Why Stake When You Can Borrow?

TL;DR

This paper develops a unifying model to analyze security risks and capital efficiency in Proof of Stake systems, revealing conditions where derivatives can either increase or decrease wealth concentration and risk.

Contribution

It introduces a comprehensive model combining Pólya processes and credit risk models to study derivative impacts on PoS security and wealth distribution.

Findings

Identifies a sharp transition between safe and unsafe derivative usage.

Shows derivatives can sometimes reduce wealth concentration, contrary to prior assumptions.

Validates theoretical results with agent-based simulations.

Abstract

As smart contract platforms autonomously manage billions of dollars of capital, quantifying the portfolio risk that investors engender in these systems is increasingly important. Recent work illustrates that Proof of Stake (PoS) is vulnerable to financial attacks arising from on-chain lending and has worse capital efficiency than Proof of Work (PoW) \cite{fanti_pos_econ}. Numerous methods for improving capital efficiency have been proposed that allow stakers to create fungible derivative claims on their staked assets. In this paper, we construct a unifying model for studying the security risks of these proposals. This model combines birth-death P\'olya processes and risk models adapted from the credit derivatives literature to assess token inequality and return profiles. We find that there is a sharp transition between 'safe' and 'unsafe' derivative usage. Surprisingly, we find that contrary to \cite{fanti2019compounding} there exist conditions where derivatives can \emph{reduce} concentration of wealth in these networks. This model also applies to Decentralized Finance (DeFi) protocols where staked assets are used as insurance. Our theoretical results are validated using agent-based simulation.