The global financial crisis rekindled the debate on the potential benefits and risks of financial integration. The main arguments in this debate can be summarized as follows: on the one hand, financial liberalization brings benefits in terms of risk diversification, consumption smoothing and financing/investment opportunities; on the other hand, it entails enhanced risks for the stability of the international financial system stemming from the cross-border transmission of financial shocks.

In this paper, we focus on the concept of contagion, borrowed from epidemiology, which has been widely used since the late 1990s to describe the mechanism of cross-border propagation of financial crises. Yet the definition of contagion is not straightforward, as it overlaps with the concept of economic and financial interdependence. For example, Kaminsky and Reinhart (2000) refer to shock propagation as the result of the optimal response of economic agents to changes in countries’ economic fundamentals; however, because of market imperfections, countries may be subject to “pure contagion” effects even in the absence of changes in their economic fundamentals (Moser 2003). There are two main mechanisms that help to explain pure contagion. First, because of information effects, when a country is hit by a financial crisis, investors tend to reassess the economic fundamentals of other economies and reduce their exposure to them (Goldstein 1998). Second, “domino effects” may occur when a crisis originating in one country spreads to others as a result of direct or indirect financial linkages. Domino effects may be associated with “cascading defaults”, when losses spread across creditors via direct claims; this mechanism is used, for example, to simulate contagion in the interbank market (see Upper (2010) for a review of the literature on this kind of contagion). A further mechanism for pure contagion relates to portfolio rebalancing, when international investors affected by a crisis in one country unwind positions in other markets owing to capital and liquidity constraints (Schinasi and Smith 2000).

After the global financial crisis, the focus on systemic risk prompted many researchers to use network analysis to describe the financial system and infer the conditions under which an idiosyncratic shock could lead to large-scale disturbances. From a macro perspective, it is often assumed that the nodes of the network are the individual economies (or their respective financial systems), while the links stand for the financial interlinkages across them. Adopting this framework, Minoiu and Reyes (2013) show that the interconnectedness of the global banking system increased during the period 1978–2010, and it tends to diminish during international financial crises. They also find that the more interconnected an economy is with the rest of the network, the more it is exposed to financial shocks, suggesting a negative relationship between integration and financial stability.

Another approach to assess the stability of financial networks is to estimate contagion effects using simulation models. Typically, under this approach, an idiosyncratic shock hitting one country causes the contagion to spread throughout the network, affecting the economies whose banking systems are less capitalized and more exposed to banks domiciled in the crisis country. According to Espinosa-Vega and Solé (2010), this type of simulation model tends to underestimate contagion risk, which becomes significant only when the shock originates in a core economy such as the United States or the United Kingdom (Degryse et al 2010). They emphasize that, as in the global financial crisis, when funding markets freeze, banks relying on short-term liabilities are forced to sell assets to obtain liquidity; if many banks do this, the ensuing fire sales may trigger a downward price spiral, further eroding banks’ capital. Indeed, by using a more complex transmission mechanism that also takes into account the funding channel, they prove contagion risks can be significant even when the crisis originates in a peripheral economy.

Most works relying on network simulation models have focused on financial linkages across the national banking systems, mainly because before the global financial crisis, cross-border banking claims accounted for a large portion of capital movements. In recent years, the share of portfolio investments has increased, while the “other investment” component (which includes cross-border banking claims; see Figure 1) has contracted. This reshuffle reflects the worldwide shift in financial resources from the banking sector to the asset management industry. Note that portfolio investments, in particular the debt component, are highly volatile; therefore, recipient countries continue to be exposed to the risk of “sudden stops”, with implications for the stability of their domestic financial systems.

In this paper, taking into account the changes in the composition of capital movements, we aim to assess contagion risks through the channel of portfolio investments using a simulation model built on the concept of financial interdependence across economies. We assume that an idiosyncratic shock hitting an economy brings about a generalized fall in the prices of domestic financial assets; the international investors that are overexposed to this economy will suffer more losses than other investors and will consequently rebalance their portfolios, reducing investments in the other countries to which they are overexposed. Finally, we assume that if the reduction in portfolio investments in a given economy exceeds an appropriate threshold, computed on the basis of the observed volatility of portfolio inflows, then this economy will also be affected by contagion, and will itself contribute to the propagation of the crisis through the process of portfolio rebalancing.

The simulation is carried out using cross-country bilateral data on portfolio investments, implicitly assuming that each economy acts as a representative investor. Contagion effects turn out to depend largely on the intensity of the portfolio rebalancing mechanism, which reflects the risk aversion of international investors and their financial constraints. Moreover, the outcomes of the simulation suggest that if global investors are affected by an idiosyncratic shock, contagion may spread even when the crisis originates in a peripheral economy.

The structure of this paper is as follows. In Section 2 we review the literature on financial shock contagion, focusing on the relationship between financial integration and stability. In Section 3 we describe the evolution of the investment portfolio network. In Section 4 we illustrate the simulation model, in Section 5 we present the main outcomes and in Section 6 we state our conclusions.

There are several definitions of contagion in the literature on financial crises. According to Moser (2003) “pure contagion” refers to situations in which financial shocks spread across borders independently of fundamental factors (fundamental-spillover contagion) and in the absence of common causes (common cause contagion). In theoretical models, pure contagion is often associated with market imperfections; for example, Calvo and Mendoza (2000) show that, when information is costly, financial integration can lead to herding phenomenons, even if economic agents are rational. A financial crisis in one economy may also act as a wake-up call, leading international investors to reassess the fundamentals of other economies (Goldstein 1998).

The importance of pure contagion mechanisms has been questioned from an empirical standpoint. According to Forbes and Rigobon (2002), who analyze comovements in financial cross-country returns, spillover effects are driven by common economic factors. Other studies, which use data on the volume of financial transactions instead of securities prices, suggest that pure contagion phenomenons are not rare. For example, Van Rijckeghem and Wedder (2003) point out that important factors are the structure of the international banking system and the presence of common lenders, particularly for emerging economies; by analyzing aggregate cross-border banking claims, they find that, during the crises in Mexico and Thailand, the countries most exposed to these economies reduced positions in other economies as well. According to Kaminsky and Reinhart (2000), the presence of common lenders helps to explain why some countries are more exposed to contagion risk; for instance, with regard to the Asian financial crisis, the idiosyncratic shock in Thailand spread to economies (such as Malaysia) that relied more on Japanese banks, which were heavily overexposed to Thailand.

Kaminsky et al (2004) empirically verify the process of portfolio rebalancing by analyzing data on emerging markets funds; they find that during the crises in Mexico (1994), Thailand (1997) and Russia (1998), fund managers undertook “contagion trading” by selling third countries’ assets. Broner et al (2006) develop a model of portfolio rebalancing, assuming that fund managers are remunerated on the basis of their performance against a benchmark. When a country is in crisis, the managers of funds overexposed to it become more risk averse and reduce their investments in third countries to which they are also overexposed. Therefore, financial interdependence across economies arises because of the presence of common investors. To empirically verify the validity of their model, Broner et al use microdata on emerging market mutual funds during the financial crises in the 1990s; they compute an index of financial interdependence across economies, which accounts for common investors and funding concentration, and they find that this indicator performs well as a proxy for country contagion risk, confirming the validity of their model.

Using aggregate data on portfolio investments after the global financial crisis, Galstyan and Lane (2013) find evidence of a “mean reversion” mechanism in cross-border country bilateral positions, which is consistent with the contagion literature; during the global financial crisis, investing countries disproportionately reduced their positions in countries to which they were overexposed. These findings suggest that the portfolio rebalancing mechanism also works at the aggregate level; this outcome continues to hold after controlling for variables relating to institutions, geography and cultural factors, which are used in gravity equations as determinants of bilateral investments (Portes and Rey 2005).

Among the factors that can enhance contagion effects through the portfolio rebalancing mechanism, an issue that has received particular attention in the literature is institutional investors’ financial constraints. Along these lines, Schinasi and Smith (2000) develop a model of asset allocation and show that the effects of portfolio rebalancing after a “capital event” (ie, when investors incur losses due to an idiosyncratic shock) may be amplified if intermediaries are leveraged. With regard to the role of mutual funds in contagion dynamics, particular attention has been paid to the mechanism of forced sales, ie, when fund managers, fearing that end-investors will redeem their shares, liquidate assets, causing spillover effects (Shleifer and Vishny 1997). Using microdata on American mutual funds, Raddatz and Schmukler (2011) find empirical evidence of contagion trading during the global financial crisis. Using data on global funds domiciled in developed economies between 1996 and 2010, Jotikasthira et al (2012) find that such funds substantially alter portfolio allocations in emerging markets in response to funding shocks in their investor base.

As mentioned above, the global financial system can be represented as a network in which the nodes are the economies and the links stand for their financial linkages. A crucial aspect of networks is their density (or interconnectedness), which can be computed as the number of existing links divided by the number of all possible links. Note that interconnectedness and interdependence are two different concepts and have different implications in terms of contagion risk; in fact, two economies that are not directly connected may be financially interdependent if they share common investors; conversely, they can be directly connected even in the absence of common investors. In this section, we first present the main contributions of the network analysis to the study of financial contagion, and then provide some evidence of the network of global aggregate portfolio investments.

The relationship between the density of the network and its stability has been discussed extensively in the literature. According to Allen and Gale (2000), the more the financial system is interconnected, the more opportunities investors have to diversify portfolio risk, thus increasing the stability of the network. Glasserman and Peyton Young (2016) provide an extensive review of the literature, mainly at micro level, arguing that the stability of the network is not determined uniquely by its structure per se, but also depends on the characteristics of financial intermediaries, such as their leverage, their reliance on short-term liabilities and their exposure to common risks. For example, Nier et al (2007) test the resilience of different banking networks to shocks and find that the relationship between the degree of interconnectedness and the stability of the networks is not monotone and hinges on the degree of heterogeneity across the nodes and the level of bank capital. According to Gai and Kapadia (2010), financial networks feature the properties of robust-yet-fragile structures; by simulating random shocks, they generally find that the high degree of interconnectedness observed in the interbank markets enables banks to diversify idiosyncratic risks. However, in the very few cases in which contagion risk materializes, the probability of it spreading throughout the network is very high.

Among the first network analysis applications on aggregate data, using Bank for International Settlements banking statistics for a sample of forty countries, Von Peter (2007) finds that the international banking system is strongly interconnected (ie, each node is on average connected with fifteen other nodes). Interestingly, only a few nodes act as global hubs, intermediating claims between other nodes that are not directly connected. Minoiu and Reyes (2013) analyze the evolution of the international banking system from 1978 to 2010, finding that financial integration, measured by means of network centrality indicators, follows a procyclical path, in line with the evolution of global capital movements. Cerutti and Zhou (2017), using aggregate bilateral banking data, find that the structure of the global network has evolved since the global financial crisis: some advanced European economies turn out to be less interconnected, whereas emerging economies have become more financially integrated.

Unlike cross-border banking claims, network analysis has not been used extensively for analyzing other types of capital movements, mostly owing to data constraints. Kubelec and Sá (2010) address this gap, using gravity equations to create a data set representing different types of asset class (foreign direct investments, equity and debt) from 1980 to 2005 for a sample of eighteen advanced economies. They find that the degree of interconnectedness of the network increased for all types of capital movements; the network looks like a robust-yet-fragile structure, with strong heterogeneity in terms of degrees and a high concentration around a few nodes. In the last decade, researchers have started to apply network analysis to portfolio investments using data from the Coordinated Portfolio Investments Survey (CPIS). For example, Chinazzi et al (2013) analyze the evolution of the portfolio investments network from 2001 to 2010 and find that, although the global financial crisis resulted in a decline in the density of the network, this effect was short-lived. They investigate whether the degree of financial integration of each country, measured by means of several network indexes, affected the impact of the global financial crisis, finding that more interconnected countries suffered less in terms of output contraction, as higher interconnectedness helped to dissipate adverse shocks.

One approach to estimating contagion effect consists in simulating an idiosyncratic shock, triggering “domino effects” through the financial linkages between the nodes. For example, using aggregated data on cross-border banking claims, Degryse et al (2010) find that a crisis in central nodes such as the United States or the United Kingdom may cause a global crisis, via the losses on bilateral claims (credit channel). This approach has been scrutinized by Espinosa-Vega and Solé (2010), who claim that simulation models such as those mentioned, which focus uniquely on the credit channel, are too simplistic and tend to underestimate the contagion risk. They develop an alternative simulation model that allows for funding shock and fire sales, and they show that the addition of the funding channel raises the vulnerability of all banking systems significantly and helps explain why numerous papers in the network literature, which focus only on credit events, do not provide compelling evidence of contagion effects.

In the remainder of this section, we describe the evolution of the network of international portfolio investments between 2002 and 2015, analyzing various centrality indicators computed using bilateral data on portfolio investment stocks. Our sample comprises the fifty reporting countries that have regularly contributed to the CPIS and that account, on average, for 83% of the amount outstanding of aggregate portfolio investments. According to our estimates, the interconnectedness index varies between 20% and 30% over this period (see Figure 2), reflecting the evolution of global portfolio investments until the flare-up of the global financial crisis in 2008; thereafter the density of the network declined, only returning to the levels recorded before the crisis in 2012.¹¹ 1 In 2015 Ireland had not contributed to CPIS. Like Chinazzi et al (2013), we find that the effect of the global financial crisis on financial integration was only temporary.

The distributions of in- and out-degree indexes, as well as other centrality indicators (see Table 1(a) in the online appendix), turn out to be strongly asymmetric, suggesting the presence of a few central nodes. Note that the asymmetry is stronger for the out-degree index and that the median value of the in-degree index is higher (17 against 9), suggesting a different pattern of diversification for lenders and borrowers. Plotting the two indexes (Figure 3) highlights that, for more integrated countries, the out-degree index tends to be higher than the in-degree index, while the opposite applies for countries that are less integrated. Indeed, developed countries, which are more financially integrated, tend to diversify international assets by investing in both other advanced economies and emerging economies (see Table 2(a) in the online appendix); by contrast, emerging economies tend to act as receiving nodes in the network, borrowing mostly from advanced economies.

The heterogeneity in terms of degrees between the central nodes and the others is also captured by the centralization index, which turns out to be very high, particularly from the perspective of investing countries (Figure 4(a)). Note that the two indexes moved in opposite directions during the global financial crisis as international investors relocated their international assets retrenching from peripheral economies. Since global investors tend to be headquartered in the financial centers (Von Peter 2007), the process of portfolio rebalancing resulted in a reduction in the out degree of the developed economies and in an increase in the funding concentration for emerging ones.

The high level of centralization of the network is associated with a limited number of degrees of separation between nodes. The closeness index is the inverse of the average distance from a node to all the others, where distance refers to the number of links on the shortest path. Note that the United States, Luxembourg (and other developed economies to a lesser extent) exhibit a score close to the maximum (equal to 1), indicating that they act as global hubs, being directly connected to almost all the other nodes (see Table 1(a) in the online appendix). Conversely, emerging economies tend to have a score slightly above 0.5, indicating that they are indirectly connected with the rest of the network through a central node. For both advanced and emerging economies, the closeness index shows an increasing trend, interrupted only during the global financial crisis (see Figure 4(b)).

High centralization and short distance characterize “small world” networks and are considered particularly important from a financial stability perspective, since, in this kind of network, local disturbances tend to have global effects (Haldane 2009). If the global hubs are affected by an idiosyncratic shock in a single economy, the contagion may spread throughout the network, affecting other economies that are not directly linked to the one where the crisis originates. In this context, financial centers play a crucial role in the transmission of financial shocks, as they represent the core of the network. There are several definitions of “core” nodes and different algorithms for their identification. Following Borgatti and Everett (1999), we may represent the global portfolio investments network by means of a “block model”, highlighting two partitions of the network, namely a “core”, characterized by a very high density, and a “periphery” with sparse linkages. Craig and von Peter (2014) developed an algorithm to detect core nodes using a loss function, which minimizes the distance of the adjacency matrix from a theoretical core–periphery structure. Applying this algorithm to our data, it turns out that the “core” of the global portfolio investments network is made up of nineteen countries, mostly advanced economies, while the “periphery” which includes all the remaining countries, is made up of all the emerging economies and a few advanced economies (see Figure 1(a) in the online appendix).

According to Craig and von Peter (2014), the peculiarity of “core” nodes consists in linking the peripheral nodes with the rest of the network. However, not all core countries identified using the algorithm seem to satisfy this condition; in fact, centrality indicators (see Table 1(a) in the online appendix) suggest that only a few countries play the role of intermediary for the whole network. In particular, the “betweenness index”, which measures the frequency with which nodes are interposed between all the other nodes along their shortest paths, presents a very skewed distribution, exhibiting very high levels only for a subset of the “core” nodes identified by means of the algorithm, and in particular for the three countries (United States, United Kingdom and Luxembourg) that together account for 40% of the global portfolio investments. Other countries also act as intermediaries, but their connections with the periphery tend to be sparse, suggesting they do not play an effective intermediation role for the network as a whole. To sum up, the structure of the global portfolio investments network seems to allow for a third category of economies: those that cannot be considered either as core or as peripheral nodes in a strict sense; however, as we discuss in Section 5, some of these economies may play a role in contagion dynamics regardless of their centrality score. The reason is that, through the balance sheets of global investors, financial centers may be a source of interdependence between countries even in the absence of direct links; in financial crises, global investors rebalance their portfolios, reducing investments in the countries to which they are overexposed. This concept of financial interdependence constitutes the main assumption underlying the simulation model we illustrate in the next section.

Our model aims to capture the mechanics of “pure contagion” events in which an idiosyncratic shock hits one economy and then spreads through the network as a result of the portfolio rebalancing process. Like Broner et al (2006), we assume that investors have heterogeneous preferences regarding which countries to invest in; in particular, investors are overexposed (underexposed) to countries about which they are more optimistic (pessimistic) than the average investor. Generally, fund managers care about their performance against a benchmark; when they perform worse than the benchmark, they reduce investments in countries to which they are overexposed, feeding contagion dynamics. As mentioned in Section 2, empirical evidence confirms the validity of this assumption; when a country undergoes a financial shock, international investors such as open-ended funds undertake contagion trading strategies, selling third countries’ assets. Consistent with this evidence, we assume that when an economy undergoes a financial crisis investors overexposed to this economy will reduce investments in other countries to which they are overexposed.

We also assume that the portfolio rebalancing mechanism works as an asymmetric process, that is, investors do not increase investments in countries to which they are underexposed. This assumption takes into account the fact that, because of financial constraints, when global investors incur losses as a result of financial shocks, they react not only by changing portfolio allocation but also by reducing the overall size of their assets. Price effects are not explicitly considered in our model, even though they are incorporated through the effects of the portfolio rebalancing for recipient economies. Consider the case in which an idiosyncratic shock leads international investors to unwind positions in some economies; in the case of a large contraction in capital inflows, the massive sale of domestic securities by foreign investors is often associated with a generalized fall in securities prices. To account for this mechanism, in our model we assume that the portfolio rebalancing “loops” if, for a given recipient economy, the reduction in portfolio inflows is large enough to be classified as a sudden stop, according to the methodology developed by Forbes and Warnock (2011). In practice, after simulating a portfolio adjustment as a reaction of global investors to an idiosyncratic shock, for each recipient economy we compare the reduction in inward investments with the reduction necessary to identify a sudden stop. Then, if the computed reduction in portfolio liabilities exceeds the standard deviation of portfolio inflows multiplied by 2,²² 2 We compute this using International Monetary Fund balance of payments statistics from 2005 to 2014 for each country in the sample used in the simulation (see Section 5). we assume that the recipient economy also undergoes a financial shock and the simulation is reiterated. Note that in our simulation model we do not consider any country-specific variable affecting the country’s absorbing capacity; therefore, what makes a node more or less vulnerable to contagion risk is its funding structure and the observed volatility of capital inflows.

To sum up, we run the simulation in three stages (see Figure 5): first, an idiosyncratic shock hits a generic economy (say, country A); second, countries overexposed to economy A rebalance their portfolios, reducing investments in third economies to which they are overexposed. For simplicity, in Figure 5 we illustrate the case in which country B is the only one overexposed to economy A; as it is also overexposed to economy C, country B will rebalance its portfolio, reducing investments in country C, and thus causing a funding shock. In the third stage, if the funding shock hitting country C exceeds the “sudden stop” threshold, the simulation loops and contagion propagates. Note that the “sudden stop” threshold varies across countries since it depends on the observed volatility of portfolio investment inflows.

A crucial aspect of the simulation is the intensity of the portfolio rebalancing mechanism, which relates to the reaction function of international investors. In this regard, we build on the work of Kyle and Xiong (2001), who develop a model in which international investors become more risk averse and reduce total investments when they incur losses, stoking contagion dynamics. To see how this mechanism is incorporated into our model, consider the case depicted in Figure 5, where economy B is overexposed to countries A and C; we denote by ${\mathrm{oe}}_{bc}$ the amount of country B’s portfolio investments in country C that exceed the latter’s share in aggregate portfolio investments. We use $X_{bc}$ to indicate the portfolio investments in country C held by residents in country B, with $X_{b\cdot }$ being the sum of portfolio investments held by residents in country B, $X_{\cdot c}$ being the aggregate portfolio investments in country C and $X_{\cdot \cdot }$ being the aggregate portfolio investments in the whole network:

If a shock hits A, then B will reduce its overinvestments $({\mathrm{oe}}_{bc})$ in country C by a country-specific factor $Q_b$ given by its share of investments in country A multiplied by a parameter $\beta$:

The country-specific factor $Q_b$ aims to capture wealth effects for country B linking the reduction in investments $(\mathrm{\Delta }{X}_{bc})$ to its exposure in crisis-hit country A ($X_{ba)}$. Note that the intensity of portfolio rebalancing, and hence the likelihood of contagion, is related to the size of the investments in economy A, meaning that size effects and not only network effects are at work. The parameter $\beta$, which also affects the intensity of the portfolio rebalancing, may be interpreted as a measure of the tightness of balance-sheet constraints in the case of a negative shock reducing the value of their portfolio investments. According to Goldstein and Pauzner (2004), balance-sheet constraints are in fact equivalent to assuming that investors’ risk aversion decreases with their net worth: when the overall value of their assets falls below a certain threshold, investors become more risk averse, as they anticipate that in the event of further losses they will have to sell some assets or issue new capital. The relevance of balance-sheet constraints for contagion effects has been explored; Schinasi and Smith (2000) developed a theoretical model with balance-sheet constraints, proving that portfolio rebalancing will trigger a contraction in investments by an amount that is a multiple of the losses borne by investors relative to their capital endowments. Financial intermediaries may also amplify contagion effects in another way; as we mention in Section 2, open-ended funds are exposed to redemption risk as end-investors may redeem their shares at short notice; when redemption pressure rises, fund managers may be forced to undertake contagion trading, selling third countries’ assets to raise the liquidity needed to pay their obligations. These intermediaries may enhance contagion risk by liquidating assets in response to funding shocks in their investor base. In our model, the coefficient $\beta$ aims also to capture redemption risk for open-ended funds.

The simulation is carried out using 2014 (CPIS) portfolio investments data for a sample of fifty-three countries.³³ 3 The simulation sample is larger than that used for network analysis, as in the latter we included only the countries that contributed to the survey every year from 2002 to 2015. For the simulation we used data relating to 2014, as Ireland did not contribute to the survey in 2015 (see footnote 1). The outcomes are analyzed in two stages: first, we conduct a sensitivity analysis in order to define our base calibration; then, we focus on the economies that may be considered as systemic in the sense that if they underwent a financial shock, the subsequent contagion effect would spread throughout the network.

We assume that twelve countries (the United States, United Kingdom, Germany, Austria, Netherlands, Luxembourg, Switzerland, Canada, Australia, Japan, Hong Kong and Singapore), which are defined as “safe countries”, are neither exposed to financial shocks nor affected by contagion; these countries include reserve currency issuers and those with a triple A rating on sovereign debt (assigned by at least one international agency). This assumption captures the fact that international investors consider these countries a safe haven in times of financial distress. Note also that some of them (for example, the United States, United Kingdom and Luxembourg) are financial centers playing a crucial role in the network and may a priori be considered systemic. From this angle we aim to fill a gap in the literature on network effects in the global financial system by assessing the contagion risk associated with noncore countries.

In order to estimate the contagion effect, we run the simulation $N$ times (where $N=41$, ie, the sample size minus the number of safe countries); each time, we assume that an idiosyncratic shock hits one economy of the sample ($i=1,\mathrm{\dots },N$), and simulate the portfolio rebalancing process illustrated in the previous section. Then we check whether any country is affected by contagion, ie, any country for which the reduction in portfolio investments by foreign investors exceeds the quantity necessary to identify a sudden stop, and we indicate by $k$ the number of countries affected by contagion (with $k=1,\mathrm{\dots },K$). In this case the simulation is reiterated until no further country is affected by contagion. Finally, for each country $i$, we compute a measure of the contagion effect (${\mathrm{CE}}_i$) as the fraction of the sample (in terms of gross domestic product (GDP), excluding the safe countries) represented by the $k$ countries:

This measure allows us to assess whether an economy is systemic in relation to the network. We also compute the average contagion effect (ACE) as the mean of the contagion effects, which represents a synthetic measure of the contagion risk referring to the network as a whole:

The ACE varies between 0% and 37% of the sample as a function of $\beta$ (Figure 6); likewise, the number of systemic economies, which we conventionally define as those that would lead to a contagion effect (${\mathrm{CE}}_i$) above 10%, varies from zero to sixteen. In our base calibration we set $\beta =4$, a value corresponding to a median contagion scenario, equivalent, on average, to 12% of the sample (in terms of GDP). This corresponds to more than seven times the sample average country GDP, considered to be the mean of idiosyncratic shocks.

The shaded area indicates the range of values of $\beta$ ($\beta =3,\mathrm{\dots },5$) used to identify the systemic economies; within this interval, the average contagion effect varies between 11% and 20%. Actually, contagion dynamics (that is, when simulation loops) tend to occur only for a limited number of countries, but in these cases the contagion effect turns out to be very large; the global portfolio network exhibits the typical properties of the robust-yet-fragile structures described in Section 3. In fact, contagion effects prove highly concentrated (Figure 7); using the base calibration, only seven countries turn out to be systemic ($\beta =4$). In fact, the contagion effect is above 50% for four countries, between 25% and 50% for three countries and below 5% for the others. The number of systemic economies varies from one (for $\beta =2$) to twelve (for $\beta =6$); this finding suggests that for most economies in the network contagion effects would be limited regardless of the model calibration.

Taking into account the results of the sensitivity analysis, we use three different estimates to identify the systemic economies, varying the parameter $\beta$ around the base calibration. For $\beta =4\pm 1$ we obtain that the number of systemic economies on the abscissa of Figure 8 varies from four to eleven. The comparison of the outcomes of the simulation conditional on $\beta$ highlights three country groups. The first group includes those economies (Ireland, Spain, Italy, France) for which contagion effects would be widespread (that is, over 50%) even when $\beta =3$ (our lower bound). The second group includes those economies (Indonesia, Korea, India) for which the contagion effect is between 30% and 40% for any value of the parameter . Finally, in the third group (Belgium, Sweden, Mexico and Brazil) the contagion effect is conditional on the intensity of the portfolio rebalancing mechanism; in particular, for $\beta =5$ (corresponding to the upper bound) Belgium and Sweden would be in the first group, while Mexico and Brazil would be in the second one, whereas for $\beta =4$ the contagion effect would not be significant for any country of this group. Note that all the emerging economies classified as systemic according to our definition are characterized as peripheral nodes using the algorithm by Craig and von Peter (2014). This finding suggests that for contagion to occur the financial crisis does not need to originate in a core country; conversely, an idiosyncratic shock in a core country would not necessarily lead to contagion as, for many countries identified as core nodes, the simulated contagion effect turns out to be limited.

It is worth noting that for $\beta =4\pm 1$ the contagion effect tends to be significantly higher for advanced economies than for emerging economies. In order to shed light on this aspect, we look into the country exposure to contagion risk using the outcomes of our simulation model under the baseline calibration, and computing for each country the average ex-post probability of being affected by contagion in the case of a crisis in a systemic economy.⁴⁴ 4 See Silva et al (2017) for a discussion of risk-related network measures. It turns out that most emerging economies are affected when contagion propagates, regardless of the country of origin of the crisis; by contrast, advanced economies are affected by contagion only when the idiosyncratic shock hits a systemic advanced economy. This asymmetry may be related to the fact that, as described in Section 3, emerging economies tend to be less diversified in terms of funding sources, and concentration risk increases the vulnerability to external shock (Minoiu and Reyes 2013). In fact, with regard to portfolio liabilities, emerging economies feature a higher concentration risk (in 2014 the Herfindahl index was 0.31 and 0.18 for emerging and advanced economies, respectively; see Table 2(a) in the online appendix). Moreover, the fact that these countries are connected to the rest of the network through a few central nodes increases their interdependence due to the effect of common lenders described in Section 2. The fact that advanced economies are affected by contagion only when the idiosyncratic shock hits a systemic advanced economy may depend on the size of these economies. In fact, among systemic economies, the portfolio liabilities of advanced economies are, on average, $4.5$ times higher than those of emerging economies. As we suggested in the previous sections, the portfolio rebalancing mechanism incorporates size effects, and this feature of the model contributes to explaining why the contagion risk is more acute if the financial crisis originates in a systemic advanced economy.

Based on the results of the simulation, the role of financial integration for contagion dynamics proves ambiguous. On the one hand, less integrated economies appear to be more vulnerable to contagion risk because of a higher funding concentration risk; on the other hand, for the whole network, contagion risk is higher, as a consequence of size effects, if the financial crisis originates in a financially integrated economy.

In order to assess whether the contagion effect varies over time, depending on the network evolution, we repeated the simulation for all years, starting with 2007, using the base calibration. We find that the contagion effect declined in the aftermath of the global financial crisis, probably as a result of a reduction in the volume of global portfolio investments; thereafter, the contagion effect increased again, reaching a new peak in 2013, presumably reflecting the increasing role of global funds and the worldwide shift in financial resources from the banking sector to the asset management industry.

The increase in the average contagion effect is also associated with the increase in the number of systemic economies. Using the base calibration and comparing the results for 2014 (Figure 9) and 2007 (Figure 2(a) in the online appendix), it turns out that only four countries (all advanced economies) could be considered systemic prior to the global financial crisis; in more recent years, a few emerging economies could also be deemed systemic as a result of their increasing financial integration.

In this paper, we estimate the contagion effect through the portfolio channel in the case of idiosyncratic shock, using a simulation model based on the concept of financial interdependence. We use aggregate bilateral data for a sample of fifty-three countries, representing more than 80% of the worldwide stock of portfolio investments. In our model we assume that countries act as representative international investors, so that, when an economy undergoes a financial shock, countries overexposed to it rebalance their portfolios, reducing investments in other economies to which they are overexposed. We simulate contagion effects, assuming recipient economies are themselves subject to contagion if the reduction in portfolio liabilities as a result of the portfolio adjustment process exceeds a given threshold computed by taking into account the observed volatility of portfolio inflows.

The outcomes of the simulation show that a few economies, on top of those identified as central nodes using network indicators, may be considered systemic in the sense that if they undergo an idiosyncratic shock, contagion effects would likely spread through the network. There are two main implications: for contagion to occur, the financial crisis does not need to originate in a central node; when contagion risk materializes, its effects tend to spread throughout the network. The simulation estimates also suggest that contagion risk, which declined in the aftermath of the global financial crisis, has resumed more recently and that the number of systemic economies has also increased. The contagion effect depends on the intensity of the portfolio rebalancing mechanism. Since this aspect may vary according to circumstances, we performed a sensitivity analysis, showing that contagion risk is also relevant under mild assumptions about the intensity of the portfolio rebalancing mechanism.

The findings of this paper underline the importance of the “portfolio channel” in the transmission of financial shocks. Given the increasing role of the shadow banking system in the intermediation of capital movements, the authorities should address contagion risk by setting out policies in a comprehensive and consistent manner, closing loopholes in prudential regulation.

The author reports no conflicts of interest. The author alone is responsible for the content and writing of the paper.

The author thanks Goetz von Peter for providing the code to detect core and peripheral nodes.