Risk-Free Interest Rates in Decentralized Finance

Decentralized Finance (DeFi) aims to use advancements in both computation and cryptography to tackle economic problems. Therefore, it must operate within the intersection of constraints from both the computer science and economic domains. We explore a foundational question at the junction of those fields: Can we synthesize variable market-clearing risk-free yield for native tokens via smart contracts? We use a stylized model representing a large class of decentralized consensus algorithms to show this is impossible. This undecidability result places bounds on what decentralized financial products can be built and constrains the shape of future developments in DeFi. Among other limitations, our results reveal that markets in DeFi are incomplete.