On the influence of conventional and automated market makers on market quality in cryptoeconomic systems

Abstract

Decentralized exchanges (DEXs) have become an alternative to centralized exchanges (CEXs) for trading assets in the form of tokens in cryptoeconomic system markets. The emergence of DEXs is strongly driven by their potential to tackle challenges for market quality originating from CEXs by design, such as opaque market-making strategies and centralization of power. However, it remains unclear to what extent DEXs can enhance market quality compared to CEXs. A core reason for this is the lack of an analysis concept for investigating influences of market makers, including automated market makers (AMMs) used in DEXs and conventional market makers used in CEXs, on market quality in cryptoeconomic systems. To better understand influences of market makers on market quality in cryptoeconomic systems, we developed an analysis concept based on our formal price model grounded in established concepts of market microstructure. We demonstrate the usefulness of the analysis concept by examining conventional market makers on CEXs (i.e., Binance and Coinbase) and automated market makers (AMMs) on DEXs (i.e., Uniswap v2 and Uniswap v3). The main purpose of this work is to support the analysis of influences of different market makers on market quality in cryptoeconomic systems. This is useful to better understand how cryptoeconomic systems can ensure high market quality and safeguard market participants, when issuing tokens.

Introduction

Cryptoeconomic systems, such as the Bitcoin and Ethereum systems, are sociotechnical systems wherein market participants (e.g., individuals, organizations, and software agents) manage ownership of assets represented as digital tokens that are secured by cryptographic techniques and can be traded instantaneously (Sunyaev, Kannengießer, Beck, Treiblmaier, Lacity, Kranz, Luckow, 2021).

By trading tokens, markets emerge. Participants in such markets need the ability to execute trades at desirable prices and manage risks, such as quickly opening/closing large trading positions. Such needs can be fulfilled when markets exhibit high market quality. Liquidity is particularly important for market quality (Chordia, Roll, Subrahmanyam, 2008).

To reach high market quality, token issuers in cryptoeconomic systems list their tokens on centralized exchanges (CEXs) in order to achieve sufficient liquidity for token issuance and trading. CEXs often provide market making services that provide liquidity to cryptoeconomic system markets. Being able to influence the liquidity of markets, market makers of CEXs can strongly affect market quality in cryptoeconomic system markets (Barbon & Ranaldo, 2023; O’Hara, Ye, 2011).

Driven by technological advances in distributed ledger technology (DLT) and the vision of decentralized cryptoeconomic systems, decentralized exchanges (DEXs) emerged (Xu et al., 2023). Instead of conventional market makers used in CEXs, DEXs typically use automated market makers (AMMs). AMMs are market makers that are implemented as software agents (based on smart contracts) that execute transparent and persistent market making strategies based on mathematical functions (Xu et al., 2023; Kirste et al., 2023). For example, AMMs like Uniswap v2 (Hayden et al., 2020) allow market participants to continuously exchange Ether (ETH) and USD Coin (USDC), while a constant-product function determines the exchange rate.

Market making strategies based on mathematical functions are transparent and assumed to be less dynamic than those of conventional market makers on CEXs (Aoyagi & Ito, 2021). AMMs seem to be useful in tackling challenges related to conventional market makers in cryptoeconomic system markets. Notwithstanding the assumed benefits of AMMs over conventional market makers, the extent to which AMMs influence market quality remains unclear.

AMM development is predominantly driven by practitioners focused on technological innovation. As a result, existing concepts from financial literature to analyze market quality are rarely adopted or modified to be suitable for cryptoeconomic system markets.

The often unclear applicability of well-known concepts prevalent in the finance literature (Amihud, 2002; Hendershott, Menkveld, 2014) make it difficult to analyze and compare the influence of conventional market makers and AMMs on market quality in cryptoeconomic system markets. An analysis concept is needed to better understand how AMMs can influence market quality in cryptoeconomic systems markets. We answer the following research questions: What is a useful analysis concept to examine, and what are the actual influences of conventional and automated market makers on market quality in cryptoeconomic systems?

Our work lays a foundation for analyzing and comparing the influence of market makers on market quality in cryptoeconomic systems. We have four main contributions. First, we present a formal price model based on well-known concepts in finance literature on market microstructure. The formal price model builds the foundation to understand price discovery, how the execution price of a trade is determined, and introduces concepts to analyze market quality. This is helpful in better understanding price evolution in markets. Second, we present an analysis concept that uses our formal price model to analyze the influence of market makers on market quality. The analysis concept supports analyses and comparisons of market quality and liquidity provided by market makers on CEXs and DEXs. This is useful for market participants to assess suitable markets for token trading. Third, we analyze the influences of conventional market makers and AMMs on market quality by applying our analysis concept to historical market data during a 6-month timeframe. To be representative, the analyzed timeframe covers sideways movements of prices as moments of equilibrium and larger price downturns due to the FTX bankruptcy, as a moment of definite non-equilibrium. The analysis reveals the influence of different market makers on market quality in cryptoeconomic system markets and showcases the utility of our analysis concept. Fourth, by offering evidence for assumptions on market makers, we support assessing market impact, market quality, and liquidity. This is useful to optimize trade execution and reduce risks in trades.

The remainder of this work is structured into six sections. In the next section, we elucidate the foundations relevant to understanding the influence of market makers on market quality in cryptoeconomic system markets. In Section “A formalized price model, data accessibility, and analysisconcept,” we present a formalized price model and an analysis concept to measure the influences of market makers on market quality. In Section “Methods,” we describe how we applied the analysis concept to analyze the influences of three different market makers types (i.e., conventional market makers on Binance and Coinbase, Uniswap v2, Uniswap v3) on market quality. We present the analysis results in Section “Liquidity-based influences of marketmakers on market quality in cryptoeconomic systems.” In Section “Discussion,” we discuss the principal findings from the analysis. Moreover, we explain our contributions to practice and research. Then, the limitations of the findings presented in this work are explained, and future research directions are showcased. In Section “Conclusions,” we conclude this work with our personal takeaways.

Background

To better understand the interrelationships between market making strategies and market quality relevant to this work, we describe the foundations of market quality, conventional market making, and automated market making. We use boldface italic characters for term definitions. Italic characters indicate the use of already defined terms elsewhere within the paper.

Market quality, market makers, and adverse selection

Price discovery and market quality

Like in conventional financial markets, traders in cryptoeconomic system markets aim to swiftly buy or sell assets (e.g., shares and stocks represented as tokens) at reasonable prices and transaction costs. Market quality characterizes the ability to do so. We introduce the aspects that contribute to market quality in the following, concluding with its definition.

The effective price paid or received by the trader in a specific trade event is not known beforehand, but the result of a price discovery process. The price discovery process has a key role for market quality. It incorporates two basic price contributions to the effective price: first, a more or less accurate reflection of the true value of the asset, and second, the price impact of the traded volume, referred to as market impact. The market impact’s price contribution to the effective price depends on the liquidity of the market.

To better understand the interrelationships of those aspects, we give a simplistic view of the price discovery process before offering more details. We split the process into two hypothetical steps, according to the two basic price contributions given above. In the first step, a true value-based reference price is assumed to be established. For perfectly efficient markets, referred to as being in equilibrium, most market participants know the information about the true value of a traded good, and all available information (e.g., past prices and future expected returns) is incorporated in prices. Therefore, the (reference) price is close to the true value (Fama, 1970; Zhang, 1999).

In the second step, trade orders (i.e., orders to buy or sell a certain volume of an asset) are collected and matched. As the trade volume related to buying and selling typically does not exactly cancel at every point in time, a so-called net order volume remains. This net order volume is absorbed by market makers who are willing to do so but at a price premium. This price deviation typically increases for increasing net order volume. The net order volume, therefore, has a directional effect on the price. In case the net order volume stems from an individual trader solely, we refer to the trade as a directional trade (Madhavan, 2000; Farmer, 2002).

The time-resolved price impact of net order volume can basically be split into two components. Firstly, the overall dynamics of instantaneous price change followed by partly price recovery, referred to as transitory price effects (e.g., price pressure effects; Hendershott, Menkveld, 2014). Secondly, the remaining persistent price change after recovery.

A market is referred to as a liquid market if the price impact of (net) order volume size is small. The relationship between net order volume size and asset price is typically referred to as the market impact function. The slope of the market impact function is approximately inversely proportional to liquidity (Madhavan, 2000; Farmer, 2002). In other words, the more liquid a market, the smaller the slope of the market impact function and hence the price impact of net order volume. This illustrates how liquidity has a direct impact on the effective price and market quality.

In real-world markets, prices do not adjust to value changes instantaneously. This is due to information asymmetry, nonlinear dynamic effects, and marginal arbitrage costs (Zhang, 1999; Farmer, 2002). Continuously changing environments lead to at least some transient moments of non-equilibrium. Within these moments, the actual trade orders might inherently contain information about a value attribution adaption not yet publicly known, especially also not by the market makers (Beja, Goldman, 1980; Zhang, 1999). These information asymmetries are to be considered by the market makers and lead to larger price premiums and reduced liquidity. Therefore, the above hypothetically separated steps of reference price discovery and liquidity provisioning are, in fact, a continuous, interwoven process. Information gathering about reasonable pricing is partly trade external (we refer to this as external price effects in the following) and partly from trade signals.

Based on the above-defined concepts and according to O’Hara and Ye (2011), market quality can be defined as a market’s ability to meet its dual and involved goals of efficient price discovery and liquidity.

The cost of liquidity: market makers and adverse selection risk

Market quality depends on the liquidity provided by economically rational market participants submitting non-matching bid/ask orders (e.g., via limit orders to the order book) at which they are willing to buy/sell assets and thereby absorb net order volume. These market participants are referred to as market makers (Madhavan, 2000). Typically, bid prices are placed below and ask prices above the estimated reference price, respectively, such that the market making activity under close to equilibrium conditions, where the price movement resembles a random walk, is in principle profitable (Kyle, 1985). The peaks in supply and demand caused by asynchronous trading activities balance out over time, and market makers can maintain a balanced inventory (Madhavan, 2000).

In an efficient market, market makers compete for the opportunity to absorb the net order volume and thereby extract a surplus. This competition is the driving force for a small bid/ask price gap and a small slope of the market impact function.

Real markets, however, show more or less strongly pronounced transient moments of non-equilibrium, where prices do not reflect all available information (Fama, 1970; Zhang, 1999). Thereby, market makers face an adverse selection risk through asymmetric information because there potentially are asymmetries between market participants in terms of information about asset valuation (Akerlof, 1978). Informed traders exploit these asymmetries by creating a surplus of supply or demand that is absorbed by the less well-informed market makers. The price evolution under non-equilibrium conditions resembles a random walk with potentially large mean value drift or even jumps. Thereby, as it is often the case for cryptoeconomic system markets, the market maker is at risk of building up a large inventory imbalance, holding more of the less-worthy assets. The imbalance can only be re-balanced at a loss. These potential losses are referred to as adverse selection cost (Neal, Wheatley, 1998; Kyle, 1985; Akerlof, 1978).

Market makers are rational market participants depending on economic sustainability. Therefore, they need to account for the adverse selection risk in their typically opaque pricing strategies. This leads to larger bid/ask gaps, depending on the uncertainty in the market. In addition, market makers are required to adapt liquidity positions swiftly in dynamic market situations (leading to reduced liquidity associated with increased slope of the market impact function) (Bagehot, 1971; Menkveld, Wang, 2013). This adaption can even create a self-reinforcing spiral, for example, through panic selling. Market makers keep on removing liquidity when prices increasingly fluctuate. This fluctuation, however, is intensified by the continuously decreasing liquidity. Market participants, therefore, encounter higher transaction costs (large bid/ask spread and price impact) and significantly heightened price volatility in non-equilibrium. These effects severely constrain their ability to execute trades at desirable prices and manage risk by quickly opening/closing trading positions to re-balance their inventory without loss (Zhang, 2010).

To summarize, liquidity comes at a risk and hence at a cost, referred to as the cost of liquidity, the trader has to pay for. Due to the dynamics of the underlying processes, liquidity and market quality related thereto may be fragile.

Conventional and automated market making in cryptoeconomic systems

The following subsections illustrate the importance of separation of concerns between trade process operationalization (i.e., exchange operation), initial public offering (organized by the underwriter), and market making. Violating that separation in cryptoeconomic system markets can lead to financial losses of market participants and dramatic breakdowns of markets.

On the importance of separation of concerns: the interplay between exchanges, underwriters, and market makers

Exchanges make an important contribution to market quality as they provide the technical operationalization of trade processes. Exchanges bring together a reasonable amount of buyers, sellers, and market makers, forming the technical manifestation of “the market.” If the technical operationalization of an exchange is provided by a single entity or a small group of entities or institutions, the exchange is referred to as centralized exchange (CEX) in cryptoeconomic systems.

In principle, exchange operation and market making (i.e., liquidity provisioning) should be separated to prevent conflict of interest. In a nutshell, the ability to analyze incoming trade orders provides an information advantage no market participant has. Intermixing market making with exchange operations may provide an unfair advantage over all other market participants and entails market manipulation risks.

In matured markets, the exchange infrastructure is fragmented into many providers competing for market participants, jointly forming a virtual overall market (O’Hara, Ye, 2011). In immature markets (e.g., early cryptoeconomic system markets), there are only a few possibilities to exchange assets, offered by a small amount of providers. This entails the risk of dominating providers exploiting their supremacy. This dominance is problematic for traders (possibly paying excess premiums) and newcomer projects because the ability to raise capital is crucially affected by the access to trading facilities, for example, being listed on an exchange and the organization of initial public offerings (IPO) (Madhavan, 2000). In cryptoeconomic system markets, IPO is also referred to as initial coin offering (ICO).

IPOs are usually organized by so-called underwriters. The underwriter assumes the risk of purchasing the securities from the issuer and then selling them to the public or institutional investors. This places underwriters, especially in not well-developed markets, in a special position that may be exploited, as it is long known for conventional financial markets (Chen, Ritter, 2000). In addition, underwriters may become dominant market makers in the IPO aftermarket, giving them considerable ability to affect asset prices (Ellis, Michaely, O’Hara, 2000). This is most often the case for cryptoeconomic system markets.

To complete what could be regarded as the financial systems “hat trick” in unregulated cryptoeconomic system markets, the three roles of exchange, underwriter, and dominant market maker are typically closely entangled. This fraudulent entanglement has been shown to harm honest market participants massively. The breakdowns of CEXs, such as Mt. Gox in 2014 (Sidel et al., 2014; Leising, 2021), QuadrigaCX in 2019 (Deschamps, 2020; Doug, 2019; Ontario Securities Commision, 2020), and FTX in 2022 (Huang et al., 2022; Berwick et al., 2022; Scharfman, 2023), showcase the vulnerability of central parties combining exchanges, underwriters, and market makers. The entanglement of FTX and Alameda Research, as the main market maker and underwriter for FTX, showcases how market makers could fraudulently manipulate token prices (e.g., FTT, the native utility token of the FTX platform) and wrongfully use more than half of FTX’s customer funds to compensate for losses caused by risky market making (Berwick et al., 2022; Huang et al., 2022). Apparently, dependencies on fraudulently entangled intermediaries lay at odds with the core idea of cryptoeconomic systems (Nakamoto, 2008; Sunyaev, Kannengießer, Beck, Treiblmaier, Lacity, Kranz, Luckow, 2021). Decreasing the reliance of market participants on dominant parties is a key motivation for developing automated market makers and decentralized exchanges.

Automated market makers and decentralized exchanges

Automated market makers (AMMs) are market makers implemented as software agents that operate in DLT systems. AMMs determine asset prices in an automated and transparent manner. Market participants can trade with AMMs anytime, without requiring trust in intermediaries (Xu et al., 2023; Mohan, 2022). Depending on the specific AMM protocol, the general exchange process is mapped to the individual trader–AMM transactions (today’s state of the art). Alternatively, order book functionality and batch-settlement of several trade orders against each other and the AMM in a simultaneous fashion is enabled.

Strictly speaking, AMMs combine the exchange process with market making and are therefore more generally referred to as decentralized exchanges (DEXs). Making use of DLT, the shortfalls of exchange–market maker entanglement of CEXs are circumvented in a transparent and tamper-proof way by design, preventing central points of manipulation and failure.

DEXs may also provide means for holding ICOs, so-called initial DEX offerings (IDO), and thereby, in addition, remove the dependency on underwriter intermediaries, which should resolve the possibly fraudulent “hat trick” discussed above (Zargham et al., 2020).

To cope with adverse selection risks (see Section 2.1.2), conventional market makers use opaque and highly dynamic strategies to determine prices and amounts of liquidity they provide to markets. In contrast to that, AMMs are fully transparent and, in many cases, mostly persistent (Kirste et al., 2023) by applying mathematically specified price functions to determine prices, typically based on their inventory and the amount of tokens that should be exchanged (Hayden et al., 2020), thereby explicitly encoding the market impact function.

AMM designs differ in how liquidity is provided and used, prices are determined, and surplus from market making is shared. In our previous work (Kirste et al., 2023), we present an AMM taxonomy that conceptualizes the design space of AMMs. For details, we refer the reader to our work on designs of AMM  (Kirste et al., 2023) and the systematization of knowledge by Xu et al. (2023).

Contemporary AMMs commonly source required liquidity from deposits of liquidity providers. Liquidity providers are market participants that take the risk of divergence loss (also called impermanent loss) related to diverging prices and inventory of the deposited asset pairs for retrieving a proportion of the shared surplus from market making.

As there is no free lunch, we expect that, due to the design of most liquidity pool-based AMMs, the cost of liquidity might well be higher than with opaque and highly dynamic strategies.

A formalized price model, data accessibility, and analysis concept

AMMs seem to have several benefits compared to conventional market makers, such as transparent and persistent trading strategies. However, the extent to which AMMs can help to improve market quality compared to conventional market makers is barely understood. To better understand the influences of market makers on market quality, an analysis concept capable of analyzing market quality based on different data sources (e.g., trade or order book data) is needed. In the following sections, we present a concept for measuring the influence of market makers on market quality. Moreover, we explain how the analysis concept can be applied to analyze the influence of market makers on market quality.

Formalization and elucidation of the price model

Formal price model

We define the market impact function $\mathcal {M}$ as depending explicitly on the net order volume $\omega$ (the part of the total trade volume V, absorbed by the market makers). We relate $\mathcal {M}$ to the price P as follows:

$$\begin{aligned} P_{j}= & P_{j-1}+\Delta P_{j}^{ext}+\mathcal {M}(\omega _{j},j) \end{aligned}$$

(1)

The price pair $P_{j-1}$ and $P_{j}$ refer to the price “before” and “after,” while “before-after” has two distinct meanings in the following analysis. The first meaning is before and after event j, respectively (e.g., a trade of net order volume $\omega _{j}$ against the market maker or order book). The second meaning relates to a price at the beginning and end of a timeframe j (e.g., in 1-min trade data set). The effect of the value attribution adaption related external price effects, discussed in Section “Price discovery and market quality,” is represented twofold in Eq. 1. On the one hand, the price delta $\Delta P_{j}^{ext}$ corresponds to a shift of the reference price. An example is the shift of the mid-price, the price halfway between the highest bid and lowest ask price in order book-based exchanges due to order book position updates occurring independently from trades. On the other hand, the market impact function $\mathcal {M}$ may change its shape, which is indicated by the explicit dependency on j. In the order book example, this corresponds to the change in liquidity distribution due to order book updates.

A usual representation of price evolution is the normalized price action referred to as return R:

$$\begin{aligned} R_{j}= & \frac{P_{j}-P_{j-1}}{P_{j-1}} \end{aligned}$$

(2)

Applying our relation (1), it follows:

$$\begin{aligned} R_{j}= & \frac{1}{P_{j-1}}\left( \Delta P_{j}^{ext}+\mathcal {M}(\omega _{j},j)\right) \end{aligned}$$

(3)

Linearizing the market impact function provides the relation to the price normalized slope S and liquidity L:

$$\begin{aligned} R_{j}\approx & \frac{\Delta P_{j}^{ext}}{P_{j-1}}+\omega _{j}\cdot \frac{1}{P_{j-1}}\cdot \frac{\partial \mathcal {M}}{\partial \omega }|_{\omega =0,j}\end{aligned}$$

(4)

$$\begin{aligned}\approx & \frac{\Delta P_{j}^{ext}}{P_{j-1}}+\omega _{j}\cdot S_{j}=\frac{\Delta P_{j}^{ext}}{P_{j-1}}+\omega _{j}\cdot \frac{1}{L_{j}} \end{aligned}$$

(5)

Note that the slope S and liquidity L absorbed the price normalization $1/P_{j-1}$, respectively.

In the following, we introduce two more concepts in the above notation. One from financial markets analysis and one from AMM-based DEX formalism. We do so to relate them to liquidity and discuss the similarities, differences and which parts can be extracted from the data analysis below.

In the context of trade data timeframe analysis, the concept of illiquidity (ILLIQ) (Amihud, 2002) is commonly used:

$$\begin{aligned} ILLIQ_{j}= & \frac{|R_{j}|}{V_{j}} \end{aligned}$$

(6)

The concept of illiquidity can also be applied as mean over a sequence of N events or timeframes:

$$\begin{aligned} ILLIQ_{N}= & \frac{1}{N}\sum _{j=1}^{N}\frac{|R_{j}|}{V_{j}} \end{aligned}$$

(7)

An established analysis, for example, is the yearly mean illiquidity from daily returns and volumes. Illiquidity is often used because it can easily be determined from price and total volume information that is widely accessible for basically any traded asset.

A standard term from the context of AMM-based DEX formalism, related to return, is slippage (SLP):

$$\begin{aligned} SLP_{j}= & \frac{\bar{P}_{j}-P_{j-1}}{P_{j-1}} \end{aligned}$$

(8)

$\bar{P}_{j}$ refers to the mean execution price a trader trading against an AMM experiences. The difference between slippage and return stems from the fact that the AMMs typically apply a non-linear cost function prescribing a total amount of value to be paid or received for an amount of asset traded (usually referred to as swapped). When generalizing the cost function as a market impact function defined over an absolute inventory state $\Omega$ (denoted by $\mathcal {M}^{\dagger }$ in the following), and assuming no parameter updates and adaptions to the liquidity pool occurred (indicated by the superscript stat in the following equation), the mean price can be given as:

$$\begin{aligned} \bar{P}_{j}^{stat}= & \frac{1}{\omega _{j}}\int \limits _{\Omega _{j-1}}^{\Omega _{j-1}+\omega _{j}}\mathcal {M}^{\dagger }(\Omega )\,d\Omega \end{aligned}$$

(9)

Mapping parameter updates, change in liquidity pool volumes, and liquidity distribution (for liquidity concentrating AMMs) similarly to Eq. 1 provides:

$$\begin{aligned} SLP_{j}= & \frac{\Delta P_{j}^{ext}}{P_{j-1}}+\frac{1}{P_{j-1}\omega _{j}}\int \limits _{\Omega _{j-1}}^{\Omega _{j-1}+\omega _{j}}\mathcal {M}^{\dagger }(\Omega ,j)\,d\Omega -1 \end{aligned}$$

(10)

Linearizing the market impact function as with Eq. 4,

$$\begin{aligned} SLP_{j}\approx & \frac{\Delta P_{j}^{ext}}{P_{j-1}}+\omega _{j}\frac{S^{\dagger }_{j}}{2}=\frac{\Delta P_{j}^{ext}}{P_{j-1}}+\omega _{j}\frac{1}{2L^{\dagger }_{j}}\end{aligned}$$

(11)

$$\begin{aligned} with\nonumber \\ S^{\dagger }_{j}= & \frac{1}{P_{j-1}}\cdot \frac{\partial \mathcal {M}^{\dagger }}{\partial \Omega }|_{\Omega _{j-1},j} \end{aligned}$$

(12)

, illustrates the similarity to return. In the linear case, the difference lies only in a factor 1/2.

Model-based relation between CEX and DEX

The generalized formulas allow to map different AMM types to standard exchanges: DEX parameter updates, adaptions to the liquidity pool volume (e.g., for function-based liquidity-concentrating AMMs like Uniswap v2) and change of liquidity distribution (e.g., for liquidity provider-based liquidity-concentrating AMMs, like Uniswap v3) are implied in the shape change of $\mathcal {M}$ (indicated by the explicit dependence on j). This corresponds to the liquidity distribution change in the previous order book example.

The price adopting step of accordingly labeled AMMs (like Dodo) is mapped to $\Delta P_{j}^{ext}$, while this term vanishes for price-discovering AMMs (e.g., Uniswap v2, v3).

Elucidating price model terms and accessibility from exchange data

The individual terms of the price model given in Section “Formal price model” can be elucidated based on the real-world effects and the accessibility from exchange data.

Data related to exchanges can be ordered in a sequence of accessibility. Accessibility relates to principal availability, paid access, and complexity of retrieval and processing, such as retrieving historical DEX data from blockchain archive nodes. In the following, a concise overview (also summarized in Table 1) for discussing the identifiability of the basic terms is provided. Details for the specific data used and its (pre-) processing for the analysis are given in Section “Methods.”

CEX Basic time-frame cumulated trade data typically provides price (P) and total volume (V) and allows to determine return (R, Eq. 2) and illiquidity (ILLIQ, Eqs. 6 and 7). The concept of illiquidity and related input does not allow to resolve for the external price effect $(\Delta P^{ext})$ and market impact function ($\mathcal {M}$). In addition, illiquidity may diverge for small volumes and is therefore typically applied for wider time-frames and to provide an easily accessible, coarse, typically noisy, and less accurate combination of relevant effects (Amihud, 2002).

However, for trading timeframe length getting smaller and individual order volume larger, it is increasingly improbable that a matching counter-order occurs, hence the order will mainly be absorbed by the market makers and $V\rightarrow \omega$. Under this condition, and close to equilibrium ($\Delta P^{ext}\rightarrow 0$), the actual market impact function could, in principle, be resolved. However, it would mean that specific large trade events are required to exist and need to be isolated from the data. In addition, the approach does not allow to explicitly separate the net order volume dependence from the evolution over j (i.e., $\mathcal {M}(\omega _{j},j)$). The reason is that in order to approximately resolve the $\omega$ dependence requires a set of N “atomic” datasets sampling different $\omega$ values, however also sampling different shapes of $\mathcal {M}$ related to the explicit j dependence. This is indicated by unresolved $\omega _j,j$ in Table 1.

Table 1 Terms based on the price model and accessibility from exchange data

CEX timeframe cumulated, taker/maker volume enriched trade data adds additional information about the cumulated taker volume, which enables resolving for the net order trade volume ($\omega$). Analyzing return vs. $\omega$ for a set of N atomic datasets allows to determine an approximate, external price effect noised market impact function, slope and liquidity, respectively, therefrom. For close to equilibrium conditions (i.e., $\Delta P^{ext}\rightarrow 0$), the actual market impact function can be resolved.

The noisiness of so determined market impact can indicate the lead/following character of exchanges. As discussed in Section “Price discovery and market quality," reference price adaption and liquidity provisioning are a continuous, complex, interwoven process. Information gathering about reasonable pricing is partly trade external (mapped by $\Delta P^{ext}$ in the formalization) and partly from trade signals (reflected in $\mathcal {M}$, explicit dependency on j). Extracting the market impact function from timeframe cumulated, taker/maker volume enriched trade data can, therefore, be expected to be noisy, with the strength of noise being related to the underlying adoption of value attribution. If the adaption is implicitly contained in trade signals, the effect is more covered by $\mathcal {M}$.

When comparing two exchanges of the types order book-based CEXs or price adopting AMMs, one can, therefore, expect that the exchange that has more of a lead character to have a less noisy market impact function, compared to the following exchange, when determined from timeframe cumulated trade date. This is because the value attribution adaption manifests implicitly in the trade data on the lead exchange, which, however, makes it explicit. For exchanges with more of a following character, the information then is explicit and hence taken into account in the pre-trade order book update or price adoption for price-adopting AMMs. Therefore, the downstream price action on these exchanges has a larger $\Delta P^{ext}$ contribution, inducing a less well mapping of the return as a direct function of $\mathcal {M}$ and $\omega$, hence a more noisy market impact function when determined from timeframe cumulated trade data.

CEX order book-update event-resolved data permits to access the market impact function as it would be experienced by a trader trading any directional trade volume against the market makers. At any given point in time, the effect of trading a volume $\omega _{j}$ against the order book. Hence, $\mathcal {M}(\omega _{j},j)$ can be calculated from the distribution of liquidity.

CEX trade event data allows to directly access the market impact function as it was experienced by the trader trading a specific directional trade volume. However, it does not allow to explicitly separate the net order volume dependence from the evolution over j (i.e., $\mathcal {M}(\omega _{j},j)$).

CEX combined order book-update and trade event data permits to differentiate the source of order book updates in trade and non-trade-related price changes. The non-trade-related change of, for example, the midprice is related to $\Delta P^{ext}$. The order book adaption originating from trades and the trade data, respectively, provide information about the net order volume dependence of the market impact function (i.e., $\mathcal {M}(\omega _{j})$). The order book evolution after trade events is related to the evolution of the market impact function (i.e., $\mathcal {M}(j)$). Therefore, transitory price effects, such as the short-term recovery of liquidity after trades and persistent changes, can be resolved. This allows a comprehensive analysis of micro market effects and market anomalies (Chordia, Subrahmanyam, Tong, 2014; Amihud, 2002).

For AMM-based DEXs, in principle, all data is available on a per-event basis due to the publicly distributed nature of DLT systems. Given the exact AMM design and extracting the (historic) on-chain AMM’s state allows reconstructing every detail. In the following, we group sensible combinations based on the complexity of retrieval or reconstruction.

DEX with price-discovering AMM trade event data allows to determine a noisy market impact function without the need to know further parameters or AMM mechanisms. However, noise does not come from external price effects but from liquidity updates ($\Delta L$), which cannot be extracted from trade data alone. For diminishing liquidity updates ($\Delta L\rightarrow 0$), the market impact function can be determined exactly because these types of AMMs determine prices strictly following the encoded market impact function (i.e., no price jumps, $\Delta P^{ext}{\mathop {=}\limits ^{!}}0$). This does not mean there exists no external adaption of value attribution, but rather that such AMMs map any price adaption onto movement along the defined market impact function. See also the discussion of the related implications on the rational economic limit of these AMMs in Section “Discussion.”

DEX with price-discovering AMM full state reconstruction corresponds to full trade and liquidity adoption information. For price-discovering AMMs, the market impact function is fully defined for every point in time (i.e., $\mathcal {M}(\omega _{j},j)$), allowing to determine the $\omega _{j}$ dependence and the time evolution. This makes DEX with price-discovering AMM full state reconstruction data comparable to CEX combined order book-update event-resolved data.

DEX with price-adopting AMM trade event data does neither allow to determine the external price effect from price adoption (i.e., $\Delta P^{ext}\ne 0$), nor liquidity updates. The situation is comparable to CEX trade event data.

DEX with price-adopting AMM full state reconstruction allows to extract full information, including liquidity updates end external price effects, comparable to CEX combined order book-update and trade event data.

Analysis concept

The analysis concept is based on the price model given in Section “Formal price model” and measures the influence of market makers on liquidity-related aspects of market quality, such as the market impact function and especially its slope. The following subsections present the analysis concept for the subset of aspects relevant to this context.

Determining liquidity from timeframe cumulated taker/maker volume enriched trade data

Following the price model discussion given in Section “Elucidating price model terms and accessibility fromexchange data,” analyzing the influence of net order volume ($\omega$) on return allows to determine an approximate, external price effect noised market impact function $\mathcal {M}$, however, without the ability to separate the net order volume dependence from the slope evolution over j (i.e., $\mathcal {M}(\omega _{j},j)$) explicitly.

In order to sample a representative range of net order volumes, an overarching set of N subsequent atomic datasets (i.e., timeframe cumulated and indexed by j) is used as an analysis basis. N might be windows spanning over, for example, $\Delta T=6$ h, while j relates to $\Delta t=1$ min cumulated datasets.

More precisely, returns $R_j$ of all atomic timeframes j within the overarching set can be grouped into uniformly spaced $\omega$-bins, based on the return’s associated net order volume $\omega _j$ to a collection $R_N=\{(R_0; \omega _0), (R_1; \omega _1) \dots (R_n; \omega _n)\}$.

The noisy market impact function $\mathcal {M}_N$ can then be related to the distribution of the per bin determined median values $\tilde{R}_N(\omega )$, while the per bin statistics, for example, inner quantile range¹IQnR indicates the per bin representativeness of such median values. The number of datasets per bin c can be used to weight individual bins, for example, $w=\sqrt{c}$ supposing normally distributed data.

Employing the linearization given in Eq. 4 allows applying a weighted straight line fit to $\tilde{R}_N(\omega )$ and extracting the slope $\tilde{S}_N$. The weighted normalized mean squared error (WN-MSE) can be used to evaluate the fit quality.

Table 2 Overview of the analyzed historical exchange data per trading pair

Determining liquidity from order book event resolved data

Given order book-update event-resolved data, the market impact, as it would be experienced by a trader trading any directional trade volume $\omega _j$ against the market makers, can be determined at any given point in time. Hence, $\mathcal {M}(\omega _{j},j)$ can be explicitly calculated from the limit order distribution.

A sensible approach for comparing trade with order book data is to choose the same set of $\omega$-bins for both. The resulting collection of returns with one dataset per bin can then be further processed just as the set of trade data returns discussed above. To achieve relative importance of the individual bins comparable to the trade data set, the respective weights of timeframe cumulated trade data can also be used for the order book data collection fit.

Rolling window-based time evolution

The time evolution of the (noisy²) market impact function and slopes, determined following the approaches given in the previous subsections, can be analyzed by applying a rolling window of length $\Delta T$ for an analysis timeframe $\Delta \mathbb {T}$, for example, spanning over several months. To indicate the variability of the calculated market impact function and slopes, the fit quality, median, and IQnR values can be calculated from the time evolution.

Methods

To demonstrate the utility of the developed analysis concept, we analyzed the influence of market makers on market quality using the analysis concept and actual data. In the following, we describe how we proceeded in that analysis.

Data sources and preprocessing

To analyze liquidity provisioning of market makers in cryptoeconomic systems, we used historical trade data and order book-update event-resolved data from CEXs (i.e., Binance and Coinbase) and historical on-chain data from DEXs (i.e., Unsiwap v2 and Uniswap v3). To process the data, we used standard Python libraries, such as matplotlib, numpy, pandas, and seaborn.

We analyzed representative CEX and DEX markets for Bitcoin–US dollar and Ethereum–US dollar pairs in the most liquid representation per market. We considered Wrapped Ether and Ether to be on par, as well as USDT and USDC with USD. The exchanges and pairs have been selected based on trade volume and largest value locked, where applicable (i.e., liquidity pool-based AMMs). Table 2 shows the analyzed trading pairs and their 24-hour volumes.

Our analysis focuses on the liquidity-related influence of market makers on market quality. We selected two major CEXs, namely, Binance and Coinbase. The historical trade event data for CEXs was provided by tardis.dev. Based on historical trade event data, we calculated timeframe cumulated open, high, close, and low prices (OHCL data). We enriched this data by volume and net order flow ($\omega _j$), based on the individual trades executed on the CEXs. We used 1-minute timeframes to sample the trade data for the analysis.

To reconstruct the past order book for the analysis of order book-update event-based data, we used historical incremental order book data. We took snapshots of the order book every minute. Each snapshot represents the states of the order book at a specific time, including the maximum bid/ask levels available at snapshot time. We calculated returns, log returns, and illiquidity for a range of artificial net order volumes executed against the order book at every snapshot to resolve $\mathcal {M}(\omega _j,j)$ and stored this data. If the liquidity in the order book was not sufficient to satisfy large trade volumes, we asserted warnings and returned NaN values.

Fig. 1

Return over net order volume $\omega$ with fitted market impact functions weighted on the prevalence of $\omega$ for the ETH/USD pair. Horizontal: Binance, Uniswap v2, and Uniswap v3. Vertical: timeframes 2022-09-01 to 2023-02-28 (full timeframe), 2022-11-04 to 2022-11-05 (before FTX bankruptcy), and 2022-11-11 to 2022-11-12 (apex of the FTX bankruptcy)

Next, we downsampled the returns, log returns, and illiquidity of the 1-minute lower resolution time frames by calculating the median values over 1-hour for speeding up the subsequent data processing to conduct our analysis.

We selected Uniswap v2 and Uniswap v3 as AMM-based DEXs to be analyzed in this work. The AMMs used in those DEXs represent common implementations of two different liquidity provisioning approaches: function-based liquidity concentration (used in Uniswap v2) and liquidity provider-based liquidity concentration (used in Uniswap v3). Given full state reconstruction (see Section “Elucidatingprice model terms and accessibility from exchange data”), the difference in price determination in AMM-based DEXs (i.e., price-discovering and price-adopting) plays a subordinate role in this work because price-adoption is related to the external price effect $\Delta P_{j}^{ext}$. Therefore, in our analysis, Uniswap v3, a price-discovering AMM with liquidity provider-based liquidity concentration, is representative also for price-adopting liquidity pool-based AMMs with automatic liquidity concentration, such as Dodo.

To sufficiently reconstruct AMM states for the timeframe in the scope of the analysis, we gathered on-chain data related to state variables of smart contracts used in Uniswap v2 and Uniswap v3. For Uniswap v2, we gathered data on the actual reserves of token0 and token1. For Uniswap v3, we gathered the slot0 data (e.g., sqrtPriceX96 and tick), and current liquidity. Moreover, we gathered data of all neighbor ticks up to a price change of plus-minus 3% of the state’s current token price, resulting in 300 ticks with a tick spacing of 10 for the WETH/USDC pair. Because liquidity is less likely to fluctuate on Uniswap v2 and Uniswap v3, we reconstructed AMM states hourly within our analysis timeframe.

We analyzed BTC and ETH as the tokens with the largest trading volume. We selected the trading pair with the highest trading volume on the individual exchange. For example, Binance has pairs such as BTC/USDT, BTC/USDC, BTC/BUSD, and BTC/TUSD. There, we selected the pair with the highest 24-hour trading volume. For Uniswap v2 and Uniswap v3, we used pairs with Wrapped ETH because the trading volume was higher than with native ETH.

We use the WN-MSE to quantify the fit quality of the market impact function linearization to the sampled market impact at time j. The WN-MSE uses trading net order volume dispersion and emphasizes outlier impact, providing a comprehensive efficacy measure of the market impact function fit. The fit of the market impact function is weighted based on trading activities. Relative errors allow to compare the effectiveness of the fit of the market impact function between different timeframes and datasets. Additionally, taking the mean of squared errors helps to compute a singular, overall indicator of the fit quality. The mean of squared errors places greater emphasis on outliers, and negative values are eliminated. This multifaceted approach helps to compute a detailed and accurate assessment of how well our fit of the market impact function represents the real market impact function.

Timeframe selection

To demonstrate the applicability of our analysis concept and measure the influence of different market makers on market quality in cryptoeconomic systems, we selected a 6-month time frame ($\Delta \mathbb {T}=6M$) from 2022-09-01 to 2023-02-28 for our analysis. The timeframe includes mostly sideward movements of Bitcoin and Ether prices in 2022-09, 2022-10, 2022-12, and 2023-02, while it also covers the FTX bankruptcy in 2022-11 as a black swan event with a massive downturn of 26% for Bitcoin and 35% for Ether within three days. Bitcoin and Ether prices fully recovered in 2023-01. The time frame of the FTX bankruptcy in 2022-11 can be regarded as a moment of non-equilibrium for Bitcoin, Ether, and other tokens of cryptoeconomic systems. We assume that the selected timeframe is suitable for analyzing the influence of different market makers on market quality because this timeframe covers moments of equilibrium and non-equilibrium

Liquidity-based influences of market makers on market quality in cryptoeconomic systems

This section presents the results of the analysis concept’s utility demonstration. First, we show the fit quality that is achieved by our analysis concept to validate its suitability. Second, we present the time evolution of the market impact function’s slope based on different types of data. Finally, we compare the influence of conventional and automated market makers on slope evolution and, hence, market quality.

Validating derived market impact functions and slope metrics

Figure 1 illustrates fitted market impact functions, net order volume distributions as bar plots, and WN-MSE values for Binance, Uniswap v2, and Uniswap v3, examined at three distinct timeframes: full 6 months, 1 day before, and 1 day during the FTX bankruptcy. The vertical lines illustrate the 95% IQnR of the number of atomic datasets per $\omega$-bin, indicating the region of main trading activity. The three timeframes sample overall, normal, and extreme price actions and can be regarded as representative of equilibrium and non-equilibrium conditions.

The results illustrated in Fig. 1 offer evidence for the consistent fit quality that is achieved by applying the analysis concept (see Section “Analysis concept”). This validates the chosen approach. achieved by and, hence, the validity of the chosen approach. Figure 2 shows the results of the WN-MSE for the fitted market impact function over time for the BTC/USD pair on Binance. The fit quality is sufficient for our analysis even during moments of strong non-equilibrium, as evidenced during the FTX bankruptcy (in early 2022-11). Here and for the following analyses, we indicate the fitting precision by analyzing the WN- MSE’s median and 95% IQnRs. Subsequently, we report the WN-MSE median and IQnR of the WN-MSE.

Results from time evolution of the market impact function’s slope metric

In the following subsections, we present the results from analyzing the time evolution of the market impact function’s slope metric.

Market impact function’s slope metric is in line with market microstructure theory

Figure 3 illustrates the evolution of the market impact function’s slope for timeframe cumulated maker/taker enriched trade data (first row), order book event-resolved data (second row), and the log price (third row) for the BTC/USD pair. The left and right columns juxtapose data from two conventional market makers of major CEXs: Binance (left) and Coinbase (right). The dashed lines indicate the respective median values over the complete analysis timeframe.

Fig. 2

Slope evolution of the market impact function over time (first row). WN-MSE with median and 95% quantiles lines (second row). Log-price evolution (third row). The BTC/USD pair on Binance with $\Delta \mathbb {T}=6M$ (2022-09-01 to 2023-02-28) and $\Delta T=1d$

Fig. 3

Slope of market impact function for timeframe cumulated maker/taker enriched trade data (first row). The slope of market impact function for order book event resolved data (second row). Log-price evolution (third row). The BTC/USD pair on Binance (left) and Coinbase (right) with $\Delta \mathbb {T}=6M$ (2022-09-01 to 2023-02-28) and $\Delta T=1d$

Regarding the slope metric, Figs. 1 and 3 show that the market impacts function’s slope is positive for all timeframes T. This empirical finding is in line with the basic hypothesis widely accepted in market microstructure economic literature: a positive net order volume, indicating a predominance of buy over sell orders, tends to exert upward pressure on prices and vice versa (Madhavan, 2000). This relationship underscores the interplay between market behavior and price evolution.

Fig. 4

Slope of market impact function for order book event resolved data with median lines (first row), IQnR of returns (second row) and log-price evolution (third row) for the ETH/USD pair on Binance (left, orange), Uniswap v3 (left, green) and Uniswap v2 (right, blue) for a rolling window width $\Delta T=1d$ over the analysis period 2022-09-01 to 2023-02-28 $\Delta \mathbb {T}=6M$

Median slopes from trade and order book data are comparable

The median slopes determined from timeframe cumulated maker/taker enriched trade data approximates the median slopes of order book-update event resolved data. For Binance (top and middle in the left column of Fig. 3), the median slope values are closer ($0.56e^{\text {-}9}$ trade vs. $0.65e^{\text {-}9}$ order book data) than with Coinbase ($1.43e^{\text {-}9}$ trade vs. $1.16e^{\text {-}9}$ order book data). Overall, Binance has a 2.56 times flatter slope of the market impact function, indicating higher liquidity than Coinbase. This finding aligns with the more noisy trade data-derived slope of the market impact function for Coinbase. This present noise causes the large deviation of the market impact function slopes’ median values for Coinbase. The higher liquidity and the larger trade volume at Binance compared to Coinbase indicate that Binance could be regarded as a lead market. We discuss this observation in more detail in the following subsections.

Order book event-resolved data provides an accurate representation of the market impact function

For Binance, the time evolution of slopes derived from timeframe cumulated trade data and book-update event-resolved data (illustrated in Fig. 3) shows remarkable similarities. This indicates that the noisy market impact function approximates the real market impact function. Therefore, as discussed in Section “Elucidating price model terms and accessibilityfrom exchange data,” the effects from value attribution adaption leading to external price effects $\Delta P^{ext}$ and market impact function shape change can be assumed to be small in cumulated maker/taker enriched trade data on Binance. In contrast, the noisy market impact function on Coinbase strongly deviates from the non-noisy market impact function derived from order book-update event-resolved data. Therefore, the external price effects are larger on Coinbase.

Overall, the analyses support the price model-based argumentation given in Section “Elucidating price model termsand accessibility from exchange data.” The order book event-resolved data provides a more accurate representation of the market impact function’s slope. Order book snapshots offer a clearer insight into the exchange-local market’s intrinsic behavior by focusing on immediate market conditions and excluding external effects.

Lead markets can be identified via noisiness of the market impact function

The larger volume, higher liquidity, and smaller noise of the trade data derived slope for Binance, compared to Coinbase, is in line with the predictions based on the price model given in Section “Elucidating price model terms and accessibilityfrom exchange data.” Consequently, the theoretical and data-based analyses imply that Binance potentially assumes the role of a lead market for Bitcoin, while Coinbase appears to act as a following or reactive market.

Market makers avert adverse selection costs—liquidity is reduced in non-equilibrium

When examining the timeframe cumulated maker/taker enriched trade data for CEXs (e.g., Binance and Coinbase) illustrated in Fig. 3, notable peaks in the slope of the market impact function can be observed in early November 2022. Those peaks correspond to an increased slope of the market impact function, indicating reduced market liquidity. The peak in early November is particularly noteworthy because it aligns with a significant downturn in Bitcoin’s logarithmic price due to the FTX bankruptcy event. The correlation underscores the sensitivity of the market impact function’s slope to major market events, leading to liquidity shifts. This shows that market makers remove liquidity in moments of non-equilibrium to avert adverse selection costs.

Function-based liquidity-concentrating AMMs provide inferior average liquidity and market quality

Figure 4 provides a detailed visualization of the evolution of the market impact function’s slope (first row) for order book-update event resolved data on Binance (orange lines), Uniswap v2 (blue lines), and Uniswap v3 (green lines) for the ETH/USD pair. The second row illustrates the corresponding 95% IQnRs of the respective slopes. The log price of Ether is given in the third row.

Uniswap v2 is a representative of function-based liquidity-concentrating AMM implementations, which were invented way before the liquidity provider-based liquidity-concentrating AMMs. Therefore, we first compare Uniswap v2 against Binance. The median slope of the market impact function of Uniswap v2 ($1.32e^{\text {-}7}$), compared to Binance ($1.09e^{\text {-}9}$), is approx. 120 times larger. This indicates inferior average liquidity and market quality on Uniswap v2..

Function-based liquidity-concentrating AMMs show less detrimental external price effect-based liquidity dynamics

Although Uniswap v2 provides inferior average liquidity compared to Binance, it shows much smaller relative changes in liquidity over time (see the middle row in Fig. 4). These changes are uncorrelated to external events (e.g., the FTX bankruptcy). Obviously, the sharp changes in the market impact function slope on Uniswap v2 are caused by major liquidity providers temporarily removing their liquidity. In contrast, minor changes in the market impact function’s slope on Uniswap v2 are correlated with external price-based trading against the AMM and follow the convex shape of the programmed market impact function.

One could, therefore, argue that function-based liquidity-concentrating AMMs, such as Uniswap v2, have the potential to provide more reliable liquidity to the market, especially in strongly non-equilibrium conditions, thereby ensuring certain levels of market quality. Nevertheless, the liquidity on Uniswap v2 was way lower (approx. factor 120) than with Binance, even under strong non-equilibrium conditions with the FTX bankruptcy.

Liquidity provider-based liquidity-concentrating AMMs potentially provide CEX-competitive overall market quality, however may suffer stronger adverse selection costs

Function-based liquidity-concentrating AMMs (e.g., Uniswap v2) persistently distribute liquidity across the AMMs price range based on the implemented function. This differs from liquidity provider-based liquidity-concentrating AMMs (e.g., Uniswap v3). In these AMMs, liquidity providers have more individual influence on the liquidity distribution, for example, by specifying price ranges in which their liquidity will actually be distributed.

With a deviation of about a factor of 2.06, the median slope of the market impact function of Uniswap v3 (top-left subfigure, green line in Fig. 4) is about two orders of magnitude closer to Binance’s market impact function slopes compared to Uniswap v2.

The slope’s time evolutions of Binance and Uniswap v3 show similarities. However, the slope evolution for Uniswap v3 is more dynamic. This similarity indicates that liquidity providers of Uniswap v3 avert adverse selection costs by redistributing their liquidity, similar to CEXs. Therefore, one could argue that liquidity providers on liquidity provider-based liquidity-concentrating AMMs could pursue similar market making strategies as on order book-based exchanges through frequent liquidity reallocation. Such AMM designs inherit the disadvantages of conventional market makers, such as liquidity removal in moments of non-equilibrium to avert adverse selection costs. The effect of liquidity removal in moments of non-equilibrium can be seen in the second row when looking at the IQnR of returns. For Binance and Uniswap v3, returns show a large per bin dispersion (large IQnR values), indicating large liquidity changes. In contrast, the IQnR of returns for Uniswap v2 show a small dispersion, indicating small liquidity changes, especially compared to Binance and Uniswap v3.

Depending on the AMM design, frequent liquidity reallocation can lead to even stronger overall liquidity fluctuation than on CEXs, as is the case for Uniswap v3. This worsens the market quality for such AMMs, especially in moments of non-equilibrium.

Discussion

Principal findings

Although AMM-based DEXs seem promising to tackle challenges of CEXs (e.g., separation of concerns, transparent and persistent liquidity provisioning), the extent to which AMMs operated in DEXs can enhance market quality compared to conventional market makers used in CEXs remains unknown. This makes the targeted use of AMMs and conventional market makers in cryptoeconomic systems to reach high market quality difficult. To analyze the influence of market makers on market quality in cryptoeconomic system markets, we present a formal price model and derive an analysis concept. We demonstrate the utility of our analysis concept by analyzing and comparing AMMs operated in DEXs (i.e., Uniswap v2, Uniswap v3) and conventional market makers on CEXs (i.e., Binance and Coinbase).

The analysis results show that trade data includes external price effects leading to noisy market impact functions. This is particularly observable in the comparison between market impact functions derived from cumulative maker/taker enriched trade data and order book-update event-based data (see Section “Results from time evolution of the marketimpact function’s slope metric”).

In the analysis of external price effects and the noisiness of the market impact function for Bitcoin, we observed that the slope of the market impact function on Binance is much less noisy than the slope of the market impact function on Coinbase. This indicates that for Bitcoin, external price effects on Binance are smaller, compared to Coinbase. Binance can be supposed to form a lead market and Coinbase a following market. This is supported by the overall smaller slope of the market impact function and larger trade volume on Binance.

For AMM-based DEXs, the analysis results show a substantially larger slope of the market impact function for function-based liquidity-concentrating AMMs (e.g., Uniswap v2). We argue that the slope and, hence, the cost of liquidity of these AMMs will, in principle, always be larger compared to sufficiently adopted CEXs and DEXs with other AMM designs. The reason lies in the price discovery combined with the inherently opposed relationship between experienced divergence loss and retrieved surplus from market making: increasing the pool size decreases the slope of the market impact function, which is desirable in equilibrium conditions³. However, in non-equilibrium conditions, when price adaption to external value changes is necessary, a larger amount of assets is required to be traded at economically disadvantageous prices. Thereby, the absolute divergence loss increases with pool size. In contrast, the absolute surplus from market making, which depends on the trading volume transacted by the AMM, is unlikely to increase accordingly. Thus, if the liquidity provided increases more than the transacted volume, the liquidity providers receive less reward per deposited value unit, and a rational economic limit to pool size exists, which in turn hinders adoption and increase of trade volume. This chicken-egg problem prevents the slope of the market impact function from growing comparably small to CEXs and other AMM designs.

Contributions to research and practice

To support analyses of the influences of market makers on market quality, we applied concepts established in finance literature on market microstructure to cryptoeconomic systems. Thereby, we offer a novel theoretical lens for analyses of the performance of market makers in terms of their influences on market quality. In particular, we contribute to the better analysis and design of market makers for cryptoeconomic systems in four ways.

First, we present a formal price model based on well-established concepts in finance literature. Thereby, we offer a foundation to better understand price formation in markets. This supports market participants in analyzing the different components of price evolution.

Second, we present an analysis concept that uses the formal price model to investigate the influence of market makers on market quality in cryptoeconomic system markets. This is useful to assess and compare market quality and liquidity on different CEXs and DEXs. For example, market participants can assess lead markets and following markets by analyzing the external price effects and noisiness of the market impact functions.

Third, we describe how to use the analysis concept to analyze the influences of conventional market makers and AMMs on market quality by applying our formal price model and analysis concept on historical data. Through that analysis, we show the influences of different market makers on market quality in cryptoeconomic systems. This supports practitioners in using the analysis concept for future analysis of market quality.

Fourth, by offering evidence for theoretic assumptions on conventional market makers, we support assessing market impact, market quality, and liquidity in cryptoeconomic system markets. This is useful to predict market quality and associated risks of trade execution. Thereby, they can optimize trade execution and reduce trade risks.

Overall, this work lays a foundation for analyzing and comparing CEXs and DEXs in terms of their influences on market quality. This helps understand the origins of benefits and drawbacks of AMMs compared to conventional market makers and helps guide the future design of AMMs.

Limitations

In the scope of this work, we focused on the largest two CEXs (i.e., Binance and Coinbase) by 24-h trading volume because we assumed those CEXs to be the most representative conventional market makers. Conventional market makers used in other CEXs (e.g., Kraken, KuCoin, and OKX) may apply other market making strategies. Therefore, the presented findings on CEXs apply to Binance and Coinbase at the time of observation but cannot ultimately be generalized to any CEXs.

Even though we used extensive data for the market maker analysis, we did not differentiate between market makers and regular traders. We assumed that all market participants who place limit orders into the order book act as market makers. Thus, our results do not examine individual institutional market makers, but the collective behavior of market makers and market participants. This approach seems reasonable because, to the best of our knowledge, liquidity is mainly influenced by this collective behavior.

To compare conventional market makers with AMMs, we analyzed Uniswap v2 and Uniswap v3 as representatives of function-based and liquidity provider-based liquidity-concentration AMMs. We selected these AMM-based DEXs because they have the highest 24-hour trading volume, which is, at least, partially comparable to the 24-hour trading volume of CEXs.

Recent developments brought forth new AMM designs with unique characteristics. For example, supply-sovereign AMMs are promising to overcome the dependence on liquidity providers and the liquidity problem related to adverse selection cost by design. However, we do not provide any analyses for supply-sovereign AMMs. The reason is that to date, to the best of our knowledge, no sufficiently adopted real-world implementation exists.

Future research

Supply-sovereign AMMs seem promising to overcome the dependence of AMMs on liquidity providers. However, supply-sovereign AMMs are not intended to provide a means of exchange for arbitrary assets. Instead, supply-sovereign AMMs are envisioned to control the token supply of cryptoeconomic systems to issue and trade those tokens. By controlling the token supply, supply-sovereign AMMs can overcome the adverse selection cost of liquidity problem by design. This is because the AMM as issuer can guarantee liquidity without depending on external liquidity providers. Supply-sovereign AMMs form the lead market by design, with a market maker guaranteeing liquidity based on their transparent market impact function. In contrast, liquidity provider-based AMMs (e.g., Uniswap v2, Uniswap v3) must follow the lead market, typically located elsewhere due to the rational economic limit of market impact function’s slope. Thereby, liquidity providers on liquidity provider-based AMMs suffer losses from buying and selling tokens at disadvantageous prices to arbitrageurs exploiting price discrepancies between the AMM and the lead market. With supply sovereign AMMs, the previous drawback is resolved in a twofold way. No liquidity providers are averting adverse selection risk and divergence loss, and there is no need to follow an external lead market. This can help to greatly enhance market quality, especially in non-equilibrium conditions.

Due to the principal differences between supply-sovereign AMMs and AMMs with other designs (e.g., Uniswap v2, Uniswap v3) and the lack of supply-sovereign AMMs implementations, a detailed analysis of possible advantages and drawbacks should be better understood in future analyses of influences of supply-sovereign AMMs on market quality. We plan to perform such analyses in subsequent work.

Conclusions

Conventional market making and exchange operations entail risks of low market quality. This can facilitate market manipulation by fraudulent entanglement of exchanges, market makers, and underwriters, harming honest market participants. AMM-based DEXs operating in cryptoeconomic systems seem to tackle those challenges, by employing persistent and transparent market making strategies. However, the extent to which AMMs can help improve market quality compared to conventional market makers is barely understood.

Drawing from finance literature on market microstructure, we developed a formal price model and an analysis concept for market quality. The analysis concept allows to analyze and understand the influence of market makers on market quality in cryptoeconomic systems.

We show that, depending on AMM designs, AMMs operated in DEXs have the potential to provide CEX-competitive market quality. However, the problem of low market quality due to the significant removal of liquidity in non-equilibrium conditions remains unsolved. The root cause of liquidity removal lies in adverse selection costs that strongly influence the economic sustainability of market making strategies. Considering fundamental economic principles, it seems plausible that these drawbacks will not be overcome with approaches for which adverse selection costs of liquidity are a major concern.

Supply-sovereign AMMs focus on the issuance and trading of own tokens of cryptoeconomic systems, while the AMM controls the supply. Supply-sovereign AMMs eliminate dependence on liquidity providers. This can help overcome the liquidity problem related to adverse selection cost by design. Thus, supply-sovereign AMMs are promising to become state of the art for new projects that envision keeping sovereignty over their tokens and offer markets with high liquidity and market quality. This can be regarded as well aligned with the core idea of cryptoeconomic systems to create decentralized, self-sovereign systems without the need for central authorities.