spillovers and correlation spillover cycles. Liow [23] studied time-varying comovements of Asian real estate and the linkages of local, regional and global stock markets over the period of 1995 to 2009. Correlations of assets are interpreted to indicate co-movement and integration across financial markets. The integration of markets is also interpreted to indicate interdependence of markets which can lead to transmission crises.

finding significant mean-volatility linkages under different volatility regimes. Consequently, this has implications on diversification benefits that these markets

The weekly data is for the five BRICS countries (general equities, real estate, commodities and bonds) for the period 1 January 2007–31 December 2017 obtained from Bloomberg. The out-sample is from 2007 to 2017 and in-sample from 2012 to 2017. The in-sample is for parameters estimation and out-sample for evaluating forecasting performance. The use of weekly data ameliorates concerns over nonsynchronicities and bid-ask effects in daily data [13]. The phenomenon of using returns to illustrate the descriptive nature of volatility spillovers is synonymous with [6, 27]. The returns are logarithm returns and they are consistent with VAR model. All returns are calculated based on the indices of those countries. The indices are as follows; (i) general equities, Brazil IBRX 50 for Brazil, Moex Russian index for Russia, Nifty 50 for India, SSE50 for China and JSE top 40 index for South Africa, (ii) listed real estate, IMOB for Brazil, for Russia the index is created based on PIKK Group, PJSC LSR Group, World Trade Centre 'ordinary shares' and World Trade Centre 'preferred shares' because Russia does not have a listed real estate index-the market capitalisations of those firms where aggregated over time, Nifty Realty for India, SHROP for China and all Property index (J803) for South Africa, (iii) commodities, BM&F BOVESPA for Brazil, MICEX Oil and Gas Index-from the Moscow exchange for Russia, Nifty Commodities for India, CCI for China and JCGMSAG (gold mining index) for South Africa and (iv) bonds, for Brazil-Brazil 8 7/8 04/15/24 bond, Russia-RFLB 08/29/18 bond, India-Nifty 10 yr. benchmark, China-GT USDCN 15yr bond and South Africa-SAGB 10 ½ 12/26 bond. Skintzi and Refenes [28] used indices to investigate regional and country shocks. This article is the first one that uses indices to illustrate shocks in the BRICS countries. According to [28], one of the advantages of modelling volatility shocks using indices is that

can offer.

**3.1 Data**

**Figure 1.** *BRICS log returns.*

**137**

**3. Data and modelling**

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

Liow [23] demonstrates through an Asymmetric Dynamic Conditional Correlation (ADCC) model, also a specific class of multivariate GARCH models. Liow [23] finds time-varying conditional real estate-stock correlations at local, regional and global stock markets and some asymmetry and furthermore real estate-global stock correlation is impacted significantly by volatilities at local, regional and global levels. In this period, Liow [23] also finds that real estate and stock volatilities are more substantial in influencing co-variances more than correlations during and post the global financial crises. Hoesli and Reka [24] provided evidence on a national and international basis by investigating volatility spillovers between the U.S. and the U.K. real estate market, The U.S. and Australian real estate market as a national analysis and the U.S equity and real estate markets as an international analysis. The period of the study extends from 1990 to 2010 and the volatility spillovers are studied using the covariance matrix of the asymmetric t-BEKK (Baba-Engle-Kraft-Kroner) specification. On a national basis, the U.S is the net transmitter of volatility spillovers; this can be expected as the subprime crisis originated in the U.S. On an international basis, the three markets have more influence of volatility of the global market than the reverse, indicating quite the importance of these developed markets.

Liow and Ye [25] employed both univariate and multivariate switching regime beta models in the period of 2000–2015 to illustrate regime-dependant excess return distribution and volatility spillovers pre and post the global financial crises. The study examines the developed markets of the U.S., the U.K., France, Germany, Australia, Japan, Hong Kong and Singapore and their linkages with the world stock market and world real estate markets. The study uses switching regime models to allow for different economic conditions as well to capture the changes in the stochastic volatility process driving the real estate markets. The study reports a higher volatility parameter in response to the global financial crises compared to the 'normal' period. The real estate market linkages with the world market were affected differently by the global financial crises however they are amplified postcrises particularly for the European region, while the Asian real estate markets displayed reduced volatility spillovers with world markets in low volatility state post-crises.

Regime changes are associated with significant shifts in the fundamental relation between the risks and return trade-off and the probability that a switch can be initiated from one regime to another [26]. In [26], it was incorporated multiple regimes changes by modelling the return-volatility transmissions of real estate through the multivariate regime-dependent asymmetric dynamic covariance (MRDADC) model. They study the real estate markets of the U.S., the U.K, Japan, Hong Kong and Singapore for the period of 1990 to 2009. Firstly, the study finds that asymmetry, variance and covariance, associated with multiple regime changes, jointly influence return-volatility transmission in real estate markets and secondly the study finds that the five markets generally interact well with one another by

finding significant mean-volatility linkages under different volatility regimes. Consequently, this has implications on diversification benefits that these markets can offer.
