August 31st, 2022

Recently I have been on a quest to understand AMM’s from a historical context (pre-DeFi). This 2013 paper by Othman et al titled “A Practical Liquidity-Sensitive Automated Market Maker” takes an axiomatic approach to unify AMM designs by characterizing AMMs by three properties - path independence, translation invariance, and liquidity sensitivity.

1 - Three properties to characterize AMMs - path independence, translation invariance, and liquidity sensitivity

Path Independence

Path independence means that market state transitions remain the same for trader costs and payments in aggregate. From a trader's point of view, it does not matter whether the trader makes one large trade or executes smaller sequential trades. From a probabilistic point of view, this ensures that the conditional probability of outcomes throughout time remains independent.

August 30th, 2022

I read a paper from 2009 by Agrawal et al titled “A Unified Framework for Dynamic Pari-Mutuel Information Market Design” and these are my takeaways:

1 - Hanson’s Logarithmic Market Scoring Rule (LMSR) AMM designs a truthful, efficient prediction market using pari-mutuel designs.

Pari-mutuel betting is an antiquated term used to describe (modern) prediction markets. However, since Hanson’s LMSR paper came out in 2002, there wasn’t better words to describe the concept of automated market making.

Parimutuel betting (from French pari mutuel, "mutual bet") is a betting system in which all bets of a particular type are placed together in a pool; taxes and the "house-take" or "vigorish" are deducted, and payoff odds are calculated by sharing the pool among all winning bets. In some countries it is known as the Tote after the totalisator, which calculates and displays bets already made. - Wikipedia

May 27th, 2022

What is a Replicating Market Maker?

Decentralized exchanges (DEXs) have fueled immense growth and activity on the Ethereum blockchain, trading over 1 trillion USD in volume in 2021. Constant function market makers (CFMM) such as Uniswap are the most widely used DEX designs and offer permissionless ways for users to provide liquidity and trade tokens. CFMMs allow investors to permissionlessly construct short gamma portfolios and provide liquidity for a spot market for these portfolio positions.

Replicating Market Makers (RMMs) extends the DEX design space even further, allowing for the creation of permissionless liquid derivatives. Formulated by Angeris et al. [Replicating Market Makers, March 2021], an RMM is a more general type of CFMM that can replicate different financial derivative payoffs. RMM liquidity pools act as spot price markets for derivatives and do not rely on external oracles, eliminating oracle manipulation attack vectors.

Using convex analysis, Angeris et al. [Replicating Monotonic Payoffs Without Oracles, September 2021] provide a general method to construct various derivatives. Estelle et al. [Primitive RMM-01, October 2021] showed the first implementation on the Ethereum mainnet, replicating the Black Scholes price of a European covered call. Estelle et al. [Replicating Portfolios: Constructing Permissionless Derivatives, May 2022] then derived more theoretical results, expanding the arsenal of possible derivative implementations to binary options, cash or nothing calls, straddles, and liquidation free lending.

April 17th, 2022

This paper extends the results of DeFi Liquidity Management via Optimal Control (Tarun, Kshitij, Guillermo, Alex, Victor) by optimizing liquidity management and supply issuance via bonding and staking. The result is increased capital efficiency of bond supply issuance, decreased risk by minimizing price volatility, and sustainable long term supply emissions growth. By implementing this liquidity management model in practice, this will add an additional layer of risk management and capital efficiency to POL (protocol owned liquidity)  assets and increase decentralized exchange volume.

History of Liquidity Management

Given the recent explosion of financial innovation in DeFi (decentralized finance) and the broader decentralized web3 movement, a novel way to obtain liquidity has been through the rise of decentralized exchanges using constant functions such as xy=k to create liquid markets for web3 native assets. Although this opens up a decentralized, permissionless way to provide liquidity, centralized exchanges currently dominate volume with more than 5x the amount of monthly volume compared to decentralized exchanges. 

April 2nd, 2022

“DeFi Primitive Risk Methodology (DPRM) is an open source risk management library (currently in development) that lets users perform both quantitative and qualitative risk analysis on groups of DeFi primitives using stochastic methods to simulate first and second order effects from any combination of tokenomics designs.”

Problem - Risk Management in DeFi is hard

In DeFi, a plethora of innovation is occurring with the creation of many new macro DeFi  primitives such as liquidity pools, bonds, and staking. Within these macro DeFi primitives exists a myriad of micro DeFi primitives. Together, the combination of these two groups of primitives create a composable set of tools for developers that allows for an infinite amount of creativity when designing novel tokenomics. Since most of the smart contracts are publicly verified, anyone can take primitives from various protocols and mix and match them to create something new. While this approach often creates novel systems, it’s often not always apparent that novelty translates to innovation. It’s difficult to understand the second order effects that each newly created group of primitives have, specifically in the context of financial risk management.

Currently the industry standard is to launch tokenomics systems without having completed robust financial risk analysis. Individuals shoulder all of the liabilities and responsibilities in determining financial risk and must use their best judgment and ‘DYOR’ to validate the tokenomics of a protocol before using it. The process of risk analysis requires considerable effort to perform. Unfortunately the average DeFi individual often does not have the resources and knowledge to answer important questions such as:

January 13th, 2022


This research was done in an effort to understand what the ideal trading strategy is for tokens with rebase mechanics. The rebase yield is amplified when a protocol is in the early days and has a high rebase rate. The (3,3) vanilla strategy captures 100% of the rebase yield and sets a high benchmark to beat.

Analysis is performed on a 6 month historical data time frame ranging from June 21st - December 14th 2021 and compares a custom built quantitative trading model vs (3,3). The quantitative model utilizes a crossover momentum strategy based on the 15day vs 30day Crypto Speculation Index (CSI)

January 13th, 2022

Overview of CFGI

The goal of CFGI attempts to quantify buying and selling opportunities based on the overall fear and greediness of the market and tries to predict when market corrections will occur and when buying opportunities present themselves.

CFGI gathers data from five sources - Volatility (25%), Market Momentum/Volume (25%), Social Media (15%), Dominance (10%), and Trends (10%).Why those weights specifically?

January 2nd, 2022
1) Overview of Stablecoin Industry in 2021
  1.1) Limitations on the Growth of the Stablecoin Industry
  1.2) Algorithmic Stablecoins

2) UST-LUNA: A Two-Token Seigniorage Shares System
  2.1) Historical Two-Token Seigniorage Models
  2.2) How UST Maintains Peg
  2.3) Growth Focused Fiscal Policy

3) BEAN: A Credit-Based System
  3.1 How BEAN Maintains Peg
  3.2 Historical Fiat Debt
  3.3 Beanstalk Debt
  3.4 Organic Demand via STALK/SEED

1.0 Overview of Stablecoin Industry in 2021

DeFi has seen a massive amount of growth in TVL, recently surpassing 250b TVL as of the end of 2021. As DeFi continues to mature, participants continue to look for more ways to earn high, volatility-risk free yields and arbitrage opportunities resulting in higher capital efficiency within the ecosystem. These drivers have resulted in extraordinary demand for multi-chain stablecoins. In the past year, stablecoin supply grew over 500% from 29b to 150b per The Block. This stat does not even include many of the popular stablecoins like DAI, FEI, and FRAX, which amount to an additional ~$25b more to the stablecoin market.

Most notable has been the explosive demand for UST, the stablecoin native to the Korean blockchain Terra. Terra founder Do Kwon says rising demand for UST is the main factor behind a 65% increase in the price of Terra’s LUNA token over the past couple of weeks due to the UST seigniorage mechanic. Seigniorage is the profit the protocol makes from issuing new UST by burning LUNA. A combination of high yield opportunities and a growth driven fiscal policy have been driving demand for UST, causing UST supply to skyrocket. The growth driven fiscal policies have attracted dozens of new projects and are expected to launch in the first quarter of 2022 after completing their audits. In December 2021, UST surpassed DAI, becoming the fourth largest stablecoin behind USDC, USDT, and BUSD.

December 8th, 2021


  • 1) What is Olympus?
  • 2) Staking OHM
  • 3) Treasury Asset Accumulation
  • 4) Hypothetical Bank Runs
  • 5) Premium over Backing OHM Valuation
  • 6) Future Innovations (Will spin this off into part 2)
  • 7) Conclusion & Data Sources

Disclaimer: the data was pulled during the first half of December 2021. Data is subject to change and future readers can refer to the dune dashboards for up to date data. Long term plans include embedding the data sources into this article so that the data is shown in real time.

December 4th, 2021

At the time of this writing, December 4th 2021, Concave has no token. Concave has no website. Concave does not officially exist yet the discord is filled with over 25,000 people and a vibrant community has sprouted up. Either this is the biggest Ponzi in crypto or it’s going to be one hell of a project with no in between. I wrote this “thesis” on my philosophical take on Concave in consideration for the “Philosopher Role”.

November 15th, 2021

TLDR - Use $300m allocation to become the dominant liquidity director on Tokemak through strategic LP positions in TOKE/ETH and ILV/ETH to accrue TOKE tokens

Strategic Proposal:

This is my strategic proposal in response to the Yearn Millenium Prize. Below I propose a strategy that utilizes the newest innovations in DeFi and allows Yearn to play a leading role in the emerging LaaS (liquidity as a service) DeFi industry. The strategy has the potential to organically scale to over $1b and will serve as one of the largest catalysts of change, creating an enormous amount of value for both DeFi and the web 3.0 ecosystem as a whole. The expectation for this strategy to be successful is that it creates more value than it takes and that the ‘returns/gains’ will only be a by-product of the value generated to the rest of the ecosystem.

With a $300m allocation, this strategy will create a liquidity highway and position Yearn as the dominant Tokemak liquidity director by directing liquidity to Illuvium which is the NFT RPG game where you mine, harvest, capture, and fight Illuvials with an open beta set to launch in Q1 2022.

November 12th, 2021

Graph Representation of a DAO

An organization can be represented as a graph by allowing each node to be a department and each edge to be a shared responsibility between two departments.

In the above example, the following nodes are operations, treasury, sales, and marketing, and two miscellaneous departments. Notice that there is a connection between every node. This type of graph is called a complete graph or fully connected. If any node is removed, the graph will still remain complete. In other words, none of the functions of the remaining nodes will be affected because the graph is still a complete graph, which can be seen as an equivalent definition for ‘decentralization’.

Example - Complete Graph of a DAO, maximally decentralized
Example - Complete Graph of a DAO, maximally decentralized
November 2nd, 2021

Why is liquidity important?

Liquidity is important because all of crypto runs on liquidity just like the world runs on fossil fuel energies. Protocols and platforms that have high liquidity depth will be able to support more efficient trades. Over time this creates a monopolistic moat vs other protocols and platforms similar to how corporations like Google and Microsoft print money at will.

Liquidity mining has proven to be the go to method for DeFi startups to bootstrap liquidity. This was initially used to great success to attract liquidity to protocols. However this is a costly endeavor and it has been found that the yield farmers, who are the primary liquidity providers, are economically incentivized to sell often to lock in yields. This increases sell pressure, erodes treasury buying power, and decreases the token value for long term holders of the protocol.

Capital efficiency is a key metric for treasuries because they spend millions of dollars a week in incentives to source liquidity for their projects. The liquidity as a service (LaaS) industry is quickly catching steam, attracting $5B USD TVL in less than a quarter by offering greater liquidity depth and a higher capital efficiency. This nascent sector is being shaped by protocols such as Curve Bribes,  Olympus Pro, Tokemak, and UMA.