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  • Akshay Agrawal
  • Alex Evans
  • Guillermo Angeris
  • Kevin Zhang
  • Khurram Dara
  • Kshitij Kulkarni
  • Mandy Campbell
  • Parth Chopra
  • Stefan Cohen
  • Stephen Boyd
  • Tarun Chitra
  • Theo Diamandis
  • TuongVy Le
Succinct Proofs and Linear Algebra
Abstract The intuitions behind succinct proof systems are often difficult to separate from some of the deep cryptographic techniques that…
  • Alex Evans,
  • Guillermo Angeris
  • Research
09.21.23
The Specter (and Spectra) of MEV
Abstract Miner extractable value (MEV) refers to any excess value that a transaction validator can realize by manipulating the ordering…
  • Guillermo Angeris,
  • Tarun Chitra,
  • Theo Diamandis,
  • Kshitij Kulkarni
  • Research
08.14.23
The Geometry of Constant Function Market Makers
Abstract Constant function market makers (CFMMs) are the most popular type of decentralized trading venue for cryptocurrency tokens. In this paper,…
  • Guillermo Angeris,
  • Tarun Chitra,
  • Theo Diamandis,
  • Alex Evans,
  • Kshitij Kulkarni
  • Research
07.20.23
Our Comment on The SEC’s Proposed Amendments to Exchange Act Rule 3b-16
This week, we submitted a comment in response to the SEC’s proposed amendments to Exchange Act Rule 3b-16 regarding the…
  • TuongVy Le
  • Regulatory
06.15.23
Opinion: A House Bill Would Make It Harder for the SEC to Argue Crypto Tokens Are Securities
The proposed Securities Clarity Act by Representatives Tom Emmer and Darren Soto would significantly reduce uncertainty for both crypto investors…
  • TuongVy Le,
  • Khurram Dara
  • Regulatory
06.01.23
Opinion: Regulators Should Not ‘Front-Run’ Congress on Stablecoins
Growing consensus on the need for comprehensive legislation on payment stablecoins provides Congress with an opportunity to enact sensible regulation…
  • TuongVy Le,
  • Khurram Dara
  • Regulatory
05.17.23
Our Comment on The SEC’s Proposed Custody Rule
This week, we submitted a comment in response to the SEC’s proposed custody rule, together with Dragonfly Capital, Electric Capital,…
  • TuongVy Le
  • Regulatory
05.09.23
A Note on the Welfare Gap in Fair Ordering
In this short note, we show a gap between the welfare of a traditionally ‘fair’ ordering, namely first-in-first-out (an ideal…
  • Theo Diamandis,
  • Guillermo Angeris
  • Research
03.27.23
Why I Joined BCC as Head of Marketing
I couldn’t be more excited to be joining BCC as Head of Marketing — amplifying the great work of Stefan,…
  • Mandy Campbell
  • Hiring
12.15.22
Podcast:  Why the Legal Process for FTX and Sam Bankman-Fried Could Take Years
Tuongvy Le joined Laura Shin on the Unchained Podcast on December 9, 2022 to discuss how the legal process for…
  • TuongVy Le
  • Regulatory
12.09.22
Podcast:  A Legal Perspective on Sanctions Against Tornado Cash 
Tuongvy Le appeared on the Zero Knowledge Podcast on September 14, 2022 to discuss the Tornado Cash sanctions:  what kind…
  • TuongVy Le
  • Regulatory
09.14.22
Multi-dimensional On-chain Resource Pricing
Public blockchains allow any user to submit transactions which modify the shared state of the network. These transactions are independently…
  • Theo Diamandis
  • Basics
08.16.22
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
Why I Joined BCC
I am excited to announce that I’ve joined Bain Capital Crypto as a Partner and Head of Regulatory & Policy.…
  • TuongVy Le
  • Hiring,
  • Press Release
05.16.22
Introducing CFMMRouter.jl
We created CFMMRouter.jl for convex optimization enthusiasts, twitter anons, and Tarun Chitra to easily find the optimal way to execute…
  • Guillermo Angeris,
  • Theo Diamandis
  • DeFi,
  • MEV
04.05.22
Why I’m Excited to Join Bain Capital Crypto
I’m thrilled to announce I’m joining Bain Capital Crypto as a Partner. I’ll be helping Stefan Cohen, Alex Evans and the rest of…
  • Press Release
03.14.22
Introducing Bain Capital Crypto
We are excited to announce Bain Capital Crypto (BCC), our first $560mm fund, and the launch of a new platform…
  • Stefan Cohen
  • Press Release
03.08.22
Navigating Privacy on Public Blockchains
This post is an exposition on the landscape of privacy in the context of public blockchains (a.k.a. decentralized ledgers, crypto, and Web3). The first part touches on why privacy is a key hurdle to wide-scale adoption and what different aspects of privacy are. The second part surveys three different approaches to privacy: via zero-knowledge proofs, aiming for anonymity only, and via a new abstraction called MOCCAs.
  • Wei Dai
  • Privacy
02.16.22
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
Back

Introducing Bain Capital Crypto

  • Stefan Cohen
03.08.22
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We are excited to announce Bain Capital Crypto (BCC), our first $560mm fund, and the launch of a new platform to support the renegades and pioneers building the next generation of internet infrastructure. We designed this dedicated investment firm to support crypto/web3 builders from seed through growth with a highly technical and collaborative approach. 

Bain Capital Crypto grew out of our work at BCV, which has actively invested in the crypto space through both protocols and companies for the last seven years. We believe that we are at the precipice of a monumental technology shift towards open, community-driven, and decentralized services. 

Touching how we play, work, and transact, this seismic shift may prove the most important technological development of our lifetimes.

The combination of a generational shift of internet users (builders and creators) and open technology enables an infinite design space for developing user-built and controlled applications. We are in the very early innings of this transformation. 

The teams building these new pillars of the internet require a new type of investment firm that can support them from ideation through scale. To provide the highest level of service to these emerging builders, BCC has three key areas of expertise: 

  • Technical and economic research: As the next wave of internet and financial infrastructure gets built, we believe teams will require deep technical support thinking through critical design decisions.
  • Governance design and participation: Crypto protocols require a dedicated level of active participation on topics related to code contribution, risk parameter adjustment, DAO organization, and management. We intend to participate actively in these ecosystems.
  • Participation across stages: Given the early liquidity dynamics of crypto protocols and limited capital intensity, protocol teams require investors that can participate across the liquidity spectrum, supporting teams in both private and public markets. We have the flexibility to participate across capital stages and even leverage protocols with our own capital.

We are pleased to launch Bain Capital Crypto, an early-stage crypto-native fund with this suite of builder-oriented services.

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