Optimal Collaterals in Multi-Enterprise Investment Networks

TL;DR

This paper investigates how optimal collateral contracts can mitigate systemic risk in networked investment markets, revealing differences between acyclic and cyclic networks and highlighting the need for external intervention in complex cases.

Contribution

It introduces a mechanism-design framework for optimal collateral schemes in network investments, contrasting acyclic and cyclic networks, and analyzes computational complexity of the problem.

Findings

Acyclic networks require no additional collateral for systemic risk management.

Cyclic networks need external schemes beyond bilateral contracts.

Minimum collateral can be arbitrarily higher in cyclic networks compared to non-network environments.

Abstract

We study a market of investments on networks, where each agent (vertex) can invest in any enterprise linked to her, and at the same time, raise capital for her firm's enterprise from other agents she is linked to. Failing to raise sufficient capital results with the firm defaulting, being unable to invest in others. Our main objective is to examine the role of collateral contracts in handling the strategic risk that can propagate to a systemic risk throughout the network in a cascade of defaults. We take a mechanism-design approach and solve for the optimal scheme of collateral contracts that capital raisers offer their investors. These contracts aim at sustaining the efficient level of investment as a unique Nash equilibrium, while minimizing the total collateral. Our main results contrast the network environment with its non-network counterpart (where the sets of investors and capital raisers are disjoint). We show that for acyclic investment networks, the network environment does not necessitate any additional collaterals, and systemic risk can be fully handled by optimal bilateral collateral contracts between capital raisers and their investors. This is, unfortunately, not the case for cyclic investment networks. We show that bilateral contracting will not suffice to resolve systemic risk, and the market will need an external entity to design a global collateral scheme for all capital raisers. Furthermore, the minimum total collateral that will sustain the efficient level of investment as a unique equilibrium may be arbitrarily higher, even in simple cyclic investment networks, compared with its corresponding non-network environment. Additionally, we prove computational-complexity results, both for a single enterprise and for networks.