The Dominance of Uniswap v3 Liquidity

May 05, 2022

New research published today shows that Uniswap Protocol v3 has deeper liquidity in ETH/USD, ETH/BTC and other ETH pairs than leading centralized exchanges. This research demonstrates that AMM market structure – which is largely crypto-native today – can surpass order-book exchanges and transform traditional financial market structure to be more liquid, stable, and secure.

The complete research report and our open-sourced methodology are below (and in pdf form here), and we are making our code and data freely available. In summary:

• For ETH/USD, Uniswap has ~2x more liquidity than both Binance and Coinbase.
• For ETH/BTC, Uniswap has ~3x more liquidity than Binance and ~4.5x more liquidity than Coinbase.
• For ETH/mid-cap pairs Uniswap has on average ~3x more liquidity than major centralized exchanges.
Market depth comparison for ETH/USD stables and ETH/BTC

The research also finds that many stablecoin pairs have much more liquidity on Uniswap v3 than centralized exchanges. For USDC/USDT, Uniswap v3 has about ~5.5x more liquidity than Binance.

## Deeper on-chain markets

The decentralized nature of AMMs and more passive liquidity provision opened up market making activities to a broader set of market participants. In traditional centralized exchanges, market making is dominated by high-frequency traders that compete in both the quality of the market making algorithm as well as execution speed, leading to an unnecessary arms race in trading technology and suboptimal market structure.6 Batched auctions instead of continuous limit order books could resolve some of the issues associated with the competition for speed, but market making would be still reserved for high frequency traders.

AMMs unlock a much larger set of more passive capital that was previously sitting on the sidelines. This is because general institutional and retail users have risk-and-return profiles that differ from those of specialized market makers on centralized exchanges. As a result, AMMs are able to attract more diverse capital sources to participate as market makers and hence deepen liquidity. In earlier versions of AMMs, e.g. Uniswap v2, passive liquidity providers can enter a market making position without any additional intervention. Uniswap v3 introduced concentrated liquidity that requires some rebalancing. Even with rebalancing needs, the vast majority of capital deployed for liquidity provision on v3 are relatively passive. Table 2 shows that around two-thirds of liquidity positions are held greater than one day. Overall, the Uniswap protocol has attracted around 130,000 unique liquidity providers.7

Table 2. Duration of Uniswap v3 LP Positions

## Beyond digital assets

Decentralized AMMs is an innovation in market structure with impact far beyond digital assets. The lack of liquidity in thinly traded assets has been a recognized challenge to central limit order exchanges.8 This emphasis for innovation in market structure exists because liquidity challenges can be detrimental to both investors and issuers. For investors, low liquidity not only increases transaction costs but also deters willingness to invest in assets that might have high expected returns.9 For issuers, poor market liquidity can raise the cost of capital and increase the chance of default.1011

In a future with more tokenized assets, the Uniswap Protocol has the potential to not only supplement but also directly compete with traditional exchanges in trading a variety of assets, facilitating both deeper and more stable liquidity. This increase in liquidity can improve the price discovery process for thinly traded assets and ultimately foster capital formation and economic growth.

## Conclusion

Uniswap v3, deployed less than a year ago, has gained dominance over traditional forms of central limit order books in providing a trading venue for deep liquidity in digital assets. As more passive and diverse capital sources are unlocked through decentralized AMMs, market liquidity and efficiency will likely continue to deepen beyond traditional limit order books.

We will highlight other advantages over traditional forms of exchange and price discovery in future studies.

## Appendix A - Additional Figures

Figure A1. Market depth comparison for ETH-dollar pairs (aggregating across pairs)
Figure A2. Market depth comparison for USDC/USDT
Figure A3. Market depth comparison for (W)BTC/ETH

## Appendix B - Methodology

We describe the methodology for calculating market depth in Uniswap V2 (constant product AMM) and Uniswap V3 below.

Let $m(\delta)$ be market depth defined as the amount of asset $x$ that can be exchanged for asset $y$ for a given $\delta$ percent of price impact (e.g. $\delta=2\%)$. Let $p_0$ be the current spot price of asset $x$ in units of asset $y$, and $L$ be the liquidity amount locked in the pool. Market depth for Uniswap V2 expressed in units of asset $x$ is calculated as

$m(\delta)=\left|\frac{L}{\sqrt{\left(1+\delta\right)p_{0}}}-\frac{L}{\sqrt{_0}}\right|.$

Market depth calculation in Uniswap V3 is more complicated as the liquidity distribution is an aggregation of individual liquidity provider positions.

Let $\lambda_{x}(i)$ be the amount of asset $x$ locked in the liquidity range between tick $i$ and $i+s$, where $s$ is the tick spacing for the pool. Let $\lambda_{y}(i)$ be the amount of asset $y$ in this tick range. It can be shown that for lower tick $i$ and associated lower bound prices $p_a$ and upper bound price $p_b$, assets $x$ and $y$ locked in the tick spacing are$\lambda_{x}(i)=\frac{L}{\sqrt{z}}-\frac{L}{\sqrt{p_{b}}}$

and

$\lambda_{y}(i)=L\left(\sqrt{z}-\sqrt{p_{a}}\right)$where $z=\begin{cases} p_{a} & \forall p_0\le p_{a}\\ p_0 & \forall p_0\in\left(p_{a},p_{b}\right)\\ p_{b} & \forall p_0\ge p_{b} \end{cases}.$

Market depth for Uniswap V3 expressed in units of asset $x$ is

$m\left(\delta\right)=\frac{1}{s}\sum_{i=i_{0}}^{i_{0}+d(\delta)}\left|\lambda_x(i)+p_0^{-1}\lambda_y(i)\right|,$where $i_0$ is the current tick associated with $p_0$ and $d$ is the tick-equivalent of the percentage price change $\delta$.

Derivation for V2 market depth

Let $m(\delta)$ be market depth defined as the amount of asset $x$ that can be exchanged for asset $y$ for a given $\delta$ percent of price impact (e.g. $\delta=2\%$). The bonding curve is described by $xy=L^{2}$.Using the price relationship $p =\frac{y}{x}$, we can also express the bonding curve as $p =\frac{L^{2}}{x^{2}}$,$p =\frac{y^{2}}{L^{2}}$,$x =\frac{L}{\sqrt{p}}$, or $y=L\sqrt{p}$.

After a trade of $\Delta x$ units of asset $x$ for $\Delta y$ units of asset $y$, the bonding curve is

$\left(x+\Delta x\right)(y+\Delta y)=L^{2}.$We solve for $\Delta x$ s.t. $p_{1}/p_{0}-1=\delta$, substituting $p_0=y/x$ and $p_1=(y+\Delta y)/(x+\Delta x)$, the expression becomes $\frac{y+\Delta y}{x+\Delta x}\frac{x}{y}-1=\delta.$

Substitute into the post-trade equation, we get

$\left(x+\Delta x\right)^{2}\left(\delta+1\right)p_{0}=L^{2}.$Market depth in units of asset $x$ is therefore$m(\delta)\equiv |\Delta x|=\left|\frac{L}{\sqrt{\left(1+\delta\right)p_{0}}}-\frac{L}{\sqrt{p_0}}\right|$

Derivation for V3 market depth

Let $j$ be an index for lower tick boundary and $s$ be the tick spacing (e.g. $s=60$). Let $p_0$ be the current price and $p_{a}$, $p_{b}$ be the prices associated with upper and lower ticks of a tick-space range. More explicity, $p_a=1.0001^j$ and $p_b=1.0001^{(j+s)}$.

Starting with real reserve curve of a single position, Equation 2.2 from v3 white paper:

$\left(x+\frac{L}{\sqrt{p_{b}}}\right)\left(y+L\sqrt{p_{a}}\right)=L^{2}$For $p_0\le p_{a}$,$x =\frac{L}{\sqrt{p_{a}}}-\frac{L}{\sqrt{p_{b}}}=L\frac{\sqrt{p_{b}}-\sqrt{p_{a}}}{\sqrt{p_{a}p_{b}}}$$y =0$For $p_0\ge p_{b}$,$x =0$$y =L\left(\sqrt{p_{b}}-\sqrt{p_{a}}\right)$For $p_0\in\left(p_{a},p_{b}\right)$,$x =\frac{L}{\sqrt{p_0}}-\frac{L}{\sqrt{pb}}=L\frac{\sqrt{p_{b}}-\sqrt{p_0}}{\sqrt{p_0p_{b}}}$$y =L\left(\sqrt{P}-\sqrt{p_{a}}\right)$

This can be written more concisely as

$x =\frac{L}{\sqrt{z}}-\frac{L}{\sqrt{p_{b}}}=\frac{\sqrt{p_{b}}-\sqrt{z}}{\sqrt{sp_{b}}}$$y =L\left(\sqrt{z}-\sqrt{p_{a}}\right)$ where $z=\begin{cases} p_{a} & \forall P\le p_{a}\\ p_0 & \forall P\in\left(p_{a},p_{b}\right)\\ p_{b} & \forall P\ge p_{b} \end{cases}$

Let i be the integer index identifying a tick. Let $\delta$ be percentage change in price and $d$ be the associated change in ticks such that

$\delta =\frac{p_{1}}{p_{0}}-1=\frac{1.0001^{i_{0}+d}}{1.0001^{i_{0}}}-1$Let $\lambda_{x}(i)$ be the amount of asset $x$ locked in the liquidity range between tick $i$ and $i+s$, where $s$ is the tick spacing for the pool. Let $\lambda_{y}(i)$ be the amount of asset $y$ in this tick range. It can be shown that for lower tick $i$ and associated lower bound prices $p_a$ and upper bound price $p_b$, assets $x$ and $y$ locked in the tick spacing are$\lambda_{x}(i)=\frac{L}{\sqrt{z}}-\frac{L}{\sqrt{p_{b}}}$

and

$\lambda_{y}(i)=L\left(\sqrt{z}-\sqrt{p_{a}}\right),$with $z$ defined above.

Market depth for Uniswap V3 expressed in units of asset $x$ is

$m\left(\delta\right)=\frac{1}{s}\sum_{i=i_{0}}^{i_{0}+d(\delta)}\left|\lambda_x(i)+p_0^{-1}\lambda_y(i)\right|,$where $i_0$ is the current tick associated with $p_0$ and $d$ is the tick-equivalent of the percentage price change $\delta$.

1. We thank Austin Adams for assisting with the research. We are grateful for comments from Hayden Adams and Matteo Leibowitz.
2. We provide daily market depth calculated on the top 1,000 liquidity pools by historical volume and the code to generate this data.
3. Fees Uniswap v3 has several fee tiers ranging from 1 bp that are popular for stablecoin-only pairs to 100 bps for the most volatile long-tail assets. Centralized exchanges charge transaction fees as well. For instance, Coinbase Pro has fees that range from 5 bps to 60 bps depending on the monthly transaction volume. Additionally, centralized limit order books have bid/ask spreads that vary based on the market and time.
Gas cost On-chain transactions through AMMs have gas costs that depend on network congestion. The median cost of a swap transaction on Uniswap v3 has been $31 per trade since its inception. 4. A ETH/dollar trade executed on Coinbase Pro that results in an average price impact of 0.05% (corresponding to a notional size of$650,000 at 0.1% market depth assuming linear scaling of price impact with notional) would only have an average price impact of 0.0375% on Uniswap v3. This is equivalent to a dollar saving of around $81 dollars on the price impact and around$36 of saving net of gas and fees. The fees are similar on v3 and Coinbase Pro and the average gas cost is $45. For Uniswap v3, the weighted average of fee tiers is around 20 bps. For Coinbase Pro, the fee is 20 bps for the 650k - 1m volume tier. 5. For$5mm notional, the average price impact is roughly 0.5% on Uniswap v3 and 1% on Coinbase. The fee is about 2 bps lower on Coinbase.
6. Budish, E., Cramton, P., & Shim, J. (2015). The high-frequency trading arms race: Frequent batch auctions as a market design response. The Quarterly Journal of Economics, 130(4), 1547-1621.