BrownFi V1 launched over 3 months ago to address key pain points in LPing, specifically Uniswap V2's low capital efficiency and Uniswap V3's high Impermanent Loss that requires constant monitoring. Our elastic liquidity model has proven effective, generating real revenue for LPs compared to the Buy n' Hold strategy—even despite the decline in $BERA price. Several users have shared their experiences on X:

• Actual PnL of LPing on BrownFi after 2 months

• Jason's LPing portfolio

• Paven's LPing portfolio

• 
  

Many other early adopters have confirmed similar results. From the takers' side, integrations with Ooga Booga and KyberSwap aggregators have processed $5,502,947 in trading volume across 10,712 unique wallets within just 3 months. This represents approximately $1.8 million in monthly trading volume against only $40k-$50k TVL on BrownFi—clearly demonstrating the platform's exceptional capital efficiency.

These results have strongly motivated us to improve our protocol. Today, we're thrilled to announce BrownFi V2, which makes liquidity providing easier for everyone while maximizing returns with minimal effort.

Let’s dive in V2!

Improving security of the protocol

Improving security is the highest priority of BrownFi. In V2, we add another security layers with Oracle Adapter (enables two price sources to ensure reliable price feeds to pair contracts), Admin Roles and Timelock to Effective Setting.

Admin Roles

We define three independent admin (setter) roles associated with specific parameter settings: Oracle Price Setter (OracleSetter), Business Setter (BizSetter), and Protocol Supervisor (Pauser). After deployment, the deployer must transfer these roles to appropriate new admin addresses.

• OracleSetter: Acts on a specific pool. This role can set the adapter contract address, price feedID, and minimum valid time for a price update.

• BizSetter: Acts on a specific pool. This role configures pool parameters that align with the pool owners' business goals, including transaction fees, liquidity concentration, and protocol revenue sharing ratios.

• Pauser: Acts on all pools. This role can pause the entire protocol in case of attacks or emerging vulnerabilities.

*No administrator can withdraw funds from liquidity pools.

Timelock for Effective Settings

To prevent accidental and sudden changes in the protocol, we implement timelocks for setting changes before they become effective, with the exception of protocol pausing.

• All admin role changes require a 48-hour timelock to become effective. During this waiting period, the protocol continues to operate using the previous admin addresses.

• All OracleSetter settings require a 48-hour timelock to become effective. During this waiting period, the protocol continues to operate with the old settings.

• The "Pause the entire protocol" setting and all Bizsetter settings are immediately effective.

Enhancing Resilience of Liquidity Pools

BrownFi is an AMM that uses oracle pricing to eliminate stale token prices in pools. This approach consistently provides global prices to takers, preventing toxic flow, impermanent loss (IL), and Loss-versus-Rebalancing (LVR) threats common in non-oracle AMMs like Uniswap. The only significant risk when providing liquidity on BrownFi is inventory imbalance, which occurs when market movements cause disproportionate token ratios in pools (e.g., too much ETH but very little USDC in an ETH-USDC pool). Inspired by Uniswap V2's design, which maintains a 50-50 ratio in USD value between tokens all the time, we've implemented several improvements in V2 to reduce this risk and enhance pool resilience as follows.

Price and Skewness

In V2, we introduce pool skewness that adjusts the oracle-fed price before each swap. The concept is simple: if a swap would increase inventory imbalance, the price becomes more expensive to discourage that trade. Conversely, if a swap would help balance the inventory, the price becomes cheaper to encourage it.

We compute the absolute skewness of the pool as follows:

$$S=\frac{xP^0_x-yP^0_y}{xP^0_x+yP^0_y}$$

*Where (x,y) are token balances, and $$(P^0_x, P^0_y)$$ are the oracle-fed prices for token0 and token1 in the pool.

If token0 reserve exceeds token1 reserve $$(xP^0_x≥yP^0_y)$$, the pool offers a higher price for token0 and a lower price for token1:

$$\begin{cases} P_x=P^0_x(1-\lambda S) \ P_y=P^0_y(1+\lambda S) \end{cases}$$

If token1 reserve exceeds token0 reserve $$(xP^0_x≤yP^0_y)$$, then the offered prices will be:

$$\begin{cases} P_x=P^0_x(1+\lambda S) \ P_y=P^0_y(1-\lambda S) \end{cases}$$

*Where λ is a configurable parameter defined by maximum imbalance target (80-20) of the pool. The default value is λ=0 with a limit range of [0,1].

Unlike V1, BrownFi V2 prevents any trade with the order size ≥ 80% of the reserve from going through (the transaction will be reverted). This protects against inventory depletion from large orders without needing to increase the concentration liquidity parameter Kappa, which would negatively impact pricing for smaller order sizes.

Adding Liquidity with 50-50 Ratio Requirement

In V1, LPs had to add/remove liquidity according to the USD reserve ratio of the two tokens in the pool. This created poor UX, as LPs needed to calculate this ratio before adding liquidity—a ratio that constantly changed after every swap. Furthermore, these liquidity operations didn't alter the reserve ratio, meaning they couldn't help balance the pool.

In V2, we've improved this process by allowing LPs to add liquidity with a simple 50-50 USD value split, while removing liquidity still follows the V1 method (LPs can manually rebalance to 50-50 after withdrawal if desired). This change creates a better UX and helps rebalance pool reserves more quickly.

All set!

These small improvements enhance the resilience of liquidity pools, mitigate inventory imbalance risks, and ensure that pools can quickly rebalance and resume normal operations if the inventory of one token becomes exhausted.

There are some other small improvements in this version 2 you can check in the table below, or refer to this technical document:

With V2, we strongly believe that BrownFi can operate steadily and resiliently with enhanced security layers that maximize returns for LPs through trading fees and price impact premiums. This version marks an important milestone for BrownFi, enabling us to scale to multiple chains and assets for DeFi liquidity providers. We're confidently implementing V2 across 5 EVM chains (Arbitrum One, Base, BNB, Bera and Viction) with several mature trading pairs available at launch:

• ETH - USDC (Arbitrum & Base)

• ETH - USDT (Arbitrum)

• WBTC - ETH (Arbitrum)

• cbBTC - ETH (Base)

• BNB - USDT (BNB chain)

• BERA - HONEY (Bera)

• C98 - VIC (Viction)

• etc.

Additionally, this version allows anyone to create a new pool in a permissionless manner. This process follows a design similar to Uniswap V2, with adaptations to accommodate BrownFi's oracle-based AMM, including setting oracle price feeds and liquidity concentration parameters (Kappa) for specific pairs.

We hope that the team and community members can join forces to make LPing both easy and profitable in the DeFi ecosystem.

About Us

BrownFi is an innovative oracle-based AMM, high capital efficiency (like Uniswap V3), flexible & simple LP management for average users, with arbitrage resistance.

• Website: https://brownfi.io/

• Twitter: https://x.com/BrownFidex

• Community: https://t.me/brownfiammcommunity

• Announcement: https://t.me/brownfiamm

Leaderboard

Check your rank HERE

Duration

The competition will run for 12 days, from April 24, 2025 at 07:00:00 UTC to May 5, 2025 at 06:59:59 UTC.

Criteria

Rankings on the Leaderboard are determined by points. Winners will be selected based on the points they accumulate during the campaign.

Participants can earn points by performing swaps between whitelisted pairs. Each 1 HONEY or 1 USDC.e in trading volume earns 1 point. The whitelisted pairs are:

• BERA - HONEY

• BERA - USDC.e

• HONEY - USDC.e

Any swaps not involving whitelisted pairs will be disqualified from the competition.

E.g.:

• If you swap 100 HONEY to BERA, you will earn 100 points on the Leaderboard.

• If you swap 100 HONEY to iBGT - token is not whitelisted, this swap won't earn you any points.

Prizes

• 1st winner: 250 HONEY

• 2nd winner: 150 HONEY

• 3rd winner: 100 HONEY

Terms & Conditions

• The Campaign will run from April 24, 2025, at 07:00:00 UTC to May 5, 2025, at 06:59:59 UTC. BrownFi retains the right to amend the campaign's start and end dates with reasonable notice.

• BrownFi maintains the right, at its sole discretion, to disqualify any participant who violates, cheats, or exploits the campaign.

• BrownFi reserves the right to change the rules & conditions at its sole discretion.

• Any participant engaging in sybil attacks or any form of cheating will have all points and rewards forfeited.

• Rewards will be distributed directly to winners' wallets within 10 days of the campaign's end.

What You’ll Do

• Use BrownFi AMM: Provide liquidity, swap and explore our cool features on the Boba Network.

• Earn Rewards: Any transactions from 1st March to 10 April, 2025 will be automatically count for the trading competition with total award of $2500 Boba tokens. Let be one of the top performers.

How to Participate

1️⃣ Interact with BrownFi AMM on Boba Network:

• Connect Your Wallet: Use Metamask or EVM-wallets to connect to the BrownFi AMM on Boba Network mainnet:

https://mainnet.brownfi.io/#/swap

• Perform Transactions: Swap or provide liquidity on BrownFi AMM, simply as using Uniswap V2.

2️⃣ Engage with the BrownFi Community:

• Follow us on Telegram Channel: Join the Telegram

• Follow us on Telegram: Join the Telegram Group

• Follow us on X: Follow BrownFi on X.

🏆 Prizes:

• 🥇 Top 3 Participants with the most volume, TXs, and liquidity provision will receive $2500 Boba tokens.

• Criteria: Volume of transactions, number of TXs, and liquidity amount provided.

• Note: Only users who follow us on Telegram and X are eligible for awards.

How to bridge your fund to Boba Network

You may try Toaster Finance, a cross-chain bridge & swap aggregator supporting Boba Network, to transfer your funds to Boba Network.

Campaign Duration

• Start: 1st March, 2025

• End: 10th April, 2025

💪 Don’t miss out on this exciting opportunity to be part of the BrownFi journey! Try out our features, compete for rewards, and help us shape the future of DeFi on Boba. We also have separate retro programs later for all early adopters (including LPers and traders on BrownFi). Please stay tuned for future announcement.

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• The only thing a trader cares is average trading price with small slippage as possible. Higher liquidity concentration makes lower price impact, smaller slippage.

• BrownFi AMM offers capital efficiency and trading experience equivalently to Uniswap V3 pools. Particularly, BrownFi pool with $$K=0.001$$ is mostly equivalent to Uniswap V3 range $$\pm1%$$.

• If $$K=2$$, then BrownFi pool and Uniswap V2 are identical.

A little math of AMMs

Uniswap V2 introduced automated market making (AMM) based on a constant product market making (CPMM) formula $$x * y=k$$, where the token price is defined by token reserve in the pool $$p=y/x$$. Consider the pool with token reserve (10, 10), liquidity and swap constant $$x* y=10* 10=100$$ with the initial price $$P= 1$$. A swap out of $$\Delta x$$ of token X must provide $$\Delta y$$ of token Y in exchange. The CPMM formula gives us $$(x-\Delta x)(y+\Delta y)=k \Rightarrow \Delta y = \frac{k}{x-\Delta x}-y.$$

Uniswap V3 introduced the concentrated liquidity market making (CLMM) based on the orginal constant product (i.e. the CPMM formula), allowing us to find a curve limited by a price range such that it can serve the trade with optimal capital. Regarding Uniswap V3 model, a liquidity position is defined by both token reserve $$(x, y)$$ and a price range $$[p_a, p_b]$$. The liquidity and swap constant of V3 model reads

$$(x+\frac{L}{\sqrt{p_B}})(y+L\sqrt{p_a})=L^2$$,

where L is the virtual liquidity (comparable to the equivalent V2 model, i.e. $$x* y =L^2$$).

For simplicity and without loss of generality, we take price lower bound $$p_a = 1.0001^{-n}$$, price upper bound $$p_b = 1.0001^n$$, symmetrically. For $$n=100, p_a= 1.0001^{-100} \approx 0.99$$ and $$p_b=1.0001^{100} \approx 1.01$$, resulting $$\pm1%$$ range. For $$n=200, p_a= 1.0001^{-200} \approx 0.98$$ and $$p_b = 1.0001^{200} \approx 1.02$$, resulting $$\pm2%$$ range. Let consider 3 ranges of the same token reserve.

• Uniswap V3 pool1 has reserve (10,10), range [-9.5%, +10.5%] (i.e. $$n=1000$$). The constant product is $$(x+\frac{205}{1.0001^{500}})(y+\frac{205}{1.0001^{500}})\approx 205^2$$ having liquidity leverage (so capital efficiency) $$\frac{205}{10} \approx 20.5$$

• Uniswap V3 pool2 has reserve (10,10), range $$\pm2%$$. The constant product is $$(x+\frac{1000}{1.0001^{100}})(y+\frac{1000}{1.0001^{100}})\approx 1000^2$$, having capital efficiency $$\frac{1000}{10} \approx 100$$

• Uniswap V3 pool3 has reserve (10,10), range $$\pm1%$$. The constant product is $$(x+\frac{2000}{1.0001^{50}})(y+\frac{2000}{1.0001^{50}})\approx 2000^2$$, having capital efficiency $$\frac{2000}{10} \approx 200$$

Because $$x=y$$ and $$\frac{1}{\sqrt{p_B}}=\sqrt{p_a}$$, we have $$(x+\frac{L}{\sqrt{p_B}})^2=L^2, x+\frac{L}{\sqrt{p_B}}=L$$. A swap out of $$\Delta x$$ of token X must provide $$\Delta y$$ of token Y in exchange. The CLMM formula gives $$(x+\frac{L}{\sqrt{p_B}}-\Delta x)(y+L\sqrt{p_a} +\Delta y)=L^2 \Leftrightarrow (L-\Delta x)(L +\Delta y)=L^2$$

and hence $$\Delta y=\frac{L^2}{L-\Delta x}-L.$$

BrownFi AMM introduced a novel oracle-based AMM model. Given a token reserve $$(x, y)$$ and an amount $$\Delta x$$ of token X to be swapped out, trader must pay $$\Delta y$$ of token Y in exchange, simply defined by:

• $$\Delta y = P(1+\frac{R}{2})\Delta x$$, where $$P$$ is the global price fed by oracle;

• The term $$\frac{R}{2} $$is related to slippage (alternatively, price impact), where $$R=\frac{K * \Delta x}{x-\Delta x}$$;

• Kappa ($$K$$) is the parameter controlling liquidity concentration on BrownFi's pools.

We consider four liquidity concentration on BrownFi AMM, controlled by $$K_1=1, K_2=0.1, K_3=0.01, K_4=0.001$$.

What do traders care?

The average trading price is the only thing a trader cares, defined by $$\frac{\Delta y}{\Delta x}$$. Smaller price impact, closer trading price to global price, better experience for average traders. Higher liquidity concentration makes lower price impact, smaller slippage, better trading experience. Standardizing token reserve (10,10), initial price $$P=1$$ for all pools of Uniswap and BrownFi's AMMs, we will compare price slippage $$\frac{\Delta y}{\Delta x}-1$$ between them. In prior to comparison, we find the intersections of the slippage curves (equivalently price impact curves). Each intersection represents order size (over the total of 10 token reserve) and percentage of slippage.

Slippage (price impact) comparison

• Easily see that Uniswap V2 causes greater slippage than all BrownFi pool (for $$K<2$$). Particularly, if $$K=2$$, then BrownFi and Uniswap V2 are identical.

• Regarding three Uniswap V3 pools, each BrownFi pool ($$K_3, K_4$$) has lower slippage on the left side of the intersecting point, greater on the right, respectively. Particularly, BrownFi $$K_4=0.001$$ is mostly equivalent to Uniswap V3 range $$\pm1%$$.

Further on capital efficiency comparison, we have:

Contact us

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About BrownFi AMM

BrownFi is an innovative oracle-based AMM, offering high capital efficiency and simple UX for average LPers. BrownFi is designed to solve the pain-points of LPers on the Uniswap V3 model:

• Fact 1: Half of LPers on UniV3 are lost due to high impermanent loss and Out-of-Range;

• Fact 2: ~$858M dollars are lost for arbitrageurs.

LPers on BrownFi AMM enjoy high capital efficiency, being permanently-active for trades & fee collection, arbitrage resistance, hence earn more than ever

BrownFi has retroactive and referral program for users and liquidity contributors. Details will be announced later.

About Viction

Viction is an EVM-compatible layer-1, designed with a focus on user experience, prioritizing zero-gas transactions, speed, security, and scalability to contribute to the creation of a more secure and open world. BrownFi is excited to bring innovative & highly-efficient liquid solutions to the Viction ecosystem and the best UX to its users.

How to trade and provide liquidity on BrownFi AMM?

All UX on BrownFi AMM is similar to Uniswap V2. Traders can swap instantly between C98 and VIC tokens. More pairs will come. LPers can add/remove liquidity similarly to Uniswap V2, much simpler than V3 model.

Go to trade on BrownFi AMM

https://mainnet.brownfi.io/#/swap

After token approval, your swap or supply action may fail due to delay on fetching events from the underlying blockchain. Just refresh your dapp, then click swap or supply liquidity. It will go through.

Wallet connection

Users may connect Metamask, Walletconnect or Coin98 wallet extensions on web-browsers for transactions. Simple tips to connect Coin98 wallet:

• 1. Install Coin98 wallet extension on your web browser

• 2. You must DISABLE wallets supporting Viction chain like Metamask.

• 3. Open your Coin98 wallet, go to settings, then Override wallet, set Coin98 wallet as default. All done, now you can use Coin98 wallet on Brownfi. When you connect wallet, clicking Metamask symbol will link to Coin98 wallet.

Contact us

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References

BrownFi AMM contracts’s audit report by Verichain https://github.com/verichains/public-audit-reports/blob/main/Verichains Public Audit Report - BrownFi AMM Smartcontracts - v1.0.pdf

BrownFi AMM contracts deployed on Viction mainnet:

• Router https://www.vicscan.xyz/address/0x0194CcfC49C3ebc7457E0b41B9c6b840C22f5985

• Pool C98/VIC https://www.vicscan.xyz/address/0x3273c19716b2f4e95b563a099923e539c5aef1b3

• Price feed provided by Pyth oracle

• How Impermanent loss (IL) and arbitrage cost appear

• All the costs of liquidity providers (LPs) on AMMs

• How BrownFi (as an innovative oracle-based AMM) mitigates IL & arbitrage loss, ensures LP gains

Impermanent Loss is common in all markets

Impermanent Loss (acronym IL, aka divergent loss) is simply the opportunity cost of adding liquidity into an AMM pool vs holding the individual tokens. IL disappears if and only if the price returns to the pool-entering price, otherwise IL becomes permanent loss. Formally, IL is measured by $$IL=\frac{Pool.Value}{Hold.Value}-1$$, being negative whenever price increases or decreases. In fact, divergent loss is a common phenomenon appearing in all financial markets, including CEXes and AMMs, at the side of market makers (MMs), or liquidity providers (LPs). However, MMs on CEXes can actively adapt to price changes very quickly, e.g. removing bids/asks with stale price and replacing them with updated orders surrounding the newly middle price. LPs on AMMs, unfortunately, have no way to do the similar actions, because they are passive to price change. Price of an AMM pool (constructed on constant product market making, aka CPMM model) is purely defined by the ratio of two token reserves, which is changed per swap by arbitrageurs or normal traders.

Why do LPs accept IL?

When providing liquidity on Uniswap and other AMMs, LPs have an ONLY hope that accumulative trading fee can cover the loss, even help them gain. Differently, MMs on CEXes earn via price spread advantage.

The costs of liquidity provision other than IL

It is impossible to completely remove IL, even higher liquidity concentration causes higher IL (e.g. on Uniswap V3’s pools). Luckily, there are some ways to mitigate IL. For example, Balancer has modified the 50/50 inventory model of Uniswap V2 to build another version of CPMM with custom inventory ratio, hence reducing IL.

However, inventory imbalance, in turn, is an issue of Balancer, plus opportunity cost of adverse selection in the following. Interestingly, CPMM and impermanent loss are path-independent, i.e. IL is the same for any possible price trajectories (other than its initial and final values). Although IL is zero if the initial and final prices stay the same, that concept fails to isolate the adverse selection costs (caused by arbitrageurs) faced by LPs on most AMMs. In reality, there are always price discrepancies between CEXes (continuous price discovery in real-time) and DEXes (discrete price discovery per block time), giving opportunities for arbitrageurs to take profit at the expense of LPs. Then LP costs should be increasing in the number of opportunities for AMM arbitrage. And the frequency of such opportunities is very different if the price stays the same (no arbitrage) versus if it jumps around a lot (lots of arbitrage). Half of LPs on Uniswap V3 suffer losses due to high IL and out-of-range positions. Sorella Labs has tracked (in real time) that, since the Merge, LPs on Ethereum have lost over $750M due to arbitrate. In general, A16Z researchers have raised the loss versus rebalancing (LvR) problem, which put arbitrage cost as the opportunity loss of liquidity provision.

How oracle-based BrownFi AMM protects LPs?

Suppose an AMM pool (e.g. on Uniswap V2 and V3 with bonding curve $$x* y=k$$ for both) has 1 ETH and 1000 USDC. Suppose further that at a very good moment for ETH, the market price jumps from $1000 to $4000. This requires a swap of 1000 USDC to receive 0.5 ETH, and the post-trade pool ratio is 0.5 ETH : 2000 USDC. In this case, the decision to provide liquidity would have doubled your money from a $2000-value portfolio on deposit to a $4000-value one upon withdrawal. Consequently, providing liquidity on the AMM cause your loss of $1000.

If you sell 0.5 ETH on a high liquid CEX (e.g. Binance) at $4000, after that, your portfolio (0.5 ETH, 3000 USDC) value is $5000 dollars, equal holding portfolio.

Now, let’s see how BrownFi works with the initial (1 ETH, 1000 USDC) reserve and the same trade of buying $$dx=0.5$$ ETH at the market price $4000. With a high liquidity concentration (parameter Kappa $$K=0.001$$), BrownFi’s pricing formulas read.

• Price impact factor $$R=K\times \frac{dx}{x-dx}=0.001 \times \frac{0.5}{1-0.5}=0.001$$

• Trading price $$P_t=4000(1+R/2)=4002$$, so paying $$dy=dx * P_t=2001$$ USDC.

Thus, the LP portfolio on BrownFi AMM is (0.5 ETH and 3001 USDC) valued $5001 dollars, higher than holding. Without trading fee, what is $1 dollar greater than the holding portfolio? It is exactly the price impact cost BrownFi AMM charges per trade. It is LPs’ incentives (plus trading fee) to provide liquidity.

You may ask “trading on BrownFi AMM (and Binance) is worse than Uniswap V2” (because paying USDC doubly). NO. In fact, the trade on Uniswap is made by smart arbitrageurs who have the best tools to hunt profitable opportunities effectively upon price discrepancies at the expense of LPs and/or normal traders (i.e. LvR problem). Let’s see next.

Now, assume the 2nd trade that the market price stays the same at $4000, and a normal trader wanna buy 0.1 ETH. The Uniswap pool, after the first trade, has 0.5 ETH and 2000 USDC. Solving by $$xy=k$$ formula $$(0.5 – 0.1)(2000 + dy)=0.5\times 2000$$. The trader pays $$dy=500$$ USDC, meaning 25% more expensive than the market price. The post-trade pool is 0.4 ETH and 2500 USDC, priced $6250 per ETH, much higher than the market price. This, again, gives an arbitrage opportunity to sell 0.1 ETH back to the pool (the 3rd trade), receiving 500 USDC, roughly taking 100 USDC profit at the expense of the previous trader. Eventually, the portfolio on Uniswap pool is (0.5 ETH and 2000 USDC) valued $4000, as same as the value after the 1st trade with IL of $1000.

After the first trade, BrownFi AMM pool has 0.5 ETH and 3001 USDC. Then we have the 2nd trade (buying $$dx=0.1$$ ETH)

• Price impact factor $$R=K\times \frac{dx}{x-dx}=0.001\times\frac{0.1}{0.5-0.1}=0.00025$$

• Trading price $$P_t=4000(1+R/2)=4001$$, so paying $$dy=dx * P_t=400.1$$ USDC with negligible slippage.

The portfolio on BrownFi AMM pool is now (0.4 ETH and 3401 USDC) valued $5001, still higher than holding, and no arbitrage opportunity.

Without loss of generality, the previous examples take an extreme price volatility (for easy computation & reading) to illustrate that Uniswap V2 and V3 models are exposed to both IL and arbitrage loss. Arbitrageurs take profits at the expense of either LPs or ordinary traders. In contrast, BrownFi is an oracle-based AMM, always offering trade at market price plus a price impact cost. Therefore, by eliminating arbitrage opportunities, BrownFi AMM mitigates overall loss and guarantees gains of LPs.

The following table summarizes the state changes from the initial portfolio of 1 ETH, 1000 USDC throughout 3 trades with the market price of 1 ETH = $4000 dollars, and 1 trade when the price returns $1000. With this setting (same token reserve and price path), Uniswap V2 & V3 are identical by using the same formula $$x\times y=k$$. Trading fee is ignored for simplicity (but no impact on our consideration). If you choose a lower price (e.g. $2000 or $500), the absolute values change with small numbers of many decimals, but the relative quantities and implied properties are still the same. Thus, it doesn’t affect our conclusions on the nature of exchange models. ETH reserve is green while USDC reserve is white.

In the table 2, LPs on Uniswap has zero IL when the price returns to the initial pool setting. However, at the end of the illustration, arbitrageurs earn $1600 at the cost of LPs ($1000 at the 1st trade and $500 at the 4th trade) and normal trader ($100 at the 3rd trade). On the other sides, LPs on Binance and BrownFi have $1500 gains, because they always offer liquidity at market price (arbitrageurs could not take profit at the 1st and 4th trades).

Is BrownFi AMM better Uniswap?

It is worth clarifying that impermanent loss is only suitable for Uniswap and AMMs (e.g. Balancer, Sushiswap, Pancakeswap) using CPMM models, which offer independent price discovery mechanisms. Regarding BrownFi and other oracle-based AMMs (e.g. Dodo, Lifinity) possessing price-ambience, a universal consideration of LP costs, including arbitrage cost, is more precise. In the two table above, by copying the initial pool setting, universal market price and trades, BrownFi outperforms CEX and holding with a small gain +$1 for LPs, while Uniswap makes them a huge loss for arbitrageurs. In practice, under market dynamics, market making is more complicated with many scenarios. However, one thing is still valid that BrownFi, in general, all oracle-based AMMs, are resistant to arbitrage and sandwich attacks (given sub-second blocktime and reliable oracle), thus ensure better gains for LPs by taking LvR from arbitrageurs. In reality, blockchains with long block time (e.g. Ethereum) facilitate arbitrage trades, while blockchains with sub-second block time make them much harder.

Don’t get me wrong, Uniswap and CPMM-AMMs discover price independently, hence are the only choice for tokens unlisted on CEXes. BrownFi only works if a reliable price source is available. Uniswap and CPMM-AMMs play a vital role in decentralized finance (DeFi). BrownFi, an oracle-based AMM, is a complementary solution to the CPMM-based AMM models. If oracle-price is reliable and dominant (e.g. tokens listed on CEXes with good liquidity), BrownFi AMM is potential to outperform Uniswap V3. Readers can find a comprehensive article about oracle-based AMMs here.

In general, profit and loss of LPs is PnL = pool value - hold value. The pool value contains IL, trading fees, LvR. To mitigate overall cost (e.g. IL, LvR) of LP and make LPs gain, there are 3 methods:

• Reduce impermanent loss (Uniswap V2 does). Higher liquidity concentration, higher IL. In fact, IL on Uniswap V3 is greater than V2, narrower range, larger IL.

• Reduce arbitrate attacks (or LvR in general), hence arbitrage gains are transformed to LP gains. This is what BrownFi does.

• Combining the two methods above in an equilibrium based on suitable and flexible market making strategies. This is the advanced feature BrownFi offers along with simplified UX for average LPs to help them optimize profit and minimize loss (so optimal PnL).

BONUS: In reality, token reserve and trades are very different, not the same as in the previous illustration (i.e. copying Uniswap). IL and LP loss vary according to market movement (in real time) and liquidity provision strategies. For instance, MMs on Binance can suffer huge IL if they sell a large amount of 0.8 ETH at $1000 price, then their portfolio value at $4000 price is $2600 (much lower than Uniswap $4000 and holding $5000). This is similar to providing liquidity on Uniswap V3, if you add LP with a narrow range at low price, then price jumps very high, you suffer great IL. Don’t be upset. We will have another article analyzing loss and gain of Uniswap’s neutral liquidity provision strategy and other strategies (including BrownFi AMM). Remember NO free lunch. Please stay tuned for the next article, where we will describe how BrownFi helps LPs optimize their PnL.

Contact us

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🔹 What You’ll Do:

• Test BrownFi AMM: Swap, provide liquidity, and explore our groundbreaking features on the Starknet Sepolia testnet.

• Earn Rewards: Join the competition to earn up to $250 USDT by being one of the top performers.

How to Participate:

1️⃣ Interact with BrownFi AMM on Starknet testnet:

• Faucet ETH/STRK: Visit the Starknet Faucet here to get ETH and STRK tokens for the testnet.

• Connect Your Wallet: Use Braavos or ArgentX wallets to connect to the BrownFi AMM on Sepolia testnet: BrownFi AMM.

• Perform Transactions: Swap or provide liquidity on BrownFi AMM. Use at least 0.01 ETH or 5 STRK. For a full guide, read this.

2️⃣ Engage with the BrownFi Community:

• Follow us on Telegram Channel: Join the Telegram

• Follow us on Telegram: Join the Telegram Group

• Follow us on X: Follow BrownFi on X.

3️⃣ Maximize Your Activity:

• Compete for Rewards: The top 3 participants with the highest volume, most transactions (TXs), and largest liquidity provision on the testnet will win $250 USDT.

🏆 Rewards:

• 🥇 Top 3 Participants with the most volume, TXs, and liquidity provision will receive $250 USDT.

• Criteria: Volume of transactions, number of TXs, and liquidity provided.

• Note: Only users who follow us on Telegram and X are eligible for rewards.

⏳ Campaign Duration:

• Start: October 9, 2024

• End: October 30, 2024

📢 Important Notes:

• The final rankings will be calculated based on total volume traded, transactions, and liquidity added during the task period.

• BrownFi holds the rights to modify the campaign terms and conditions without prior notice.

🔗 Get Started Today:

• Faucet ETH/STRK: Starknet Faucet.

• Connect to BrownFi AMM: Test BrownFi.

• Telegram Group: Join Telegram.

• Follow us on X: BrownFi on X.

💪 Don’t miss out on this exciting opportunity to be part of the BrownFi journey! Test out our features, compete for rewards, and help us shape the future of DeFi on Starknet.

• Participate Sonic Boom ~$45M airdrops (Sonic is previously Fantom)

• Swap, add/remove LP on BrownFi AMM - Sonic testnet

• BrownFi’s incentives and referral program

Sonic Boom

Sonic is rebranded from Fantom, building a new EVM-compatible layer-1 with scalability and a native bridge to Ethereum. Sonic Boom is a unique bounty program rewarding 190.5M $S airdrop (1S ~1FTM) for building apps & growing communities on Sonic. Currently, Sonic is in testnet phase, hence users can examine apps on its testnet with zero cost. Crypto users should participate BrownFi testnet on Sonic testnet to get airdrop in the future. BrownFi AMM is deployed on Sonic testnet, opening 2 swap pairs:

• S/DIAM is equal FTM/USD

• S/CORAL is equal FTM/ETH

• Faucet tokens (S, Diamond, Coral) at https://testnet.soniclabs.com/account

• Add/remove liquidity and swap tokens on BrownFi AMM testnet

User incentives

Community-centricity is one of BrownFi’s core values. All airdrop & community rewards from Sonic Boom airdrop and Sonenium incentives (if BrownFi receives) will be distributed to the community as follows.

• 70% to ordinary users, weighted by onchain reputation scores, social engagement, etc. Details will be announced later.

• 15% for the referral program (up to 2 levels).

• 5% reserve for unforeseen distribution (likely to community leaders/KOLs or adding to referral programs, etc). Leaders/KOLs should contact the BrownFi team for verification and approval, otherwise, they will be considered as ordinary users.

• 10% for other marketing purposes.

Regarding referral program, you simply connect your wallets on https://testnet.browndex.io/ to obtain referral links, then invite your friends to use BrownFi AMM testnet. More users you refer, more rewards you will receive. However, all users MUST actively interact with BrownFi AMM protocol (add/remove LP, swap tokens on Sonic testnet, and/or Sonenium Minato testnet) to be ELIGIBLE for airdrop and referral program.

REMARK: users should create new wallets to interact with BrownFi AMM on testnets. This is to avoid scam and phishing attacks, affecting your real assets on mainnets.

Onchain activities are a key factor to weight airdrop amount in the future. Onchain reputation score is aggregated on multiple wallets and multiple chains that users own and interact with. More onchain activities, higher reputation and better rewards. BrownFi incorporates adaptive Pagerank to score onchain reputation and machine learning algorithms to prevent Sybil attacks. This is to protect real users, guarantee fairness among users and contributors.

BrownFi’s retros & token incentives: Independently from the Ecosystem’s incentives, BrownFi has its own airdrop and retros, which will be announced later. Again, community centricity is our core value.

ZERO cost, ZERO risk to interact with BrownFi AMM on testnets, but you EARN airdrops, gems and many more rewards.

About BrownFi AMM

BrownFi is developing an innovative AMM based on oracle-price, offering high capital efficiency (100X Uniswap V2), flexible market making and simple UX for average LPs. BrownFi AMM is to fill the gap between Uniswap V2 & V3 models, saving LPs from huge lose and serving average LPs with the best UX and optimal returns.

BrownFi won 1st prize - DeFi track at Openbuild-Starknet hackathon, received Seed Grant from Starknet Foundation and Developer Grant from Dfinity Foundation.

BrownFi AMM’s advantages:

• Price ambience: NO out-of-range like Uniswap V3, Maverick, TraderJoe

• Resistance to arbitrage & sandwich attacks

• High capital efficiency (100X Uniswap V2)

• Adjustable liquidity concentration and simple LP management

• Save average LPs from high IL, offering optimal returns

• One-sided liquidity provision at protocol-level

Contact us

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(i) Classify Uniswap & CPMM-AMMs versus oracle-based AMMs.

(ii) CPMM suites new tokens, but exposes to high impermanent loss, arbitrage and sandwich attacks.

(iii) Half of Uniswap V3’s LPs lose due to high IL while suffer complex LP management. On the entire Ethereum, LPs have lost $745M since the Merge.

(iv) Oracle-based AMMs outperform CPMM over CEX-listed assets, bridged cryptos, particularly tokenized real-world assets.

Uniswap disrupted centralized exchanges

Uniswap revolutionized the decentralized exchange (DEX) landscape by introducing a novel automated market maker (AMM) model. This model, pioneered by Uniswap, leverages liquidity pairs (aka pools) of two tokens to facilitate peer-to-peer trading without the need for a centralized order book. Prior to Uniswap, decentralized exchanges like IDEX, Ether Delta, and FolkDelta relied on off-chain limit order books (LOBs), which suffered from slow speeds, poor user experience, and low liquidity. While Bancor and Kyber attempted to address these issues with their peer-to-peer trading models based on token reserves, they ultimately faced challenges with liquidity exhaustion and complex asset management. For a more comprehensive overview of the evolution of DEXes, please refer to [1, 2].

Uniswap pioneered a revolutionary spot trading model, Automated Market Making (AMM), in November 2018. Its core innovation, the constant product function $$x\times y = k$$, disrupted traditional price discovery mechanisms like LOBs. Uniswap's model democratized liquidity provision, allowing anyone to create and contribute to liquidity pools of any pair of tokens. This innovation fueled the DeFi boom of 2020-2021. Other AMMs, such as Kyber, Sushiswap, and Pancakeswap, adopted the constant product model, solidifying it as a cornerstone of DeFi. Uniswap and CPMM-based AMMs offer several key advantages:

• Permissionless listing: anyone can create a liquid pool pairing two any tokens.

• Crowdsourcing liquidity: everyone can contribute to any liquid pool.

• Seamless trade: users easily swap for their wished tokens without KYC or intermediaries, provided unbounded liquidity.

• Non-custodial security: all trades are securely executed onchain by smartcontracts, eliminating the need of centralized intermediaries.

Balancer expanded the CPMM model to support multi-asset liquidity pools, using the equation $$x_1 \times x_2 \times … \times x_n=k$$. Curve introduced a constant sum market making (CSMM) model, $$x+y=k$$, tailored for stablecoin pairs (e.g. DAI, USDT, etc).

Despite Uniswap and CPMM-based AMMs have achieved significant success, they face challenges such as low capital efficiency, high slippage, and impermanent loss (IL). Uniswap V3 addressed these issues by introducing liquidity concentration, a modification of the original CPMM model. However, as research by Vladislav Goncharov [3] indicates that nearly half* of Uniswap V3's liquidity providers still experience losses due to high IL and out-of-range positions*. Moreover, managing concentrated liquidity positions can be complex and requires specialized financial knowledge and professional skills, making it less accessible to average users.

The need of Oracle-based AMMs

Impermanent loss (IL) is an inherent risk faced by market makers (MMs) across all financial markets. MMs on CEXs and LOB-based DEXs have active control over their liquidity provision strategies, enabling them to mitigate IL. Unfortunately, LPs on CPMM-based AMMs have limited influence over pool prices. This passive role exposes LPs to price deviations between AMMs and external markets. Arbitrageurs can exploit these discrepancies, profiting at the expense of LPs. For instance, if the external market price for ETH is 2500 USD, a CEX market maker can quickly adjust their bids and asks around 2500 to maintain a competitive price, in real-time manner. However, on a CPMM-based AMM, the pool price is determined solely by the token reserve ratio (e.g. 1 ETH : 2510 USD), making it impossible for LPs to adjust the price to match external market conditions. Moreover, price on AMMs is discretely updated block by block, not continuously as CEXes, causing gaps in price moves. This leaves the opportunity for arbitrageurs to profit, ultimately reducing the gains of LPs. According to Sorella Labs, LPs on Ethereum have lost $750M for arbitrageurs since the Merge (see real time tracking on Sorella website).

Obviously, oracle-based AMM models offer a significant advantage by eliminating arbitrage opportunities, including round-trip and sandwich attacks. Research by Álvaro Cartea and financial scientists at the University of Oxford [4] demonstrated that LPs on CPMM-AMMs are often providing liquidity at a loss. To address this issue, they proposed alternative models that leverage oracle prices. The paper of Philippe Bergault and financial mathematicians in Paris [5] introduced an AMM model combining external price, showing that even with lagged oracle data and adverse market conditions, optimized oracle-based mechanisms outperform traditional CPMM-AMMs. Additionally, S. Jiang et al [6], B. Krishnamachari et al [7], and D.J. Im [8] have further improved AMM design using oracle prices. These advancements aim to protect the interests of LPs and average traders by mitigating the risks associated with traditional AMM models.

Oracle-based AMMs rely on accurate price quote from external markets. To assess the dominance of external markets, we can compare trading volumes. As of September 19, 2024, the total ETH trading volume (24H) on all DEXes was less than $1.2 billion (source: DefiLlama), while the volume on the top 50 CEXes was approximately $11.8 billion (source: CoinGecko). This significant disparity, nearly a 10x difference, highlights the dominance of CEXes in terms of trading volume.

In summary, Uniswap and CPMM-AMMs, with their independent price discovery mechanisms, offer a unique advantage to provide liquidity for new tokens that may not be available on centralized exchanges. However, their passive market-making nature, susceptibility to arbitrage and sandwich attacks, and potential for huge LP losses, particularly with popular and highly liquid assets, present limitations. Oracle-based AMM models emerge as a promising alternative and complementary solution. By incorporating external price feeds, these models can address the shortcomings of traditional AMMs, potentially offering a more efficient and profitable liquidity provision mechanism (read examples how oracle-based AMMs outperform Uniswap). This implies that oracle-based AMMs can be the best solution to trade tokenized real world assets onchain, whose volume on CEXes is dominant.

BrownFi AMM plays a role

All emerging L1 and L2 ecosystems rely on bridged assets (e.g., wETH, wBTC, wDAI, ckUSDT, USDC) and their native tokensfor liquidity onchain. Oracle-based AMMs offer a simple and capital-efficient solution for swapping native tokens against bridged assets (e.g., STRK/ETH, STRK/USDC, SUI/wETH, SUI/USDC, ICP/ckUSDT). Unlike CPMM-AMMs, which are best suited for CEX-unlisted tokens, oracle-based AMMs excel in trading CEX-listed crypto-assets. Dodo and Lifinity are notable examples of successful oracle-based AMMs. However, Dodo's capital efficiency is limited, with a maximum of 10x compared to Uniswap V2, and Lifinity restricts liquidity provision to a strictly selected group of LPs. BrownFi addresses these limitations by introducing an innovative oracle-based AMM with 100x higher capital efficiency than Uniswap V2, flexible market making, a user-friendly interface, and open access for all LPs. BrownFi's mathematical model, inspired by the statistical properties of Limit Order Books, enables these advanced features.

Remember that DEXes cannot replace CEXes, CPMM cannot replace limit order-book. They all live together to provide multiple market making and trading options under various circumstances. Although CPMM-based AMMs (e.g. Uniswap) are a popular solution for onchain liquidity in general, oracle-based AMMs (e.g. BrownFi) play the role of a complementary block in DeFi. Specifically, regarding average users farming onchain liquidity of CEX-listed assets with well-liquid, BrownFi AMM fits better, and is potential to outperform Uniswap V3.

Contact us

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References

[1] Daniel Phillips, 2023, The Evolution of Decentralized Exchanges

[2] Thuat Do et al, 2023, Derivable: A Novel Derivatives Pricing Markets based on a Family of Asymptotic Power Curves

[3] Vladislav Goncharov, 2023, Hackernoon, Half of Uniswap v3 Users Lose Money — Here's Why

[4] Álvaro Cartea, et al, University of Oxford - Institute of Quantitative Finance, 2023, Automated Market Makers Designs beyond Constant Functions

[5] Philippe Bergault et al, 2024, Automated market makers: mean-variance analysis of LPs payoffs and design of pricing functions

[6] S. Jiang, J. Chen, F. Li, H. Geng and H. Chi, "DCAMM: Dynamic Curve-Based Automated Market Maker," GLOBECOM 2023 - 2023 IEEE Global Communications Conference, Kuala Lumpur, Malaysia, 2023, pp. 4491-4496, doi: 10.1109/GLOBECOM54140.2023.10437668.

[7] Bhaskar Krishnamachari, Qi Feng, 2021, Eugenio Grippo Viterbi School of Engineering, University of Southern California, Dynamic Automated Market Makers for Decentralized Cryptocurrency Exchange

[8] Daniel Jiwoong Im, Alexander Kondratskiy, Vincent Harvey, Hsuan-Wei Fu, 2024, UAMM: Price-oracle based Automated Market Maker

Faucet ETH, STRK

To test BrownFi AMM, you need ETH or STRK tokens, faucet at

https://starknet-faucet.vercel.app/

Wallet connect

Using Braavos or ArgentX wallets to connect with the BrownFi AMM dapp on Sepolia testnet

https://brownfi.vercel.app/

Swap on BrownFi AMM testnet

Your balance on corresponding paying side must be positive. You may enter the amount you wish to pay, or receive. Try with small amount to avoid exceeding liquidity.

After signing the transaction on the wallet extension, just wait a moment for confirmation. Bingo, it’s done

https://sepolia.starkscan.co/tx/0x4091973e11a4da26fb6c3a7de4263e498b142a08b9bac60ea4bff00116f2284

Liquidity provision on BrownFi AMM

Providing liquidity on BrownFi AMM is simple as doing on Uniswap V2. Click Pool, then New Position

Enter your expected amount of ETH (or STRK), the other amount is automatically calculated in correspondence. Then Approve and Sign on wallet extension popup. Wait a while to click Add, then Confirm, and Sign one more time on wallet extension popup. Check your complete transaction on wallet activities and Starkscan.

Capital efficiency & slippage

In this TX, the swap drew out 50% of ETH reserve but slippage (aka price impact) was 0.65% incredibly low. The same trade drawing 50% pool reserve on Uniswap V2 would imply a price impact 100%, i.e. the trade price would be doubled or halved.

This swap drew out 83% of ETH reserve but slippage was 0.8%, incredibly high capital efficiency. BrownFi AMM is going to boost liquidity (100x better than Uniswap V2 and the likes) on Starknet, thank to our innovative PLOB model.

BrownFi AMM fills the gap between Uniswap V2 and V3, offering a complementary solution to unlock high capital efficiency with flexible market making strategies and UX simplicity. Imagine that $1M liquidity on BrownFi AMM is equivalent to $100M liquidity on Uniswap V2. Thus, BrownFi AMM fits liquidity-boosting demand of new ecosystems and new tokens with very limited capital.

Readers refer to a conceptual introduction of BrownFi.

Contact us

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The Math behind BrownFi AMM

For all spot exchanges, price discovery mechanism is the core function. Uniswap invented CPMM model $$ x\times y=k$$, making it the most popular and widely used pricing mechanism among AMMs. BrownFi AMM employs an elastic Parameterization of Limit Order-Book (PLOB) from a published research papers on IEEE Access to construct a novel pricing mechanism associated with a rectangle liquidity distribution.

• Given a pair of tokens X and Y, where X is base token (e.g. ETH) and Y is quote token (e.g. USD), with corresponding token reserve $$(x, y)$$.

• For any trade, e.g. an amount-OUT $$dx$$ of token X $$(dx<x)$$, we compute price impact $$R= \frac{\Kappa \times dx}{x-dx}=\frac{\Kappa\times\delta x}{1-\delta x}$$ which is directly proportional to the relative order size $$\delta x=dx/x$$ (rectangle-shape liquidity distribution) or $$\delta x=\sqrt{dx/x}$$ (V-shape liquidity distribution). Liquidity concentration parameter Kappa $$\Kappa \quad (0<\Kappa\leq 2)$$ offers low (or high) slippage if it is small (or large), respectively.

• We compute the average trading price $$P_t = P_0(1 + \alpha R)$$, where $$P_0$$ the current market price (possibly fed by external or internal oracle), and a reversal coefficient$$\alpha = 1/2$$.

• Finally, we compute the amount-IN $$dy=dx\times P_t$$ based on the amount-OUT and the computed average trading price, then execute swaption. Moreover, we update the new pool-internal price (if needed) as $$P_{new} = P_0(1 + R)$$.

Mathematically, for $$\Kappa=2$$, our elastic PLOB model is proven to be equivalent to Uniswap CPMM model $$ x\times y=k$$, hence Uniswap V2 is a special case of BrownFi's elastic PLOB model. When order size $$dx$$ is large or close to the reserve $$x$$, price impact (so is trading price) will be large or super-large (tending to infinity), formally, $$\lim_{dx \to x} R(dx)=\infty$$. This makes BrownFi elastic similar to Uniswap V2 (however, BrownFi doesn’t possess path-independence like the CPMM model), hence the liquidity is unbounded. Elasticity and simplicity of BrownFi mathematical model make it resilient to market volatility and simple retail LPs like Uniswap V2 while offering high capital efficiency like Uniswap V3.

Simulation

To compare capital efficiency between Uniswap V2, V3 and BrownFi AMM, the idea is simple: regarding the same trade and slippage, which AMM optimally requiring less capital is more efficient. Without loss of generality, we give simple conventions:

• Consider the pair (ABC,USDT), price 1 ABC = $$P$$ USDT, taking $$P=1$$.

• Trade order: buying $$dx=10$$ ABC, and paying $$dy$$ USDT. Trading fee is zero.

• Slippage 1%. This means the actual trading price is $$P_t=1.01$$, higher 1% than the current price, hence the actual pay $$dy=(10P+0.1P)=10.1$$ USDT.

Now, we are going to find how much capital is needed by Uniswap V2 pool $$(x,y)$$ vs Uniswap V3 pool vs BrownFi AMM pool $$(x',y')$$.

Uniswap V2

The CPMM model gives $$(x-10)(y+10.1P)=xy$$. Because $$P=y/x=1$$, we have $$x=y$$ and $$(x-10)(x-10.1)=x^2$$, hence $$x=1010$$. The Uniswap V2 pool capital is (1010, 1010).

Uniswap V3

The concentrated liquidity formula of Uniswap V3 allows us to find a curve limited by a price range such that it can serve the trade with optimal capital, reading $$(x'+\frac{L}{\sqrt{p_B}})(y'+L\sqrt{p_a})=L^2$$, where $$L=\sqrt{xy}, L^2=xy$$.

Choosing a narrow price range $$[p_a,p_b]$$ where $$p_a=1.0001^{-200}\approx 0.9802, p_b= 1.0001^{200}= 1.0202$$ (volatility $$\pm 2%$$ around the market price), and we replace $$P=1, x=y=1010, \sqrt{p_a}=1/\sqrt{p_b}$$ and $$x'=y'$$ to obtain: $$(x'+\frac{1010}{1.0001^{100}})^{2}=1010^2 \Leftrightarrow x \approx 10.05$$The Uniswap V3 bin capital is (10.05, 10.05), satisfying buying amount.

BrownFi AMM

Regarding the conventions of amount-OUT $$dx=10$$ ABC and amount-IN $$dy=10.1$$ USDT, we consider three liquidity compression/concentration $$K=2, K=1$$ and $$K=0.001$$.

Liquidity concentration K=1

• $$dy=dx \times P_t \Rightarrow P_t=10.1/10=1.01$$

• $$P_t=1+R/2 \Rightarrow R = 0.02$$

• $$R=\frac{K\times dx}{x-dx} \Leftrightarrow \frac{10}{x-10}=0.02 \Leftrightarrow x = 510$$

The BrownFi pool capital is (510, 510).

Liquidity concentration K=0.01

• $$R = 0.02$$

• $$R=\frac{K\times dx}{x-dx} \Leftrightarrow \frac{0.1}{x-10}=0.02 \Leftrightarrow x = 15$$

The BrownFi pool capital is (15, 15).

Liquidity concentration K=0.001

• $$R = 0.02$$

• $$R=\frac{K\times dx}{x-dx} \Leftrightarrow \frac{0.01}{x-10}=0.02 \Leftrightarrow x = 10.5$$

The BrownFi pool capital is (10.5, 10.5).

Comparing capital efficiency

For any price, to compare the capital between the two pools, we compute the ratio of their capital amounts. For the given trade, we summarize the capital amounts of the computed pools:

• Uniswap V2 pool (1010, 1010) = 2020

• Uniswap V3 bin (10.05, 10.05) = 20.1

• BrownFi $$K=0.001$$ pool (10.5, 10.5) = 21

• BrownFi $$K=0.01$$ pool (15, 15) = 30

• BrownFi $$K=1$$ pool (510, 510) = 1020

Conclusion

We conclude with some advantages of BrownFi AMM.

• BrownFi $$(K=0.001)$$ is as capital-efficient as Uniswap V3 (range $$ \pm 2%$$) and 100X better than Uniswap V2.

• BrownFi AMM always concentrates liquidity around market price, hence LPs always get trading fee (LPs on Uniswap V3 suffer out-of-price-range). On the other side, thank to price impact, our AMM is still elastic to large orders, thus, offers unbounded liquidity (i.e. traders cannot draw out token reserve).

• BrownFi AMM offers simple UX for retail LPs like Uniswap V2. Furthermore, LPs can adjust their liquidity concentration parameter $$K$$ according to their prediction on market volatility, no need to specify price range, so more flexible than Uniswap V3 and V2.

Two limitations those BrownFi AMM requires oracle price-feeding to operate smoothly against malicious price manipulation/arbitrage, and our model is not path-independent. Overall, BrownFi AMM fills the gap between Uniswap V2 and V3, offering a complementary solution to unlock high capital efficiency with flexible market making strategies and simplicity. Imagine that $1M liquidity on BrownFi AMM is equivalent to $100M liquidity on Uniswap V2. Thus, BrownFi AMM fits liquidity-boosting demand of new ecosystems and new tokens with very limited capital.

Readers refer to a conceptual introduction of BrownFi.

Contact us

Website, Twitter, Telegram

Problem: the gap between Uniswap V2 vs V3

Constant Product Market Making (CPMM), invented by Uniswap, is a legacy model of Automated Market Making (AMM) protocols in Decentralized Finance (DeFi). Uniswap V1 and V2 utilize the invariant $$ x*y=k$$, making it the most popular price discovery mechanism in DeFi, reused by many other Decentralized Exchanges (DEXes). It unleashes liquidity provision for everyone, every tokens, and allows instant trade (i.e. swap), all with simplicity, atomicity, infinite liquidity. However, traders usually suffer a high slippage at trades. A swap pool requires super-large liquidity to offer low slippage (e.g. liquidity value must be 202X larger than the trade order size to ensure 1% slippage). This implies a low capital efficiency (CE), thus, in particular, bad experience and liquid-boosting challenge for new ecosystems or ill-liquid trading pairs. That is why Uniswap V3 comes to improve CE. By liquidity concentration technique, Uniswap V3 can guarantee the same 1% slippage with ~2X capital larger than the order size. This means Uniswap V3 offers capital efficiency 101X higher than V2. Unfortunately, liquidity on Uniswap V3 is bounded by bins (defined by price tick ranges). Therefore, managing liquidity positions across tick ranges is complicated and only suitable for professional liquidity providers (LPs) with extensive financial knowledge and skills. Average LPs find it very difficult to manage price ranges frequently against market volatility, also tick spacing, fee tiers. Maverick Finance, TraderJoe, improves UX of Uniswap V3’s concentrated liquidity model, but introducing hidden risks and/or centralized control out of the core protocol. Furthermore, those concentrated liquidity paradigms only fit well-established tokens with high liquidity and relatively low volatility. This article shows that oracle-based AMM models offer a significant advantage by eliminating arbitrage opportunities, including round-trip and sandwich attacks inherited by Uniswap and other CPMM-AMMs. Additionally, half of LPs on Uniswap V3 is providing liquidity at loss due to high impermanent loss and out-of-range positions, while oracle-based AMMs outperform CPMM regard CEX-listed assets. In summary:

• Uniswap V2 and the likes: simple and general but low CE.

• Uniswap V3 and the likes: high CE but complicated UX, not fitable for retail LPs, not fitable for new tokens with low liquid and high volatility.

• LPs on Ethereum have lost $750M since the Merge (Sep 2022). In particular, half of Uniswap V3’s LPs lose for high IL.

• Oracle-based AMMs outperform Uniswap and CPMM-AMMs over CEX-listed assets in the sense of profitable returns for average LPs.

This is a gap between Uniswap V2 and V3. Resolving it (i.e. finding a high CE with simple UX for retail LPs) will bring huge benefits for emerging blockchain ecosystems where capital is limited and quality liquidity is ill and highly dependent on bridged assets, also most LPs are average users.

Solution: an innovative oracle-based AMM

BrownFi introduces a novel spot AMM model based on oracle price, to offer high capital efficiency, flexible market making, while keeping simple UX, fungibility & reusability of LP tokens of Uniswap V2. The core concept of BrownFi AMM employs an elastic Parameterization of Limit Order-Book (PLOB) from a published research papers on IEEE Access, a notable scientific journal. In brief, the core function of BrownFi AMM is based on an invention of a NOVEL pricing mechanism:

• Given a pair of tokens X and Y, where X is base token (e.g. ETH) and Y is quote token (e.g. USD), with corresponding token reserve $$(x_0, y_0)$$.

• For any trade, e.g. an amount-OUT $$dx$$ of token X, we compute the average trading price $$P_t = P_0 * (1 + \alpha *R)$$, where $$R$$ denotes price impact factor, $$P_0$$ the current pre-trade price (fed by oracle), and a reversal parameter $$\alpha>0$$.

• Price impact factor $$R= \Kappa * f(\delta x)$$ is directly proportional to a function $$f(\delta x)$$ of relative order size $$\delta x=dx/x_0$$. Liquidity concentration parameter $$\Kappa$$ (Kappa) offers low (or high) slippage if it is small (or large), respectively.

• Finally, we compute the amount-IN $$dy=dx*P_t$$ based on the amountOUT and the computed average trading price, then execute swaption.

Mathematically, for $$\Kappa=2$$, the elastic PLOB model is proven to be identical with Uniswap CPMM $$ x*y=k$$, i.e. Uniswap V2 is a special case of BrownFi's elastic PLOB model. Note that our Kappa is not as same as in the liquidity invariant $$xy=k$$ of Uniswap. Elasticity in BrownFi AMM is implemented in the price impact function $$f(\delta x)$$, more explicitly, $$\lim_{\delta x \to 1} f(\delta x)=\infty$$. This means when order size $$dx$$ is large or close to the reserve $$x_0$$, price impact (so is trading price) will be large or super-large (tending to infinity). Elasticity plays an important role to ensure that liquidity never runs out, despite large swaps. BrownFi’s liquidity elasticity (more precisely, price impact elasticity) is closely similar to Uniswap V2 (which is not available on Uniswap V3), hence making BrownFi AMM resilient to market volatility. Moreover, our simple mathematical model allows us to make all trading and liquidity provision experiences on BrownFi AMM as simple as Uniswap V2, fitting all average LPs.

Simulation & Backtest

The PLOB model has two shapes of liquidity distribution: Rectangle vs Vshape. The former is equivalent to a flat order-book, close to Uniswap V3 bins, while the later is similar to the statistical liquidity distribution of legacy limit order-books. BrownFi applies rectangle liquidity distribution while the research papers gives extensive investigations on Vshape.

In the following, we simulate the rectangle liquidity model, which is closest to Uniswap V3 bins. For the same trade setting (order size 10 tokens, slippage 1%, price $$P=1$$, zero trading fee), Uniswap V2 requires $2020 capital, while Uniswap V3 is $20.05 and BrownFi (small Kappa $$\Kappa =0.001$$) is $21. From comparison, we see that BrownFi is as good as Uniswap V3 (range $$ \pm 2%$$) and 100X better than Uniswap V2.

Further, in the published research papers, back-testing results showed that the elastic PLOB model outperformed Uniswap V2 in 8-month time-frame, brings better gains for LPs (i.e. turning impermanent loss to impermanent gain).

Conclusion

BrownFi AMM fills the gap between Uniswap V2 and V3, offering a high CE like Uniswap V3 with simple UX for retail LPs like Uniswap V2. Our simulation shows that BrownFi AMM offers capital efficiency as equivalent as Uniswap V3 (range $$ \pm 2%$$) and 100X better Uniswap V2.

It is worth to mark that BrownFi AMM does not directly compete Uniswap V2 and/or V3. BrownFi is a novel oracle-based AMM, a complementary solution to unlock high capital efficiency with flexible market making strategies and simplicity, hence fitting liquid-boosting demand of new ecosystems with limited capital. Readers refer to math and capital efficiency comparison of BrownFi and the need and advantages of oracle-based AMMs.

Contact us

Website, Twitter, Telegram, blog