Understanding the consequences of diversification on financial stability

There is growing similarity in the asset side of banks’ balance sheets due to increased participation in the same global markets (Cai et al. 2012; Liu 2015; Wagner 2010). We consider the consequences of this on financial stability. A major motivation for the increasing similarity is rooted in the standard financial and perhaps intuitive diversification advice “Don’t put all your eggs in one basket”. In fact, the seminal work of Markowitz (1952) on portfolio selection provides evidence that diversification across various asset classes reduces the aggregate risk of a bank’s portfolio. It is thus reasonable to conclude that if each bank becomes less risky due to diversification then the financial system should become more stable. Moreover, several reports before the 2007 financial crisis found little evidence for a systemic breakdown of the financial system owing to the high diversification levels at individual banks due to the extent of financial innovation (Bartram et al. 2007; Elsinger et al. 2006; Furfine 2003). However, the financial system still came close to near collapse even though banks, especially the big ones, had become largely diversified.

This conundrum stems from an individual bank not considering the fact that other banks are pursuing the same risk objective by diversifying their balance sheets across the same set of asset classes. This results in individual banks becoming less differentiable. From a systemic perspective, a less differentiable set of banks increases fragility and exacerbates the risk of joint failures of a large part of the financial system, which can have serious consequences on social welfare. This phenomenon draws a parallel in ecological studies where genetic diversity, for instance, is shown to result in greater resilience to disease spread (see Tilman 1999, for a detailed discussion).

Thus, diversification appears to serve multiple roles; on one hand, it makes banks less risky but on the other hand it increases the risk of joint failures. This dual role of diversification on financial stability has prompted active discussions amongst policy makers and academics in a growing number of studies. For instance, the reports by Allen and Carletti (2006), Allen and Gale (2005), Wagner (2008, 2010), Wagner and Marsh (2006) show that diversification increases the likelihood of a systemic crisis due to the homogenization of the financial system even though it is desirable in terms of reducing the probability of an individual bank failure. Similar findings are reported by Battiston et al. (2012). In a related work, Caccioli et al. (2014) study the role of diversification on financial contagion due to overlapping portfolios and showed that the system undergoes two phase transitions with increasing diversification between which global cascades can occur. This finding is also reported in the work by Raffestin (2014). Tasca et al. (2014) show that diversification can have ambiguous consequences on the stability of the financial system by studying the joint impact of leverage and diversification on financial stability using a structural risk model based on the framework proposed by Merton (1974). They show that a critical leverage value can result in alternating phases of stability and instability depending on the diversification strategy. Finally, while our focus is on diversification, however our work is also related to the literature on bank herding since they both lead to concentrations in the same set of activities (see, for instance, Acharya and Yorulmazer 2005, 2007).

We contribute to this strand of literature by studying the consequences of diversification on the stability of the financial system in terms of idiosyncratic and systemic risk endogenously produced from an evolving stylised economy, which sets our work apart from previous studies. Moreover, our approach provides a simple mechanism for analysing the full effect of regulatory responses to negative externalities associated with the impact of diversification on financial stability and the wider economy.

Our approach consists of a deliberately simplified agent based model that couples a financial system and the real economy. There is a large literature on macro-finance interaction models including Bask (2012), De Grauwe and Macchiarelli (2015), Lengnick and Wohltmann (2016), Naimzada and Pireddu (2014), Westerhoff (2012). These works couple agent-based financial(stock) market and mainstream macro models. However, we deviate from these models by focusing on externalities resulting from credit/loan network rather than traded equities/shares.¹ In a nutshell, the model implements a self-organising economy populated by rationally bounded heterogeneous agents including firms, households and banks interacting within different markets without central coordination (see Fagiolo and Roventini 2012 for an elaborate discussion on decentralised economic systems). The model dynamics leads to the emergence of bank–bank and bank–firm links that are strategically formed and terminated. These networks serve as channels of contagion and shock propagation. In this sense, the model shares some similarity with the strand of literature on multilayer network theory and financial contagion (Caccioli et al. 2015; Montagna and Kok 2016; Lux 2016; Martinez-Jaramillo et al. 2014; Poledna et al. 2015) since it leads to the formation of different network structures that serve as contagion reinforcing mechanisms.

The rest of this paper is organised as follows. In Sect. 2, we describe the main features of the model. Section 3 characterises the stability features of the financial system due to diversification. We then propose a regulatory policy that permits diversification without exacerbating systemic risk in Sect. 4. Finally, a summary of our findings is presented in Sect. 5.

For the purpose of this study, we extend the CRISIS Mark 1 agent based model extensively studied in Delli Gatti et al. (2011), Gualdi et al. (2015), Klimek et al. (2015), Poledna and Thurner (2016). The original CRISIS Mark 1 model specifies a closed system that couples the real economy and a limited financial system. A closed system in this sense implies that all money stay within the economy and is held by the agents. We extend the model to include different production sectors in the real economy. Furthermore, we include simplified credit and interbank markets so that banks play an active role in the economy unlike the original model specification in which the banking sector is passive.

Figure 1 provides a high-level view of the agents and their interactions within the model discussed elaborately in the following sections:

In a nutshell, the model implements a self-organising economy populated by rationally bounded heterogeneous agents namely firms, households and banks interacting within different markets without central coordination. Households interact with firms on the labour and consumption market, banks interact with other banks on the interbank market while firms and banks interact within different sectors on the credit market resulting in a constantly evolving (i.e. links are strategically formed and terminated) bank–bank network and bipartite network of bank–firm links respectively.

We validate the model in terms of its ability to reproduce phenomenological laws observed in real economies namely Okun (Prachowny 1993) and Beveridge curves (Nickell et al. 1960). Moreover, we observe the emergence of alternation of booms and recessions in aggregate output and Zipf distribution of firm sizes (Axtell 2001). See “Appendix A” for an elaborate discussion on the model calibration and validation.

The economy we consider comprises different sectors and each firm is assigned to a sector. We exogenously control the level of diversification (diversity) of the financial system using a single parameter that fixes the number of sectors each bank can lend to on the credit market. The goal of this paper is to understand the role of diversification on financial stability. As such, we abstract from strategic processes used by banks in choosing a particular portfolio structure as in Wagner (2011), who show that investors are motivated towards heterogeneous portfolio configurations due to the risk of joint liquidation.

Our model belongs to the class of “one-step” models (see Delli Gatti et al. 2011; Dosi et al. 2010; Klimek et al. 2015 for examples). In contrast, other works in the literature (Erlingsson et al. 2013; Gaffeo et al. 2008; Lengnick 2013) use models that capture heterogeneous and real-world timescales . In our model, agents carry out the following sequence of operations or decisions in each time period.

In this section, we investigate the systemic and idiosyncratic risk inherent in the financial system based due to only the bank–firm network. Idiosyncratic risk refers to the probability of a one-off or isolated bank failure. The failure of Barings bank in 1995, for instance, was an isolated event and specific to Barings (see Fay 1997 for an elaborate discussion on this event). Systemic risk on the other hand refers to the probability of a large part of the financial system failing. A good example is the 2007 financial crisis during which major financial institutions like American International Group (AIG), Bear Stearns, Lehman Brothers, Citigroup etc. either failed or had to be saved from failing by different government intervention schemes (Bullard et al. 2009).

We measure systemic risk in terms of the probability of observing a global cascade of bank defaults (i.e. joint bank failures) while idiosyncratic risk refers to the probability of observing an isolated bank default in a simulation. In our analysis, a global cascade of defaults is said to occur if the number of bank failures exceeds a defined threshold \(\theta \). Unless otherwise stated, we define \(\theta \) as 25% of the total number of banks and abstract from the impact of the bank–bank network by counting only bank failures before bail-in occurs in each time period. Moreover, we account for randomness present in the labour, consumption and credit market by averaging over 300 simulations with each simulation spanning 2500 time periods.

Figure 4 reveals that idiosyncratic risk is decreasing with diversification. In contrast, Fig. 5a shows that systemic risk is increasing with diversification. We find that the qualitative behaviour of this result is preserved by changing \(\theta \) to 50% as shown in Fig. 5b. The reason why increasing diversification appears to increase systemic risk but reduce idiosyncratic risk can be intuitively understood from the fact that banks become less diverse and increasingly exposed to the same sectors as they become more diversified (i.e. the bank–firm network becomes more connected) such that negative spill overs emanating from the real sector during a recession is able to affect many banks. However, diversification ensures that a bank’s risk is not concentrated in any one sector such that the negative impact of downturns in a sector becomes smaller on the bank, effectively reducing the probability of the bank failing.

In the previous section, we showed that diversification reduces idiosyncratic risk, however, it also makes the financial system less diverse consequently leading to more joint failures (i.e. higher systemic risk). It then becomes interesting to ask if it is possible to design polices that permit diversification without exacerbating systemic risk?

A possible way of achieving this is to increase capital requirements of banks relative to their similarity with the rest of the financial system such that banks with higher degrees of similarity are required to more capital. Moreover, it is known from the literature that higher capital requirements improves the stability of the financial system. However, higher capital requirements come at a cost of reduced lending to the real sector (see Bridges et al. 2014; Brooke et al. 2015). As such, we investigate the possibility of an alternative regulatory policy that achieves the same objective without requiring banks to hold additional capital.

The policy we consider is motivated by the fact that a bank does not internalise the impact of its activities on the build-up of systemic risk in the financial system (Acharya 2009; Wagner 2010). We model this policy by defining a similarity measure \(S_b\) for bank b relative to the rest of the financial system as:Where \(B_b\) is the set of banks registered in the same sector(s) as bank b and F(x) gives the set of firms with lending relationship(s) with bank x. We have included the constant 1 into Eq. 7 to avoid division by zero. We further define \(\Delta S_{bf}\) as the additional increase in the similarity for a bank b conditional on a credit transaction with a firm f. Finally, we implement a simple framework such that firms are more likely to transact with banks having lower \(\Delta S_{bf}\). Thus, deviating from the random bank–firm link formation process outlined in Sect. 2.1. The framework is such that given \(\Delta S_{bf}\) a firm f transacts with bank b with probability \(\omega _{bf}\) defined as:Following the intuition developed in Eq. 7, we define \(S_{bf}\) as:⁴A possible way of implementing this policy is for a central bank to compute \(\Delta S_{bf}\) and translate this into a tax that reduces lending activities of banks with high \(\Delta S_{bf}\). This could be in the form of a model that essentially increases the lending rates from such banks, which would ultimately incentive firms to transact with those banks with low \(\Delta S_{bf}\). Poledna and Thurner (2016), for instance, adopt a similar structure where the interest rate proposed by a bank is proportional to its “debtrank”. However, we do not model this translation since our interest lies in understanding the effectiveness of the policy rather than its implementation details.

We compare the stability impact of this policy relative to our benchmark model using the same initial configuration and random number seed for respective simulations. The plots in Fig. 11 show that the policy is effective at reducing systemic risk whilst keeping the benefit of diversification of reducing idiosyncratic risk. This follows from the fact that the policy induces a self-arranging network topology between banks and firms that promotes dissimilarity in the financial system even with increasing diversification which ultimately reduces the build-up of systemic risk. Although, idiosyncratic risk is relatively higher with our policy however the benefit of this risk reducing with increasing diversification is preserved.

Banks are increasingly diversifying their balance sheets across several assets in order to reduce their individual riskiness (Battiston et al. 2012; Wagner 2010). Accordingly, the true consequences of diversification particularly as it affects the stability of the financial system and the wider economy is actively being discussed by policy makers and academics (Battiston et al. 2012; Caccioli et al. 2014; Tasca et al. 2014; Wagner 2008, 2010). We contribute to this discussion by studying the impact of diversification on systemic (i.e. likelihood of joint failures) and idiosyncratic risk (i.e. risk of a one-off failure) using an agent based model that couples the financial system and the real economy. This approach not only leads to the emergence of a constantly evolving interbank and bank–firm network but also results in the emergence of shocks from the real sector that can be transmitted to the financial system via the evolving multi-layered network of bank–firm and bank–bank lending relationships.

Our findings suggest that diversification reduces idiosyncratic risk but increases systemic risk. We note that this finding leads to a higher cost for the society which ultimately results in a negative feedback on the real economy in terms of lower aggregate credit volume. Moreover, we find the emergence of a “robust yet fragile” behaviour from the model especially for low levels of diversification. This behaviour has been shown in several studies to characterise the financial system (Caccioli et al. 2014; Gai and Kapadia 2010) and simply implies that while the probability of a systemic crisis is low, the impact is however widespread (i.e. a large part of the financial system is affected) whenever it occurs. We then investigated the impact of introducing preferential attachment into the lending links of the bank–firm network and find that the risk profiles remain essentially the same as in the original model. However, we find that preferential attachment increases idiosyncratic risk but significantly reduces system risk in the financial system.

We then investigated the effectiveness of a regulatory policy that permits diversification without exacerbating systemic risk but does not require banks to hold additional capital. The policy essentially promotes bank–firm credit transactions that result in the smallest increase in the similarity between banks in the financial system. We show that this policy is effective at reducing systemic risk. This is because the policy induces a self-arranging network topology between banks and firms that promotes dissimilarity in the financial system even with increasing diversification which ultimately reduces the build-up of systemic risk. Although, idiosyncratic risk is relatively higher with our policy however the benefit of this risk reducing with increasing diversification is preserved.

Our analysis side-steps the impact of correlation between sectors even though correlation can endogenously arise in the model particularly during periods of economic downturns. Nevertheless, it would be interesting to extend this work to explicitly characterise the stability of the financial system on the joint impact of diversification and correlation.