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...eered by Evans and Archer (1968) and Elton and Gruber (1977) to a systemic context. This allows to better understand the controversial relation between the firm capital structure and diversification (=-=Jensen and Meckling, 1976-=-). Finally, our work complements existing theoretical literature that, after the 2007-2008 financial crisis, started to investigate the role of risk diversification for the stability of the financial ...

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...(z1, z2), to obtain the cumulative function Φ2. This is generally not simple, especially when the asset correlation ρ1,2 is non-constant. Various tables exist if g is a bivariate normal distribution (=-=Owen, 1962-=-; Pearson, 1931). Because this does not apply to our case, we use a method proposed by Jantaravareerat (1998), which allows us to calculate Φ2 as follows: 1. Calculate the joint probability density fu...

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...scribed as the risk that a failing agent (e.g. a bank in a financial system or a firm in a supply system) causes the failure of other agents such that failing cascades may encompass the whole system (=-=Battiston et al., 2009-=-b). This approach differs from other notions of risk (Embrechts et al., 2011) which treat the default of individual agents as an extreme event for which the probability is calculated regardless of the...

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...existing theoretical literature that, after the 2007-2008 financial crisis, started to investigate the role of risk diversification for the stability of the financial system (Battiston et al., 2009a; =-=Brock et al., 2009-=-; Ibragimov and Walden, 2007; Stiglitz, 2010; Wagner, 2009). Our results about a critical level of diversification can be used for improving macro-prudential regulations, for example by enforcing a ce...

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... literature that, after the 2007-2008 financial crisis, started to investigate the role of risk diversification for the stability of the financial system (Battiston et al., 2009a; Brock et al., 2009; =-=Ibragimov and Walden, 2007-=-; Stiglitz, 2010; Wagner, 2009). Our results about a critical level of diversification can be used for improving macro-prudential regulations, for example by enforcing a ceiling to excessive leverage....

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... Merton (1974) in which the firm’s leverage plays a major role. This approach has become popular among both academicians and practitioners thanks to its tractability and simplicity. For a survey see (=-=Bohn, 2000-=-). Moreover, the Financial Stability Board (2010) recommends it as a building block in establishing a regulatory framework that can cope with risk from systemic linkages. These linkages arise from bil...

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...atory framework that can cope with risk from systemic linkages. These linkages arise from bilateral exposures (e.g. mutual claims) and common assets which may lead to interlocking balance sheets (see =-=Kiyotaki and Moore, 2002-=-). Including these effects into a systemic notion of risk requires explicit knowledge of banks’ balance sheets and their change over time. This information is mostly confidential, due to strategic iss...

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...2007-2008 financial crisis, started to investigate the role of risk diversification for the stability of the financial system (Battiston et al., 2009a; Brock et al., 2009; Ibragimov and Walden, 2007; =-=Stiglitz, 2010-=-; Wagner, 2009). Our results about a critical level of diversification can be used for improving macro-prudential regulations, for example by enforcing a ceiling to excessive leverage. 2 Model 2.1 Ban...

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...ossible interdependence. Excessive leverage refers to the practice of banks to engage in huge debt to buy more assets, in order to increase their return on equity. As the Financial Service Authority (=-=FSA, 2009-=-) and the Financial Stability Board (FSB, 2009) jointly point out, excessive leverage by banks increases systemic risk. However, our hypothesis is that diversification can compensate some of the hazar...

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...or a firm in a supply system) causes the failure of other agents such that failing cascades may encompass the whole system (Battiston et al., 2009b). This approach differs from other notions of risk (=-=Embrechts et al., 2011-=-) which treat the default of individual agents as an extreme event for which the probability is calculated regardless of the interaction among economic agents. Instead, a systemic notion of risk requi...

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...fers to the practice of banks to engage in huge debt to buy more assets, in order to increase their return on equity. As the Financial Service Authority (FSA, 2009) and the Financial Stability Board (=-=FSB, 2009-=-) jointly point out, excessive leverage by banks increases systemic risk. However, our hypothesis is that diversification can compensate some of the hazards of excessive leverage, under optimal condit...

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... obtain the cumulative function Φ2. This is generally not simple, especially when the asset correlation ρ1,2 is non-constant. Various tables exist if g is a bivariate normal distribution (Owen, 1962; =-=Pearson, 1931-=-). Because this does not apply to our case, we use a method proposed by Jantaravareerat (1998), which allows us to calculate Φ2 as follows: 1. Calculate the joint probability density function g(z1, z2...

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...n show that n? increases for “crashing” markets, µ < 0, and decreases for “booming” markets, µ > 0. This is in line with economic intuition, i.e. diversification works well only in a booming market, (=-=Tasca and Battiston, 2011-=-). The specific dependence n?(fn, fa, N, χ) can be obtained only numerically. Table 1 gives some numbers for the minimum value, in accordance with Figure 1. 5We talk about small positive values of −10...