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


#### **Table 4.**

*Markov transition-out sample: 2007–2017.*

are rich in mineral resources. On the other hand, China and India consume most of commodities products. Surprisingly, Russia had the most stable commodity index during 2007–2017 period. Unlike Brazil and South Africa, Russia is mainly rich in oil while the other two countries are rich in minerals. The bonds indices show similar patterns to real estate indices. Numerous studies illustrate that listed real estate exhibit traits of other capital markets, especially bonds. The patterns of bonds indices are dissimilar except for China and Russia. It can be inferred that bonds volatilities of those two countries follow in the same direction. The graphs show diagnostic patterns and in order to have more depth, this article illustrates Markov transitions as shown in **Table 4**. In most studies, transition probabilities and expected durations, are used to illustrate Markov transitions.

Panel 13 (14) illustrates Markov transitions for equities (real estate) while panel 15 (16) shows Markov transitions for commodities (bonds). For equities indices, for the four countries; Brazil, China, India and Russia, there is considerable transition dependence between the two regimes as the original regimes start from as low 0.50 and increase to as high as 0.57. The non-original regimes are as low as 0.50.

Although the original regime for South Africa 0.56 (relative high) but the nonoriginal regime seems less dependent on the original regime. The expected durations of all countries are approximately 2 weeks. The quickly changing patterns in equities would be excepted given that equities markets are quite volatile that other capital markets. For real estate indices, China and South Africa show an interesting pattern-the original regimes are very low but the non-original regimes are highly dependent of the original regimes. That rare scenario is hardly observable in most countries in the world. That could be possibly due to the influence of governments which translate into financial markets in those countries. For Brazil, India and Russia, the two regimes seem to be dependent on each other. The excepted durations for real estate indices show interesting results-the expected durations are shorter their equities counter-parts mostly for first regimes. That is high unexpected. One possible explanation is that real estate indices in those countries are quite thin and represent a few constituencies. For commodities indices, the original regimes and non-original regimes are dependent. South Africa is the only country that illustrate a unique regime-non original regime is not some much dependent on original regime. All the regimes with exception of China and South Africa last for a few weeks. The reason why China and South Africa have longer accepted durations is because China consumes most commodities in the world while South Africa is a country rich in minerals. The regimes of bonds indices of all countries seem to be dependent. One possible explanation for that is that bonds are the oldest market in the capital markets. More, bonds are used mostly in those countries to finance private and public infrastructure. The expected durations of Brazil and China are entirely longer. Probably those two countries use their bond markets frequently for their capital markets offerings.

For every index type in **Figure 3** in every row, the first country is Brazil followed by China and then India; thereafter Russia. The last country is always South Africa. For equities indices, the later periods of China, Russia and South Africa show similar regimes patterns. Thus, there is a possibility that equities indexed volatilities of those move from and to with each other. For all the five countries, in year 2014, equities indexed volatilities show similar movements. Most of the 2014 year was characterised by bull markets most countries throughout the world. At that time, probably volatilities are spillover each other. The real estate indices for of all for


**Panel 17: equities**

**149**

**Brazil**

> CTP

1 2 CED

1 2.0605

**Panel 18: real estate**

CTP

1 2 CED

1 1.0000

**Panel 19:** 

CTP

1 2 CED

1 1.0000

**Panel 20: bonds**

CTP

1 2

1.0000

 0.0000

 1.0000

 0.0000

 0.5776

 0.4224

 0.0197

0.9738

 0.0262

 0.0000

 0.9999

 0.5174

 0.4826

 0.0000

1

2

1

2

1

2

1

2 1.0000 0.9802

0.0033

0.9967

0.0000

 1.0000

1

2

 1.0000

 1.6545

 21.4513

 1.1232

 1.0000

 1.0193

 3059.4310

 1.9430

2

1

2

1

2

1

2

1

2

2.9595

1.0000

 0.0000

 0.0466

 0.9534

 0.9999

 0.0000

 0.0000

0.0000

 1.0000

 0.3956

 0.6044

 0.1097

 0.8903

 0.0189

1

2

1

2

1

2

1

2 0.9811 0.9997

0.3379

0.6621

0.4853

0.5147

1

2

**commodities**

 18.3795

 65.2176

 1.8635

 1.0000

 29.1281

 1.1271

2

1

2

1

2

1

2 13.4442

 153.0187

 1.0000

1

2

0.0544

 0.9456

 0.5366

 0.4634

 0.0343

 0.9657

 0.0744

0.0000

 1.0000

 0.9847

 0.0153

 0.0000

 1.0000

 0.1127

1

2

1

2

1

2

1

2 0.8873 0.9256

1.0000

 0.0000

0.9934

0.0066

1

2

 1.9382

 1.8161

 1.6955

 37.1527

 1.0023

 40.9446

2

1

2

1

2

1

2 1.4518

1.0000

3.2839

1

2

0.5159

 0.4841

 0.5897

 0.4102

 0.9977

 0.0023

 0.6888

0.5147

 0.4853

 0.4494

 0.5506

 0.9731

 0.0269

 0.9756

1

2

1

2

1

2

1

2 0.0244 0.3112

0.3045

0.6955

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

0.0000

 1.0000

1

2

**China**

**India**

**Russia**

**South Africa**

#### **Figure 3.**

*Filtered regime probabilities-in sample: 2012–2017.*

