Collateral Unchained: Rehypothecation networks, concentration and systemic effects

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Abstract

We study how the practice of collateral rehypothecation impacts the generation of liquidity and the emergence of systemic liquidity risk, and how both depend on the structure of the financial network. We build a basic model where banks interact via chains of “repo” contracts (i.e. repurchasing agreements) and use their proprietary collateral or re-use the collateral obtained by other banks via “reverse repos”. We then extend the model to allow banks to determine endogenously the optimal amount of collateral to rehypothecate, based on the equilibrium level of Value-at-Risk. In this framework, we first show how total collateral volume and its velocity are affected by characteristics of the network such as the length of rehypothecation chains and the existence of closed (i.e. cyclic) chains of contracts, the presence of sink nodes (wherein collateral remains trapped), the direction of collateral flows, and the density of the network. We then demonstrate that a trade-off between liquidity and systemic risk exists for certain classes of networks structures. On the one hand, we show that structures where collateral flows are concentrated among fewer densely connected nodes allow for larger collateral volumes, even at low levels of network density. On the other hand, the same networks are also more exposed to larger cascades of collateral hoarding, as a result of localized liquidity shocks.

Introduction

This paper investigates the dynamics of collateral and its implications in terms of systemic liquidity risk when financial actors are connected in a network of financial contracts and can rehypothecate the collateral. Collateral is of increasing importance for the functioning of the global financial system. One reason is that the non-bank/bank nexus has become considerably more complex over the past two decades. Indeed, the separation between hedge funds, mutual funds, insurance companies, banks, and broker/dealers has become blurred as a result of financial innovation and deregulation (Singh, 2016, Pozsar and Singh, 2011). Another reason for the significant increase in collateral volumes (comparable to M2 until the recent financial crisis, see e.g. Singh, 2011) has been the diffusion of rehypothecation agreements. The role of collateral in lending agreements is to protect the lender against a borrower's default. Rehypothecation1 is the right of the lender to re-use the collateral to secure another transaction in the future (see Monnet, 2011).

Rehypothecation of collateral has clear advantages for liquidity in modern financial systems (see Financial Stability Board, 2017b). In particular, it allows parties to increase the availability of assets to secure their loans, since a given pool of collateral can be re-used to support different financial transactions. As a result, rehypothecation increases the funding liquidity of agents (see Brunnermeier and Pedersen, 2008). At the same time, rehypothecation also implies risks for market players. First, one risk associated with the additional funding liquidity allowed by rehypothecation can be the building-up of excessive leverage in the market (see e.g. Bottazzi et al., 2012, Singh, 2012, Capel and Levels, 2014). Second, rehypothecation implies that several agents are counting on the same set of collateral to secure their transactions. It follows that rehypothecation may represent yet another channel through which agents’ balance sheets become interlocked,2 and thus a source of distress propagation and of systemic risk. For instance in the face of idiosyncratic shocks, some institutions may start to precautionarily hoard collateral, which in turn constrains the availability of collateral and its re-use for the downstream institutions in re-pledging chains. This may lead to an inefficient market freeze if participants lack the necessary assets to secure their loans (Leitner, 2011, Monnet, 2011, Gorton and Metrick, 2012). The latter is the distress channel we focus on in this paper.

To analyze economic benefits and systemic consequences of rehypothecation, we develop a model of collateral dynamics over a network of bilateral3 repurchase agreements (repos) across financial actors, which we refer to as “banks” hereafter.4 A “repo” or “repurchase agreement”, is the sale of securities together with an agreement for the seller to buy back the securities at a later date. A “reverse repo” is the same contract from the point of view of the buyer.

To keep the model as simple as possible, we abstract from many features of actual repo markets, like heterogeneous collateral quality, maturity and heterogeneous haircut rates and we assume that the amount of collateral available for secured financing is set as a constant fraction of total collateral available to each agent. The latter includes the proprietary collateral endowment of each bank as well as the collateral obtained from other banks via reverse repos.

Although simple, our model allows us to identify features of the rephypothecation network topology that determine (i) the overall volume of collateral in the market, and (ii) the velocity of collateral (Singh, 2011). We show that both variables are an increasing function of the length of open chains. However, for a given length, cyclic chains (i.e. those where banks are organized in a cycle of repo contracts) produce higher collateral than a-cyclic chains. At the same time, even in networks with similar cyclic chains, the presence of sinks, i.e. nodes where the collateral remains trapped, imply differences on the total amount of collateral. Indeed collateral sinks emerge in our analysis as a crucial notion to understand the relation between network structure and collateral flows.

Furthermore, we show that the direction of collateral flows also matters. In particular, concentrating collateral flows among few nodes organized in a cyclic chain allows larger increases in collateral volume and in velocity even with small chains’ length. Finally, we investigate total collateral under some typical network architectures, which capture different modes of organization of financial relations in markets, and in particular different degrees of heterogeneity in the distribution of repo contracts and of collateral flows. We show that total collateral is an increasing function of the density of financial contracts in the random network (where heterogeneity is mild) and in the core-periphery network (where heterogeneity is high). However, core-periphery structures where collateral flows are concentrated among nodes in the core allow a greater increase in collateral already at low levels of network density.

The model described so far with fixed hoarding rates is useful to analyse the effects of network topology on collateral flows. At the same time, it is unfit to study the systemic risk implications of rehypothecation, since hoarding behaviour could also reflect the liquidity position of the other agents in the network. We thus extend the model in order to capture the fact that banks endogenously determine their level of rehypothecation and hoarding, based on their expectations on liquidity risk. More precisely, we assume that hoarding rates are set according to a Value-at-Risk (VaR) criterion, aimed at minimizing liquidity default risk. In this framework, we show that the equilibrium hoarding rate of each bank is a function of the hoarding rates and the collateral levels of the banks at which it is directly and indirectly connected. This mechanism introduces important collateral hoarding externalities in the dynamics, as an increase in hoarding at some banks may indirectly cause higher hoarding at other banks, even if only indirectly connected to it and far away from it in the network. We then use the extended model to study the impact on total collateral losses of small uncertainty shocks hitting a fraction of banks in the network, and how those losses vary with the structure of the rehypothecation networks.

We show that core-periphery structures are the most exposed to large collateral losses when shocks hit the central nodes in the network, i.e. the one concentrating collateral flows. As, core-periphery are also the structures that generate larger collateral volumes, our results highlight that these structures are characterized by a trade-off between creation of liquidity and systemic liquidity risk.

Our work is related to the growing literature on financial networks that analyses the conditions for systemic risk to emerge and the relation between network structure and the systemic impact of shocks. Within this literature, some works have focused on the shock transmission channel on the asset side, based on a mechanism of default contagion. Many of these works are based on the model of Eisenberg and Noe (2001), that addresses the problem of payment clearing in a network of obligations. Rogers and Veraart (2013) extends the model of Eisenberg and Noe (2001) to allow for the possibility of some loss amplification. However, in their extension, systemic risk can only emerge as a result of many initial defaults in the network. Similarly, the work of Acemoglu et al. (2015), identifies a trade-off on the shock size and shows that in the case of extremely large shocks, a dense network can be more fragile than a sparser one. It should be noticed that the works based on Eisenberg and Noe (2001) do not capture an important feature of the 2008 financial crisis, i.e. the emergence of systemic risk from the combination of small shocks (indeed the subprime mortgage market was small compared to global financial markets) in the presence of mispricing, leverage and interconnectedness (see also Visentin et al., 2016, for a discussion).

Motivated by the limitations of the default contagion approach, a parallel stream of works has focused on distress contagion, by building on the work by Battiston et al. (2012). This research strand builds on the idea that contagion can occur not just through the propagation of realized losses, but also through expected losses. In this framework, the presence of bankruptcy costs and specific cyclical chains of contracts are sufficient conditions for the instability of the financial system (Bardoscia et al., 2017), leading to a trade-off in the relation between financial stability and network density, even for a same level of shock size.

Remarkably, the two streams of literature on default contagion and on distress contagion can be reconciled in a unified framework of network asset valuation (Barucca et al., 2017). The impact of the network structure on systemic risk has also been investigated in terms of default probability, by providing conditions on leverage and recovery rate such that more dense networks imply a higher probability of systemic defaults (Battiston et al., 2016). These issues about contagion in financial networks and the challenges ahead for the field of financial stability are summarized in Battiston and Martínez-Jaramillo (2018).

In a nutshell, one key result of the above stream of literature is that the density of financial contracts leads to a trade-off between the benefits of individual risk diversification and the danger of systemic risk. Similarly, our work shows that higher density of collateral rehypothecation linkages leads, in some specific network structures, to a trade-off between the creation of liquidity and the emergence of systemic liquidity risk. However, while the aforementioned literature focuses on contagion in the sense of (expected) losses on asset values, our work focuses on contagion in the sense of liquidity shocks.

More specifically, our work contributes also to the recent theoretical literature on the consequences of collateral rehypothecation (see e.g. Bottazzi et al., 2012, Andolfatto et al., 2017, Gottardi et al., 2017, Singh, 2016). This literature has highlighted the role of rehypothecation in determining repo rates (e.g. Bottazzi et al., 2012), or in softening borrowing constraints of market participants and in shaping the interactions in repo markets (Gottardi et al., 2017, Andolfatto et al., 2017) or, finally, it has contributed to evaluate some welfare aspects of policies aimed at regulating rehypotheaction (Andolfatto et al., 2017). However, to the best of our knowledge, our paper is the first to study the role of the structure of the network of collateral exchanges and to explore how different network structures determine overall collateral volumes and velocity. Furthermore, our work contributes also to the literature on liquidity hoarding cascades, where it it builds in particular on the work of Gai et al. (2011). However, differently from that work, our model introduces endogenous hoarding rates that depend on the liquidity of the bank and its position in the network. In addition, it shows that the liquidity hoarding dynamics can have different consequences depending on the specific structure of the network.

The paper is organized as follows. Section 2 introduces the basic definitions used throughout the paper and the model with fixed hoarding rates. Section 3 studies in detail how the structure of rehypothecation networks determines collateral volume and its velocity. Next, Section 4 extends the model to feature time-varying hoarding rates determined according to a VaR criterion. Section 5 uses the latter model to study collateral hoarding cascades in different rehypothecation networks. Finally, Section 6 concludes, also by discussing some implications of our work.

Section snippets

A simple model of collateral dynamics on networks

In this section we build the basic model that we then use to analyse how network structure affects collateral volumes and velocity in presence of rehypothecation. We start with the basic definitions that we shall use throughout the paper. We then introduce the laws governing collateral dynamics in presence of rehypothecation and with banks having exogenous hoarding levels.

Rehypothecation networks and endogenous borrowing capacity

We shall now describe how the structure of the rehypothecation network affects equilibrium collateral outflow determined according to the model developed in the previous section. To perform our investigation it is useful to define some aggregate indicators measuring the performance of a network in affecting collateral flows. The first one is the aggregate cumulative collateral outflow, Sout, or “total collateral” henceforth, which is defined as:Sout=i=1i=NAiCout.In addition, we also introduce

The extended model: value at risk and collateral hoarding

So far we have worked with the assumption that non-hoarding rates {θi}i=1N were constant across time and homogeneous across banks. This has simplified the analysis and it has allowed us to highlight the role of the characteristics of network topology in determining collateral flows in the financial system. At the same time, this hypothesis is also quite restrictive as banks’ hoarding and non-hoarding might be responsive to the liquidity risk situation of banks and to the level of available

Collateral hoarding cascades

We now use the VaR collateral hoarding model developed in the previous section to study how different rehypothecation networks react when a fraction of banks is hit by adverse shocks. We focus on uncertainty shocks21 that cause the variable ci0 in Eq. (40) to increase to ci1=ci0(1+c˜0) for some banks i, where c˜00. The shock

Concluding remarks

We have built and analyzed a simple model of collateral flows over a network of repo contracts among banks. We have assumed that, to obtain secured funding, banks may pledge their proprietary collateral or re-pledge the collateral obtained by other banks via reverse repos. The latter practice is known as “rehypothecation” and it has clear advantages for market liquidity as it allows banks to secure more transactions with the same set of collateral. At the same time, re-pledging other banks’

Acknowledgments

We are indebted to three anonymous referees and to the editors of the Journal of Financial Stability. We also thank Joseph E. Stiglitz, Stephen G. Cecchetti, Sérafin Jaramillo, Dilyara Salakhova, Marco D’Errico, Guido Caldarelli, for valuable comments and discussions that helped to improve the paper. We also thank participants to the various conferences where earlier versions of this paper were presented. These include the Second Conference on Network Models and Stress Testing for Financial

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