Dynamic Pricing for Non-fungible Resources
Public blockchains implement a fee mechanism to allocate scarce computational resources across competing transactions. Most existing fee market designs utilize a joint, fungible unit of account (e.g., gas in Ethereum) to price otherwise non-fungible resources such as bandwidth, computation, and storage, by hardcoding their relative prices. Fixing the relative price of each resource in this way inhibits granular price discovery, limiting scalability and opening up the possibility of denial-of-service attacks.
  • Theo Diamandis,
  • Alex Evans,
  • Tarun Chitra,
  • Guillermo Angeris
  • Basics
 08.16.22
Optimal Routing for Constant Function Market Makers
We consider the problem of optimally executing an order involving multiple cryptoassets, sometimes called tokens, on a network of multiple constant function market makers (CFMMs). When we ignore the fixed cost associated with executing an order on a CFMM, this optimal routing problem can be cast as a convex optimization problem, which is computationally tractable. When we include the fixed costs, the optimal routing problem is a mixed-integer convex problem, which can be solved using (sometimes slow) global optimization methods, or approximately solved using various heuristics based on convex optimization. The optimal routing problem includes as a special case the problem of identifying an arbitrage present in a network of CFMMs, or certifying that none exists.
  • Guillermo Angeris,
  • Tarun Chitra,
  • Alex Evans,
  • Stephen Boyd
  • MEV
 12.01.21
Replicating Monotonic Payoffs Without Oracles
In this paper, we show that any monotonic payoff can be replicated using only liquidity provider shares in constant function market makers (CFMMs), without the need for additional collateral or oracles. Such payoffs include cash-or-nothing calls and capped calls, among many others, and we give an explicit method for finding a trading function matching these payoffs. For example, this method provides an easy way to show that the trading function for maintaining a portfolio where 50% of the portfolio is allocated in one asset and 50% in the other is exactly the constant product market maker (e.g., Uniswap) from first principles. We additionally provide a simple formula for the total earnings of an arbitrageur who is arbitraging against these CFMMs.
  • Guillermo Angeris,
  • Alex Evans,
  • Tarun Chitra
  • DeFi
 09.01.21
Constant Function Market Makers: Multi-Asset Trades via Convex Optimization
The rise of Ethereum and other blockchains that support smart contracts has led to the creation of decentralized exchanges (DEXs), such as Uniswap, Balancer, Curve, mStable, and SushiSwap, which enable agents to trade cryptocurrencies without trusting a centralized authority. While traditional exchanges use order books to match and execute trades, DEXs are typically organized as constant function market makers (CFMMs). CFMMs accept and reject proposed trades based on the evaluation of a function that depends on the proposed trade and the current reserves of the DEX. For trades that involve only two assets, CFMMs are easy to understand, via two functions that give the quantity of one asset that must be tendered to receive a given quantity of the other, and vice versa. When more than two assets are being exchanged, it is harder to understand the landscape of possible trades. We observe that various problems of choosing a multi-asset trade can be formulated as convex optimization problems, and can therefore be reliably and efficiently solved.
  • Guillermo Angeris,
  • Akshay Agrawal,
  • Alex Evans,
  • Tarun Chitra,
  • Stephen Boyd
  • Basics,
  • DeFi
 07.01.21
Replicating Market Makers
We present a method for constructing Constant Function Market Makers (CFMMs) whose portfolio value functions match a desired payoff. More specifically, we show that the space of concave, nonnegative, nondecreasing, 1-homogeneous payoff functions and the space of convex CFMMs are equivalent; in other words, every CFMM has a concave, nonnegative, nondecreasing, 1-homogeneous payoff function, and every payoff function with these properties has a corresponding convex CFMM. We demonstrate a simple method for recovering a CFMM trading function that produces this desired payoff. This method uses only basic tools from convex analysis and is intimately related to Fenchel conjugacy. We demonstrate our result by constructing trading functions corresponding to basic payoffs, as well as standard financial derivatives such as options and swaps.
  • Guillermo Angeris,
  • Alex Evans,
  • Tarun Chitra
  • DeFi
 03.01.21
A Note on Privacy in Constant Function Market Makers
Constant function market makers (CFMMs) such as Uniswap, Balancer, Curve, and mStable, among many others, make up some of the largest decentralized exchanges on Ethereum and other blockchains. Because all transactions are public in current implementations, a natural next question is if there exist similar decentralized exchanges which are privacy-preserving; i.e., if a transaction’s quantities are hidden from the public view, then an adversary cannot correctly reconstruct the traded quantities from other public information. In this note, we show that privacy is impossible with the usual implementations of CFMMs under most reasonable models of an adversary and provide some mitigating strategies.
  • Guillermo Angeris,
  • Alex Evans,
  • Tarun Chitra
  • Privacy
 02.01.21
Optimal Fees for Geometric Mean Market Makers
Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. Arbitrage trades have been shown to align the prices reported by CFMMs with those of external markets. These trades impose costs on Liquidity Providers (LPs) who supply reserves to CFMMs. Trading fees have been proposed as a mechanism for compensating LPs for arbitrage losses. However, large fees reduce the accuracy of the prices reported by CFMMs and can cause reserves to deviate from desirable asset compositions. CFMM designers are therefore faced with the problem of how to optimally select fees to attract liquidity. We develop a framework for determining the value to LPs of supplying liquidity to a CFMM with fees when the underlying process follows a general diffusion. Focusing on a popular class of CFMMs which we call Geometric Mean Market Makers (G3Ms), our approach also allows one to select optimal fees for maximizing LP value. We illustrate our methodology by showing that an LP with mean-variance utility will prefer a G3M over all alternative trading strategies as fees approach zero.
  • Guillermo Angeris,
  • Tarun Chitra,
  • Alex Evans,
  • Stephen Boyd
  • DeFi
 01.04.21
Liquidity Provider Returns in Geometric Mean Markets
Geometric mean market makers (G3Ms), such as Uniswap and Balancer, comprise a popular class of automated market makers (AMMs) defined by the following rule: the reserves of the AMM before and after each trade must have the same (weighted) geometric mean. This paper extends several results known for constant-weight G3Ms to the general case of G3Ms with time-varying and potentially stochastic weights. These results include the returns and no-arbitrage prices of liquidity pool (LP) shares that investors receive for supplying liquidity to G3Ms. Using these expressions, we show how to create G3Ms whose LP shares replicate the payoffs of financial derivatives. The resulting hedges are model-independent and exact for derivative contracts whose payoff functions satisfy an elasticity constraint. These strategies allow LP shares to replicate various trading strategies and financial contracts, including standard options. G3Ms are thus shown to be capable of recreating a variety of active trading strategies through passive positions in LP shares.
  • Alex Evans
  • DeFi
 06.01.20
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Expanding

10.29.24

At Bain Capital Crypto, research and investing are interlocked. Researching foundational problems has led to our most successful investments. Working with builders has inspired our most fruitful research directions. Researchers and investors participate equally in every decision we make.

Tight integration requires an unusual amount of focus. We make atypically few investments. When we find an opportunity we like, we concentrate, often leading multiple consecutive rounds. Our research is similarly concentrated in a small number of areas where we believe new results will have a transformational impact on the industry. As with investing, when we think we’re onto something, we redouble our efforts.

We’ve been investing in ZK and advanced cryptography for a few years. We were lucky to invest in Scroll in 2021, Risc Zero and Irreducible in 2022, and Worldcoin in 2023. Our research into new frameworks and results in the field is more recent but is ramping up quickly. While our original thesis was narrowly focused on scaling blockchains and certain early privacy applications, our conviction has grown. Today, we’re tripling down.

We’re excited to welcome five exceptional researchers to the BCC team to expand our focus into advanced cryptography. Kobi Gurkan is joining BCC as an investing partner and head of research. Wei Jie Koh and Andrija Novakovic are joining BCC as researchers. Nico Mohnblatt and grjte are joining as research collaborators.

Kobi was a co-founder of Geometry and the founder of Geometry Research. He was a cryptography lead at Celo and a researcher at the Ethereum Foundation. You can find his fingerprints in many of the most popular advanced cryptography libraries and tools. 

Kobi has a knack for identifying and supporting talented builders. He’s been prescient in surfacing early-stage projects as an investor, often believing in teams before anyone else. In our shared portfolio, Kobi and his partners at Geometry invested in projects such as Risc Zero and Scroll before BCC. It’s been a pleasure to partner with Kobi on those investments. Kobi has helped some of the best people in our industry get their start and mentored them through their careers. We’re delighted to have some of those folks join our team alongside him.

Wei Jie was an engineer at Consensys and a researcher at the Ethereum Foundation prior to joining Kobi at Geometry. He was one of the lead developers of MACI, a bribery-resistant quadratic voting system, and has done trailblazing work in client-side ZK proving.

Andrija was a researcher at Geometry and the Ethereum Foundation. He’s worked on Semaphore, a privacy gadget for ZK set membership proofs, and has published work on radically reducing costs for proving pairings and developing scalable private sealed-bid auctions.

Nico joined Geometry in 2022 and has quickly become prolific in the ZK community, co-hosting the Zero Knowledge Podcast and ZK Whiteboard Sessions. He’s known for his work on folding schemes, including Sangria, the first folding scheme for arithmetizations beyond R1CS.

grjte ran web2 businesses as a CEO and CTO before entering ZK through ZKHack. Within 6 months of entering the space she was the engineering lead at Polygon Miden building the Miden zkVM and the AirScript DSL before joining Geometry Research.

This group has already contributed meaningfully to the BCC portfolio. Nico has worked with Risc Zero to rigorously analyze security in their proof system. Andrija, Kobi and Wei Jie have made major contributions to Semaphore, which is one of the foundational components of Worldcoin. Andrija worked on integrating MVLookup into Scroll’s zkEVM. The whole group recently developed o1js-blobstream, bringing Celestia DA to Mina.

Like our best work at BCC, these contributions have been the result of researchers following their genuine curiosity. At BCC, our interest in resource pricing as a path to scaling blockchains originated from our work with Celestia, Fuel and Scroll. Our work on routing and CFMMs originated from investing work I was doing at Placeholder and work Guillermo and Tarun Chitra were doing at Gauntlet. We find this integrated approach to research and investing to be deeply rewarding. In the time we’ve spent together, it’s been clear that Kobi, Andrija, Nico, Wei Jie, and grjte share that ethos.

In expanding our team, we are betting that the blockchain industry will wholesale re-architect around ZK and advanced cryptography. Advanced cryptographic systems are improving rapidly and are becoming broadly usable. Meanwhile, the AI race is breaking the modern internet to the point where, in a few years, nothing we see online will be trusted. As programmable cryptography commoditizes and unverifiable infrastructure strains, we believe this an exciting time to be investing in verifiable services and applications.

To invest and partner well, our approach is to research and build at the frontiers. Kobi, Wei Jie, Andrija, grjte, and Nico significantly uplevel BCC’s ability to do that. We’re thrilled to welcome them to our team.

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