MS-AR model

We continue examining FPI flows employing, a MS-AR univariate model. It can be described as follows. A time-series variable yt can be modeled by a Markov switching autoregressive of order p (MS-AR), with regime shifts in mean and variance. It is represented as follows (^{Hamilton, 1989}; ¹⁹⁹⁴).

where ∅i are the autoregressive coefficients; μ and σ are the mean and standard deviation depending on the regime st at the time t. yt represents the stock market returns of the European and American countries. This MS-AR modeldetect potential regime shifts in the stock market returns and enable to estimate the impact of crises on stock market volatility (^{Chkili Nguyen, 2014}).

MS-VAR model

The MS-AR model arouse great research interest dealing with macroeconomic fluctuations and lead to several MS-VAR extensions first advanced by ^{Krolzig (1997)}. However, research by ^{Sims and Zhag (2006)} identified moderation in their application, even though MS-VAR models have demonstrated superior data fit; ^{Bognanni and Herbst (2015)} attribute this restrain to the complex estimation processes required. Contributing to the literature, one of the essential objectives of this study is to analyze in depth thedynamic relationship between the US stock markets and European and the rest of the Americas equity markets; therefore, we employ the Markov Switching Vector Autoregressive model developed by ^{Krolzig (1997)}. This model is a generalization of the MS-AR presented above and can be written as follows:

Where eus and et represent the US stock market returns and the stock markets returns for each European countries, and for the Canadian and Latin American countries, ut is the innovation process with a variance v(st) depending on regime st which is assumed to follow an irreducible ergodic two-state Markov process, defined by the transition probabilities pij between states as follows

Where,

The MS-VAR model provides an accurate estimation of the potential regime shifts in the stock market returns, above all, during the turbulent period analyzed in this study. The inclusion of structural breaks in the financial time-series analysis is crucialto avoid mistaken conclusions related to the dynamic behavior of stock and currency markets as well as their existent relationships.

Data

To analyze the US Foreign Portfolio Investment linkages with the rest of the European and American countries, Directed and Weighted Networks are used. To build up these Networks, we use the “Geographic Breakdown of Total Portfolio Investment Assets: Total Portfolio Investment” from the Coordinated Portfolio Investment Survey (CPIS) of the International Monetary Fund (IMF) for 2003, 2008 and 2015. It includes data for equity and investment fund shares, long term-debt instruments and short-term debt instruments. These statistics are reported in millions of US Dollars.

To test the dynamic relationship between the US stock market return and the rest of the Americas and Europe equity market returns (MS-VAR model), daily closing prices of stock indexes in US dollars are employed (thus, only shares are included). The sampleincludes nineteen stock indexes from the main European and American stock markets: Ireland (ISEQ), France (CAC 40), Germany (DAX), Portugal (PSI 20), Switzerland (SMI), United Kingdom (FTSE 100), Greece (Athex 20), Spain (IBEX), Sweden (OMX Stockholm 30), Norway (OSEAX) e Italy (FTSE MIB), Argentina (MerVal), Mexico (IPC), Canada (S&P TSX Composite), Brazil (BOVESPA), USA (S&P’s 500 Index), Chile (IPSA), Colombia (IGBC-COLCAP) y Peru (IGBVL). Transmission and effects of the global financial crisis are studied for a period including 01/01/2003 to 02/27/2015 Daily returns are estimated by taking the difference in the logarithm of two consecutive prices. Exchange rate series was gathered from Bloomberg; series for PSI 20, IBEX 35 y SMI were drawn from Euroinvestor; IBOVESPA, MERVAL, IPSA, y IPC were obtained from Economatica; COLCAP e IGBVC from Bloomberg; other indexes were gathered from Yahoo finance.

Foreign Portfolio Investment Flows Analysis

Figure 2 presents total portfolio investment outflows for each country in 2003 (pre-crisis period), 2008 (during the crisis) and 2015 (post-crisis). Latin American countries’ portfolio investment outflows are very low in comparison with the other markets. In this group of countries, stands out the high growth of Chilean outflows; it almost doubled from 2008 to 2015. Albeit, Latin American countries have lower investment levels, in comparison with European economies, all of them experienced an increment from 2003 to 2015.

Investments from France, Greece, Portugal and Spain bounded from 2003 to 2008, but fell after Global Financial Crisis and had lower level by 2015, in relation to 2008. Canada, Germany, Ireland, Italy, Norway, Sweden, Switzerland, the UK and the US increased their investments during the period from 2003 to 2008 and from 2008 to 2015. It is important to point out that, despite of the fact that, global financial crisis began in the US, portfolio outflows from this market not only increased, but doubled from 2003 to 2015.

Table 2 presents the three main business partners for each country and year under analysis. It is evident the US relevance as the common investment flows destiny. For all countries (except Portugal) the US is one of the three countries with greatest weight as FPI receptor. Not only that, but for 11 of the 18 countries (Canada, Ireland, Norway, Sweden, Switzerland, the UK, Argentina, Brazil, Chile, Colombia and Mexico), the US was the main portfolio investment receptor during the three years under study. In terms of the US investments destiny, the UK is the main receptor of US´s FPI. Another country with important share in FPI outflows is Germany which is the main investment destiny from France, Portugal and Spain flows.

Once investment flows were analyzed in general, the indegree centrality measures are estimated; results are presented in Figure 3. The indegree centrality measure estimates the number of incoming links of each node. In this case, the “nodes” are the 19 countries and the links direction show the investment destiny for each one. The node size is related to the number of countries that invest in each country, in other words, each node is as big as the number of countries which invest in a given country.

Indegree centrality measure shows that the main investment destinies in 2003 were five countries (the US, the UK, Ireland, Germany and Mexico); it means that 17 from the 19 countries invested in these economies. The second most important FPI destinies were Brazil, France, Italy, Spain, Canada and Sweden. Countries with the lowest number of incoming links were Greece and Colombia, only 13 of the other 18 countries invested in there.

Results for 2008 evidence that the list of the main FPI receptors widened and the main destinies of FPI were Spain, the US, the UK, Ireland, Germany, Brazil, Canada, Switzerland, Sweden, France and Mexico; these 11 countries had 18 incoming links each one. Countries with lowest link number were Portugal, Colombia, Greece and Peru, they had only 15 links. Thus, 2008 financial landscape was very different in comparison to the 2003 scenery. Linkages among different European and American countries developed in five years, increasing the complexity of international financial structure. This picture allows us to explain the Global Financial Crisis transmission magnitude and the number of implied and affected countries.

Changes from 2008 to 2015 were not as significant as from 2003 to 2015. However, the amount of main receptor countries and links among them diminished. Brazil, Ireland, Mexico, Canada, Spain, France, Germany, the UK and the US had 17 links. The country with the lowest number of links was Colombia, with only 13 links. Summarizing, the main destinies in 2003 were the same, despite of the global financial crisis, and their importance remained similar in 2015.

Once the incoming links were analyzed, the outdegree centrality measure is also estimated; it measures the number of outcoming links that each node has. In this context, this analysis allows to know how concentrated outward investments are from each country. The size of each node represents how diversified are its FPI flows.

Outdegree analysis for 2003 reveals that the developed countries were the main investment source. It is observed that Brazil and Chile became very important because they invested in 17 of the 19 markets, in contrast with Mexico which received FPI from several countries (see indegree analysis), but only invested in 5 economies.

In 2008, Ireland was the country with the greatest FPI outflows diversification, investing in 18 countries. The country with the lowest number of outgoing links, without considering Peru, was Mexico (10).

In 2015, the number of outgoing links increased. Countries with greatest number of outgoing links have 18 connections and countries with the lowest number of links had 15 (Colombia, Greece, Spain, Portugal and Mexico). In the case of Mexico, it tripled the number of outgoing links from 2003 to 2015.

In terms of this research, the importance of US flows is confirmed. It is one of the main destinies and origins of FPI during the whole period of study; not only has an important number of outgoing and incoming links, but, in terms of volume, is one of the main FPI receptors and investors.

The following network (Figure 5) allows observing in detail the US linkages with the rest of the countries. The links thickness represents the FPI volume from and towards the US. Dark nodes represent countries with higher outgoing than incoming flows to the US. In contrast, white nodes are countries with positive incoming net flows (incoming flows are higher than outgoing flows to the US).

Figure 5 shows the investment from and to the US. In 2003 year, the main countries with FPI flows to the US were: the UK, France, Ireland, Canada, Germany, Italy and Switzerland. The main receptors of US FPI were the UK, France and Canada. In 2008, investments from Ireland and the UK to the US increased significantly (it can be observed by the thickness of each link). By 2015, FPI flows seemingly became be more balanced; linkages between the US and the UK, Canada, Ireland, Switzerland, Germany and Norway remained strong.

It can be observed that, during the three years studied, certain countries invested more in the US, than the US in them: Argentina, Portugal, Ireland, Sweden and Norway. In 2003 there was only six countries with positive net FPI flows (outgoing to the US - incoming from the US > 0). In 2008, the number of countries with positive net FPI increased to 10, it means that the FPI flows from the US to other countries diminished or increased in a lower proportion than FPI flows from other countries to the US.

For 2015 and 2003 the situation remained very similar. In 2015 the number of countries with positive outgoing FPI flows was seven. During this year, Canada’s situation changed, it registered a positive outgoing investment to the US, in contrast with previous years. These changes evidence dynamic linkages between the US and other countries. It also reveals that US FPI outflows diminished due to Global Financial Crisis, but in the long-run the US influence in the rest of the countries is significant.

Moving on to test whether the US stock market influences the rest of the equity markets under analysis we employ the MS-AR and MS-VAR models. The data, as previously mentioned, is limited to 19 representative stock market indexes from countries included in the study.

MS-AR Results

Table 3 summarizes descriptive statistics for all stock return series. SP, SMI and TSE are the markets with less risk (low standard deviation), ATHEX, FTSEMIB and PSI registered a negative average return in the whole period. More profitable markets during the period of study are IPC, COLCAP and IGBVL. All series exhibit leptokurtosis and most of the stock market returns are negatively skewed, except for CAC 40, DAX and IPC. Return series are not normal and, in all cases at levels and first differences the null hypothesis that the series present unit root is rejected; the series are stationary.

Stock markets relationships

Testing for volatility regime switch behavior

To examine the dynamic relationship between the US stock market and the rest of the European and American equity markets, it is essential to confirm that all stock markets present regime-switching behavior. The log likelihood test (LR) is employed to testthe null hypothesis of homoscedasticity, this means that a linear model could be more suitable, against the alternative hypothesis that the regime switching model (MS-AR) depict better the stock markets behavior (Garcia and Perron, 1996). This test is estimated as follows:

where lnL is the log likelihood of the contrasting models. The best-fitted model is selected through ^{Davies (1987)} critical values. This test has been used previously in several studies (^{Kanas, 2005}; Wang Theobald, 2008; ^{Chkili Nguyen, 2014}) to prove that other stock markets exhibit a time-varying behavior, which responds to local circumstances and to the effects of crises transmission. To reinforce the tests results, it is also introduced the Akaike Information Criteria (AIC). Table 4 shows the results of both tests.

MS-AR Results

Finally, following the proof about regime-switching behavior in stock markets returns, the MS-AR models are estimated; their results are described in Tables 5 and 6.

For all markets (European and from the Americas) the variance (σ12 and σ22) are statistically significant at 1% and their values suggest the presence of two regimes. The first regime is a low volatility level and the second regime presents a high volatility level.

The stock markets from Brazil, Argentina, Greece and Norway (IBOVESPA, MERVAL, ATHEX and OSEAX, respectively) exhibit the highest volatility level in the low volatility regime. The Colombian (COLCAP), Brazilian, Argentinean and Norwegian markets present the highest volatility in the high volatility regime.

Tables 5 and 6 also present the probability of being in each regime. As expected, the probability to be in a high volatility regime (P22) is lower than the probability to be in the low volatility regime (P11), in all cases. This evidence means that the low volatility regime is more persistent than the high volatility regime. The US has the stock market with the highest level of persistence in both low (0.9664) and high volatility regime (0.99) followed by the Swedish (0.9768 and 0.9898), Swiss (0.9512 and0.9895) and Canadian (0.9523 and 0.9894) markets.

In terms of the average duration, low volatility periods last more than the high volatility ones. The US market has the largest average duration in low volatility periods (102 days), followed by the markets from Sweden (98 days) and Switzerland (95 days).Markets with the highest duration in high volatility periods are the Swedish (43 days), English (39 days), the US (29 days) and Irish (29 days) markets.

Graphic Analysis Smooth Probabilities Regime 2 (High volatility)

Regime switching approach offers additional information through a graphic resource about what regime market is in a specific date t based on observation obtained through a later date T. These are referred to as “smoothed” probabilities; according to ^{Nalewaik (2012)} is an efficient algorithm whose calculation was developed by ^{Kim and Park (1994)}.

Figure 6 presents the smooth probabilities of being in regime 2 (high volatility regime). In this study, we use it as a graphic test to identify common high volatility periods in the stock markets. The smooth probability of being in the high dependence regime (S(P2)) indicates the presence of several common high dependence episode; stands out some periods: 2008-2009 (subprime crisis), 2011-2012 (sovereign debt crisis) and 2013-2014 (global financial crisis residual effects).

MS-AR Results

As, previously, analyzed the US is the most important country in terms of Foreign Portfolio Investments, both as investor and as receptor. As a result of its size and share, the US financial and economic indicators are used as international references and basis to examine their impact on local factors (interest rates, exchange rates, indexes, etc.). Similarly, because the US stock market is the largest one in the world³ its dynamics has influenced the rest of the international equity indexes. To evidence that returns from the main European and Canadian and Latin American are influenced by US equity market returns we apply the MS-VAR model. Results are presented in Tables 7 and 8.

The variance of the stock markets is lower in regime one (low volatility regime) than in regime two (high volatility regime), for all the markets. This indicates the presence of two different volatility regimes.

Tables 7 and 8 report the correlation coefficient between the US stock index and the other American and European indexes, in low and high volatility regimes. In all cases, the correlation level is higher during turmoil episodes (high volatility periods). This finding is similar to evidence obtained by ^{Kanas (2005)}, ^{Lin (2012)} and ^{Chkili and Nguyen (2014)}. Results signal that linkages between the US market and the other markets are stronger during high volatility periods. This phenomenon is commonly known as asymmetric correlation.

Equity markets with highest correlation during high volatility regime with the US are Mexico (0.78), Canada (0.762), Brazil (0.756), Germany (0.706) and France (0.704). Stock markets more related with the US market during low volatility periods are Mexico (0.66), Ireland (0.654), Canada (0.607).

The estimated coefficients capturing the impact of stock market returns (European and American) on the US stock market returns ( α31 and α32 ) are not significant in most of the cases, except for the Italian and Mexican market. This suggests that, in the major part of the sample, the equity markets under study do not have an important effect on the US stock market.

On the other hand, the coefficients ( β31 and β32 ) capture t effects of the US stock market returns on t stock market returns (European, Canadian and Latin American markets). They are statistically significant, for most of the stock markets in the sample, but insignificant for the Mexican, Argentinean and Brazilian markets. It means that, most of the stock markets are influenced by the US equity market. These results are consistent with those of ^{Tabak and Lima (2013)} who find that Latin American stock markets and the US equity market do not present a long-term relationship and that the Mexican market seems to have an impact on the US stock market. The relation is negative in both regimes, high and low level of volatility, suggesting that an increase in the US stock market inflows leads to diminish investments in other international stock markets. This finding is consistent with practice, in international asset allocation, short-run investments look for higher returns and lower risk. Thus, when the US market exhibits positive trends, international flows are directed to this market, reducing investments in other international markets.