SWIFT INSTITUTE
WORKING PAPER 2021-001
DIGITAL ASSETS AND MARKETS:
A TRANSACTION-COST ANALYSIS OF MARKET ARCHITECTURES
ANGELO ASPRIS
ANNE HAUBO DYHRBERG
SEAN FOLEY
TALIS J. PUTNINS
PUBLICATION DATE: 13 DECEMBER 2022
The views and opinions expressed in this paper are those of the authors. SWIFT and the SWIFT
Institute have not made any editorial review of this paper, therefore the views and opinions do not
necessarily reflect those of either SWIFT or the SWIFT Institute.
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Electronic copy available at: https://ssrn.com/abstract=4301258
Digital Assets and Markets:
A transaction-cost analysis of market architectures
Angelo Aspris a, Anne Haubo Dyhrbergb, Sean Foley c, and Talis J. Putninsd,e, 1
a
The University of Sydney
b
Wilfrid Laurier University
c
Macquarie University
d
University of Technology Sydney
e
Digital Finance Co-operative Research Centre
Executive Summary
This report examines the market landscape for digital assets, including digitally recorded traditional
securities and cryptographically secured tokens that represent the building blocks of the future
tokenized economy.
First, we describe the major asset categories, comparing traditional, centralized ways of recording
asset ownership with cryptographically secured and distributed ownership records. Then compare
traditional and tokenized forms of equities, fiat currencies and stablecoins, cryptocurrencies, and
other digital tokens. We explain how subtle changes in how asset ownership is recorded has
fundamental implications for financial market infrastructure including custodianship, trading, and
settlement. For example, cryptographically secured tokens can facilitate real-time risk-free settlement
of individual trades, reducing or eliminating the need for a clearinghouse, yet create new challenges
in custodianship and safekeeping of assets.
Second, is a description of different trading mechanisms for investors by analyzing a variety of onchain and off-chain market architectures. We compare centralized limit order book markets,
decentralized limit order books, and decentralized liquidity pools (automated market makers, AMMs),
in terms of structure, performance, and suitability for trading different assets. We show that there are
substantially differences between these market types in settlement risks, latency, and throughput
capacity.
Third, based on an extensive sample of data to empirically analyze trading costs, we compare the
efficiency of different market types (e.g., limit order books vs AMMs) and trading pairs (crypto-crypto,
crypto-fiat, digital-fiat, stablecoins). We show that markets for decentralized assets are currently more
costly and less efficient than centralized limit order book markets, but the difference is largely because
decentralized markets are in their infancy and have not reached the volumes traded in centralized
markets. And that as volume shifts to the new market types, their costs fall, narrowing the liquidity
gap between centralized and decentralized market architectures – a trend that is expected to
continue.
This analysis provides a guide for investors selecting markets to trade digital assets and has
implications for how financial market infrastructure is likely to evolve as more assets join the
“tokenized economy”.
Email addresses: angelo.aspris@sydney.edu.au,
Talis.Putnins@uts.edu.au
1
adyhrberg@wlu.ca,
Sean.Foley@mq.edu.au,
2
Electronic copy available at: https://ssrn.com/abstract=4301258
and
Table of Contents
1.
2.
Digital Assets: An Introduction ....................................................................................................... 5
1.1.
Digital Securities: The Token Taxonomy ................................................................................. 5
1.2.
Protocol Layer (“Pure Currency”) Coins .................................................................................. 6
1.3.
Decentralized Application Tokens (DApp Tokens) or Utility Tokens ...................................... 6
1.4.
Security Tokens ....................................................................................................................... 7
1.5.
Stablecoins .............................................................................................................................. 8
1.6.
Non-Fungible Tokens .............................................................................................................. 9
1.7.
Concluding Thoughts: Tokenomics ....................................................................................... 10
Market Architecture...................................................................................................................... 10
2.1.
Digital Asset Exchanges ......................................................................................................... 10
2.2.
Organizational Structure of Traditional Markets .................................................................. 11
2.3.
Centralized Exchanges (CEX) in Cryptocurrency Markets ..................................................... 11
2.4.
Decentralized Finance ........................................................................................................... 12
2.5.
Decentralized Exchanges (DEXs) ........................................................................................... 13
2.6.
Not all DEXs are created equal.............................................................................................. 13
2.6.1.
Automated Market Makers (AMM) .............................................................................. 14
2.6.2.
Key Insights about AMMs: A Summary ......................................................................... 20
2.7.
3.
Data ............................................................................................................................................... 21
3.1.
4.
Construction of transactions cost metrics ............................................................................ 22
How well do the different markets facilitate trade? .................................................................... 23
4.1.
An overview of liquidity ........................................................................................................ 23
4.1.1.
Liquidity and Market adoption ..................................................................................... 27
4.1.2.
Tokenized Stocks vs Equity Market Liquidity ................................................................ 27
4.1.3.
AMM vs CEX liquidity .................................................................................................... 30
4.1.4.
Cost of Settlement ........................................................................................................ 33
4.2.
Trade Size Analysis ................................................................................................................ 34
4.2.1.
Distribution of Trade Sizes ............................................................................................ 34
4.2.2.
Trading Costs for Different Trade Sizes......................................................................... 35
4.2.3.
Price Impact Functions for the Different Markets ........................................................ 37
4.3.
5.
DEX Aggregators.................................................................................................................... 20
Can AMMs become competitive with Centralized Exchanges? ............................................ 41
Conclusion ..................................................................................................................................... 42
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Table of Figures
Figure 1: Digital Security Layers .............................................................................................................................. 6
Figure 2: Stablecoin Growth ................................................................................................................................... 8
Figure 3: Stablecoin Market Share.......................................................................................................................... 9
Figure 4: Decentralized Exchanges ....................................................................................................................... 13
Figure 5: Automated Market Makers (AMM) ....................................................................................................... 15
Figure 6: Constant Product Market Makers (CPMM) ........................................................................................... 16
Figure 7: CPMM - Price Impact ............................................................................................................................. 17
Figure 8: ETH-BTC versus S&P500 ......................................................................................................................... 22
Figure 9: Liquidity Gap and Market Share (Tokenized Equities versus Equity Securities) ..................................... 28
Figure 10: Liquidity Gap and Market Share (Centralized Exchange versus Automated Market Maker) .............. 30
Figure 11: Cost of Settlement - Gas Fees .............................................................................................................. 33
Figure 12: Trade Size Distribution ......................................................................................................................... 34
Figure 13: Calibrated empirical price impact curves for markets that trade equities. ........................................ 39
Figure 14: Calibrated empirical price impact curves for markets that trade cryptocurrencies............................. 40
Figure 15: Calibrated empirical price impact curves for all markets. ................................................................... 41
Figure 16: Projected AMM Transaction Costs....................................................................................................... 42
Table 1: Summary Statistics - Tokenized Securities (TKN). ................................................................................... 24
Table 2: Summary Statistics - Equity Securities (EQX) .......................................................................................... 24
Table 3: Summary Statistics - Centralized Exchanges (CEX) ................................................................................. 25
Table 4: Summary Statistics – Decentralized (Order Book) Exchanges (DEX). ...................................................... 26
Table 5: Summary Statistics - Decentralized (AMM) Exchanges........................................................................... 27
Table 6: Regression Analysis 1 - Market Quality (Equity Securities v Tokenized Equity) ...................................... 29
Table 7: Regression Analysis 2 - Market Quality (Equity Securities v Tokenized Equity........................................ 29
Table 8: Regression Analysis 3 - Market Quality (AMM versus CEX) .................................................................... 32
Table 9: Regression Analysis 4 - Market Quality (AMM versus CEX) .................................................................... 32
Table 10: Tokenized Securities - Trade Size Analysis. ............................................................................................ 36
Table 11: AMM - Trade Size Analysis. ................................................................................................................... 37
Table 12: Summary of Findings............................................................................................................................. 43
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Electronic copy available at: https://ssrn.com/abstract=4301258
1. Digital Assets: An Introduction
Against the backdrop of the financial crisis that unfolded in 2008 lay the birth of fully decentralized
digital assets that have been enabled by distributed ledger technology. This transformative
movement, initially embraced by technologists, anarchists 2 and enthusiasts has rapidly evolved - with
the rate of digital asset adoption exceeding any previous global infrastructure rollout - including the
internet, mobile phones, or virtual banking tools over comparable periods. 3
A comprehensive range of cryptographic assets such as payment tokens, utility tokens, stablecoins,
and non-fungible tokens are among a broad suite of digital assets used and exchanged by consumers,
corporates, and institutions. Digital assets can be distinguished from physical assets because they are
digitally identifiable and without physical form. Absent, however, from any current debate is a
concrete definition that is universally accepted. Terms such as ‘cryptocurrency’, ‘crypto-assets’,
‘digital currency’, ‘virtual currency’, ‘coins’, and ‘tokens’ have become commonplace in the modern
vernacular and are used both casually and formally to mean different things. The considerable breadth
of the concept of digital assets reflects the ongoing transformation in this sector.
Acknowledging the presence of these assets with an eye on regulation, the SEC defines digital assets
as those “issued and transferred using distributed ledger or blockchain technology”. 4 Through this
technologically neutral principle, digital assets can be seen as securities, currencies, properties, or
commodities if ownership and exchange take place on a decentralized digital ledger.
Box 1. An important distinction is often drawn between coins and tokens. Cryptocurrencies or
‘coins’ refer to a base currency - and are an integral component of the currency - being its network.
The most prominent example of a coin is Bitcoin. Tokens on the other hand, are units built on top
of one of the base networks as a secondary feature. They take advantage of a robust and established
blockchain network to create these digital assets. The most widely used (Ethereum) standard is ERC20 for fungible tokens and ERC-721 for non-fungible tokens.
1.1. Digital Securities: The Token Taxonomy
Overwhelmingly, most financial assets in circulation can be represented and owned in the form of
tokens on the blockchain. In blockchain parlance, tokens represent assets or access rights that are
managed by a distributed ledger. As access rights, they critically support blockchain networks by
enabling access to promote platform usage and incentivize adoption, as well as promote governance
by providing rights to participate in protocol development. Numerous taxonomies have been
proposed for classifying tokens and are typically based on specific properties associated with the token
(e.g. the blockchain layer) or relate to token function or purpose (e.g. utility token versus governance
token). 5 The challenge of finding an appropriate classification is beyond the scope of this work,
however, to permit a clear understanding of the different types of digital tokens which has
implications for liquidity and trading costs, we take a practical approach which emphasizes the layers
An early use cases for Bitcoin as documented by Foley et al. (2019) was the purchase of illicit substances.
http://charts.woobull.com
4
https://www.sec.gov/files/digital-assets-risk-alert.pdf
5
For example Hu et al. (2019), Corbet et al. (2020), Harvey et al. (2021), John et al. (2022).
2
3
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of the blockchain that can issue tokens or ‘tokenize’ assets. 6 Tokens can either be native to the
blockchain, issued on top of a protocol or exist on the application layer. This approach is promulgated
by Yano (2020) with a visual representation reproduced in Figure 1.
Figure 1: Digital Security Layers
In Figure 1, tokens are separated into three categories: crypto-asset tokens (“things”); decentralized
application tokens (“companies”) or Protocol coins (“economy”). A more complete categorization is
offered in Oliveira et al. (2018) and considers a range of parameters based on purpose, functionality,
governance, and technical aspects. Our discussion below explains the differences between the three
categories, with explanations provided for key token categories.
1.2. Protocol Layer (“Pure Currency”) Coins
The protocol layer (implementation layer) refers to the core architecture of a blockchain system which
covers both consensus protocols and incentives to ensure an identical and resilient distributed ledger
is created and maintained. The first blockchain coins are native tokens of public and permissionless
blockchain networks and are aptly referred to as protocol tokens. In addition to safeguarding the
network by acting as an incentive for miners/validators, native protocol tokens may be needed to pay
for transaction fees and can be regarded as the currency of the distributed network. Bitcoin, described
by Nakamoto (2008), was the first of these currencies. Apart from Bitcoin and Ethereum, popular
implementations with large market capitalizations include Litecoin, Solana, Cardano, Polkadot, Zcash,
Monaro and Dash.
1.3. Decentralized Application Tokens (DApp Tokens) or Utility Tokens
The second category of tokens in this digital asset space are known as Decentralized Applications
tokens. They are more commonly referred to as DApp tokens (or utility tokens) and are distinguishable
from the previous category in that they are generated from within the blockchain and not backed by
an off-chain security or asset. Decentralized Applications are open-source applications 7 that run
This framework gives a broad overview of the different properties and types of tokens. It is not intended to be
a detailed taxonomy of the different technical, economic, and regulatory properties that could be used to
evaluate tokens, rather the intention is to present an overview of the current landscape.
7
Decentralized applications exist in many areas including decentralized finance, social media, and gaming.
6
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autonomously on decentralized blockchain networks, often featuring a native token which serves as
a promise to allow the investor to redeem the token - like a voucher on the decentralized application.
Critically, these tokens are structured to ensure they do not transfer ownership and control rights,
which thus offers scarce legal protections to tokenholders. 8 Most utility tokens are currently created
on the Ethereum blockchain, which facilitates their creation and movement from one account to
another. An increasing number of smart-contract enabled blockchains (such as Solana and Cardano)
also allow for the creation of such tokens.
Box 2. Curve is an example of a popular decentralized application. Curve is a decentralized exchange
(DEX) that allows participants to exchange assets (primarily stablecoins) through an automated
market maker (AMM) approach. Underpinning this platform is the Curve token (CRV), an Ethereumbased token issued by the Curve DAO, which is used by participants to pay for fees, provide liquidity
and support low-slippage trading, engage in staking (locking) to support the security and operations
of the network, and participate in voting on various DAO proposals and pool parameters. CRV can
be thought of as a native utility token of the Curve protocol, where liquidity pool rewards and
incentives are paid in CRV to liquidity providers. Its value, however, also rests in the voting rights
conferred upon tokenholders in relation to the governance of the protocol. This may require
tokenholders to participate in decisions associated with modifications of certain parameters
connected with the protocol.
The value of these DApp tokens is far from straightforward and is often linked with uses and rights
which may vary significantly from one token to the next. DApp tokens can function as a service voucher
belonging to a specific protocol, but they may also grant the holder specific ownership, voting or
cashflow rights. In the case of the former, as activity in the protocol rises, the resulting demand for
the native token will positively influence its value. In the case of the latter, which more closely
resembles a traditional equity structure, value is associated with the right to future cash flows and
corresponding voting rights.
1.4. Security Tokens
Crypto-asset tokens, also known as security tokens, represent assets or values (investment contracts)
that exist in the physical world. Like stocks and bonds, their purpose is investment. Akin to
conventional forms of securitization and financialization, tokenization ensures the rights of an asset
are carried by the digital tokens which can be bought, sold, or traded on the blockchain. This process
holds numerous theoretical benefits for market participants such as efficiency gains driven by
automation and disintermediation, interoperability, enhanced liquidity, fractional ownership, and
improved clearing and settlement (Momtaz, 2021). The standardization provided by tokenizing further
promotes fractionalized ownership (i.e., stocks with high prices such as Tesla can be traded in fractions
of a share) and global access to investment opportunities that are secured over the blockchain.
Box 3. The Centrifuge blockchain is among the very first protocols to tokenize real-world assets,
linking assets such as real estate or trade receivables with decentralized finance. Functionally, this
could allow a firm to issue tokens representing their livestock to collateralize a micro financing loan,
issued on the blockchain (Yano, 2020). Mt Pelerin Group SA was the first company to tokenize all
8
Such tokens have historically been structured to fail the U.S. Howey test, avoiding “security” classification.
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its issued shares on the blockchain in the form of Ethereum tokens on 30 October 2018. The public
sale of its tokenized shares (equity tokens), up to 5% of its share capital, was compliant with the
Swiss regulatory framework with the intended use of funds covering costs related to the company’s
application for a banking license. Tokens owners, like their fellow shareholders, have voting rights
as well as dividend rights.
1.5. Stablecoins
Stablecoins (or “Stable tokens”) are designed to maintain their value relative to some external unit of
account, most typically with a peg to an underlying asset such as fiat currency. Stablecoin usage has
grown significantly since they were introduced, with aggregate market capitalizations rising from
$US5.5bn in January 2020 to nearly $200bn in May 2022 (Figure 2). This demand for stablecoins is
characterized by a growing demand for safe assets in decentralized finance. Stablecoins are however
multi-purpose coins and can be used for remittances, as financial rails to trade traditional
cryptocurrencies, a medium of exchange for decentralized finance protocols, and employed as a store
of value for assets already inside the ‘crypto’ ecosystem.
The design of stablecoins is both a complex and evolving process. Stablecoin projects can be
categorized by collateral type (on-chain vs off-chain assets), stability mechanism (asset-backed,
overcollateralization, algorithmic), or peg (Fiat, Index) mechanism.
Figure 2: Stablecoin Growth
Fiat-Collateralized (off-chain) stablecoins backed by US Dollar reserves presently dominate the
cryptocurrency landscape, with popular examples including Tether (USDT), Circle (USDC), and Binance
USD (BUSD). With the emergence of decentralized finance, several on-chain stablecoin alternatives
such as MakerDao’s Dai (Dai) and Venus Protocol’s Vai (VAI) coin have gained traction using
overcollateralization of cryptocurrency assets to preserve their peg. Algorithmic stablecoins such as
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the now infamous UST used the ability to swap a stablecoin for a ‘volatility coin’ at a fixed exchange
rate (ie $1USD) to maintain a peg. Similar to the pegging of the Argentinian peso to the USD in 2002,
such a mechanism is only as resilient as the backing supporting it. Figure 3 describes the market share
of leading stablecoins over time.
Box 4. MakerDao launched in 2014 and is a decentralized autonomous organization (DAO)
responsible for governing the Maker ecosystem. The Dai stablecoin was released in 2017, becoming
the first stablecoin on the Ethereum protocol. Dai is an on-chain multi-collateral USD stablecoin that
is highly composable, allowing DeFi developers to easily integrate it into their applications. Until
November 2019, Ether was the only collateral accepted by Maker. Following its transition to a multicollateral model, the MakerDao community have onboarded several collateral types, including
other cryptocurrencies, stablecoins, and real-world assets.
Figure 3: Stablecoin Market Share
1.6. Non-Fungible Tokens
A more complex set of token standards to enable the representation of any asset or access right (e.g.,
identities and voting rights) has recently emerged. Non-fungible tokens (NFTs) are noninterchangeable units stored on a blockchain that indicate the authenticity of ownership. Unlike
standard fungible tokens, where all units are stored as a single balance, each NFT has its own unique
ID that can be linked to additional metadata, which differentiates the token from other contracts.
NFTs are the equivalent of a conventional proof-of-purchase, such as a paper invoice or an electronic
receipt (Das, 2022), and cover a broad range of creative expressions such as digital images, video clips,
collectibles such as postal stamps and artwork, certificates, and licenses as well as physical assets such
as real estate. The validation of an NFT token can add significant value to an asset or access right by
guaranteeing provenance, which explains initial use cases in art and collectibles. Importantly for
creators of such assets, commissions can be algorithmically generated on secondary market sales,
such that a small fraction (commonly 2-10%) can be transferred to the original creator of the work any
time it is traded in the future. While NFT’s are predominantly used for the representation of digital
artwork or for blockchain-based games, their construction has the potential to be utilized to represent
more traditional assets, such as swaps or bonds with unique features.
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Box 5. In 2017, CryptoKitties, an Ethereum-based game which allows users to buy, sell, and breed
collectible digital cats was launched representing one of the first non-financial use cases for
blockchain technology. Applying the concept of card-based trading games (like basketball or
baseball cards), each ‘CryptoKitty’ is a unique NFT that is coded to the ERC-721 token standard,
which allows attributes of the collectables such as fur or eye color, body or eye shape, as well as
ownership records and transfers to be captured. At its peak, CryptoKitties attracted more than
14,000 active daily users with the ‘genesis kitten’ (ID1) selling for more than US$100,000. 9
1.7. Concluding Thoughts: Tokenomics
Distributed ledger technology has enabled the management rights of token contracts that can
represent anything from fiat currency, shares in a company, voting rights, or a virtual pet. Token
contracts can assign conditional rights to token holders and represent any digital or physical asset, or
access rights to an asset that is held by another party (Voshmgir, 2021). The ability to deploy these
token contracts can help foster markets with fewer frictions, creating more transparent and efficient
transactions between market participants. With more than 500,000 Ethereum token contracts (ERC20 compatible) in circulation on the Ethereum main network and over 9,600 cryptographic tradeable
tokens, tokens occupy an important position in the management of payments and investments and
will undoubtedly continue to redefine and revolutionize the global digital economy in ways we are
only beginning to imagine.
2. Market Architecture
2.1. Digital Asset Exchanges
Blockchain technology has provided market practitioners with an opportunity to re-imagine the
efficient and effective operation of financial markets. In the space of a few short years, liquidity in
tradeable tokens has risen dramatically. Since early 2021, centralized exchanges have routinely traded
more than $US1 trillion per month, with volumes on decentralized exchange (DEX) peaking at $200
billion in November 2021. 10 To provide context, these volumes rival some of the largest traditional
exchanges, including the LSE and ASX. While these crypto markets are traded primarily by retail
traders, a growing focus on regulating financial risks has resulted in a greater rate of adoption by
proprietary trading groups, hedge funds, and asset managers. Through their participation, the market
has expanded further, providing additional financial instrument offerings and sophisticated market
protocols in line with the more complex trading preferences and strategies of these user groups. 11
This section will provide a deep dive into the current crypto trading market landscape. We first analyze
market design advances in cryptocurrency markets - from the widely used and preferred mechanism
for traditional finance, the Centralized limit-order book (CLOB), to the DeFi engineered Automated
Market Maker (AMM) model, which is currently the most prominent type of blockchain based
https://techcrunch.com/2017/12/03/people-have-spent-over-1m-buying-virtual-cats-on-the-ethereumblockchain/
10
Source: https://www.theblockcrypto.com/data/crypto-markets/spot (Accessed: 25th March 2022)
11
Foley, Li, Malloch and Svec (2022) document the significant growth in bitcoin options and futures.
9
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decentralized exchange. 12 Following on from this, we quantitatively assess the impact of this market
structure on liquidity and transactions costs, and their implications for market efficiency and welfare.
2.2. Organizational Structure of Traditional Markets
The organizational structure of financial markets codifies the rules which regulate trading procedures
and activity. Around the world, most securities exchanges rely on a continuous double auction
undertaken by a centralized limit order book (CLOB) protocol to provide price discovery and liquidity.
Under such a system, traders submit buy and sell orders on a pricing grid with a continuous double
auction used to find a market clearing price. Order-driven markets are based on order precedence
rules that rank and match orders, typically by price and then time. 13 Liquidity in these markets is
guided by the constant flow of orders originating from market participants, absent any official
designated market makers. In markets where the supply of this immediacy is not forthcoming, market
makers are generally employed to reduce the temporal imbalances in order flow and increase the
speed of exchange. 14 These hybrid structures combine elements of order-driven and quote-driven
markets and are more commonly associated with financial derivative markets.
2.3. Centralized Exchanges (CEX) in Cryptocurrency Markets
In cryptocurrency markets, centralized exchanges are the principal venue of exchange for market
participants (Svec et al., 2020). CEXs are run by a single exchange, and institute trading rules and
procedures that are analogous to their traditional market counterparts to facilitate the price
formation process. They primarily utilize a limit-order book, which displays live buy and sell orders
which determine the exchange rate of the respective token or currency. The familiarity of this model
is enhanced by providing recognizable order types, with most major centralized exchanges offering
limit orders, market orders, and stop-loss orders (Dyhrberg et al., 2018). CEXs may accept fiat
currencies, stablecoins, tokens, and cryptocurrencies. Movements in tokens and cryptocurrencies
to/from the exchange will be evidenced on the blockchain, whilst transactions between currency pairs
will exist solely within the database architecture maintained by the CEX. Centralized exchanges
typically act as the exchange, the custodian, and the clearing house. This can be problematic in
situations where an exchanges assets are hacked – particularly given the inability to recover
immutable assets such as cryptocurrencies. 15
Box 6. Coinbase is the leading cryptocurrency spot exchange in terms of popularity and userbase.
Since its founding in 2012, Coinbase has amassed over 90 million verified users, with more than
$100bn of assets custodied, and $1.8bn in revenues in 2021. It became the first cryptocurrency
exchange to list on a traditional public exchange, with a $US100bn direct NASDAQ listing in 2021.
Coinbase earns fees and commissions from the exchange of cryptocurrencies, margin fees, and
from a variety of other lines - including its payments system and data products. Coinbase cofounded the USD Coin (USDC), a stablecoin which is pegged 1:1 to the US dollar.
We deal with the general architecture of the different models without addressing all technological issues.
Alternative architectures, such as price pro-rata mechanisms also exist. See Aspris et al. (2015) and Foley, Liu
and Jarnecic (2019) for more information on such alternative priority mechanisms.
14
See for example Anand et al. (2009), Anand et al. (2016) and Bessembinder et al. (2020).
15
Such attacks are frequent and common, as documented by Milunovich and Lee (2022).
12
13
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Of the 303 spot (cash) exchanges with active markets listed on Coinmarketcap at the end of March
2022, the majority of activity (based on traffic, trading volumes, and liquidity) is consolidated in the
top five exchanges which include: Binance, Coinbase, FTX, Kraken, and KuCoin. 16
At the time of finalizing this research report, FTX had filed for bankruptcy and had ceased trading. The
reasons for the collapse appear to be related to the business model and how FTX managed (or
mismanaged) its balance sheet, although details are still emerging. While this collapse illustrates one
of the risks in centralized cryptocurrency exchanges, the trading data from FTX prior to its collapse are
still useful to analyze the properties and costs of trading on centralized cryptocurrency exchanges.
We include data from FTX in our analysis because, among other reasons, the data allow us to
empirically compare trading of equities in two forms – tokenized and not tokenized (traditional
equities markets).
The rising popularity of cryptocurrencies has enabled the growth of these cryptocurrency exchanges,
with individual market share related to a number of factors, including the number of listings, the
quality of execution, compliance with local regulations, number of on-ramping currencies, number of
order-types, type of liquidity incentive schemes, and the number of alternative offerings.
Box 7. Cybersecurity Threats – Since 2012, there have been at least 46 cryptocurrency exchange
hacks with more than $US2.6 billion of cryptocurrency compromised. 17 The most common form of
breach is through the infiltration of private keys to an exchanges “hot wallet”. In December 2021,
one of the most trusted trading platforms, Bitmart experienced a large-scale security breach with a
stolen privacy key used to gain access to Bitmart’s hot wallet which resulted in approximately
$US150 million worth of tokens being withdrawn. Other leading exchanges such as Crypto.com
(January 2022, $US34m), Liquid (August 2021, $US97m) Kucoin (September 2020, $US250m),
Binance (May 2019, $US40m), and Mt Gox (February 2014, $460m) have been affected by
cybersecurity hacks.
2.4. Decentralized Finance
Decentralized Finance (DeFi) involves the simple idea of building traditional financial services on
blockchain-based architecture. A DeFi protocol, therefore, is an application-layer program that
provides financial service functions such as swapping (trading) or lending assets. Functionally, these
financial services exist in the form of smart contracts, which are executed software programs deployed
on top of distributed ledger technologies (DLT). 18 Presently, the value locked into DeFi applications at
the end of December 30, 2021 exceeds $US230 billion, rising from approximately $17bn twelve
months earlier. 19 Specific properties that distinguish DeFi services from traditional financial services
and contribute to their popularity include that they are non-custodial, permissionless, transparent,
interoperable, and composable. The moniker ‘financial lego’ is often used to explain technical concepts
such as composability and interoperability which are key determinants in the growth of the sector.
For historical market shares of various centralized exchanges, see Dyhrberg et al. (2022)
https://www.hedgewithcrypto.com/cryptocurrency-exchange-hacks/
18
For a more detailed explanation of the workings of smart contracts, see John et al. (2022).
19
Source: https://defillama.com/
16
17
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2.5. Decentralized Exchanges (DEXs)
Decentralized Exchanges, also known as DEXs, refer to distributed ledger protocols and applications
that enable users to transact cryptocurrencies (Aspris et. al. 2021). A critical difference between DEXs
and CEXs arises from the fact that DEXs are ‘trustless’, meaning that all transactions occur directly
through participants’ wallets. Trading on CEXs, by contrast, requires participants to hand over
management of their assets to the exchange to facilitate this process – exposing them to risk should
the CEX be hacked or go bankrupt. The creation of DEXs removes the requirement for any authority
to oversee and authorize trades, meaning that participants retain their private keys and trade directly
from their wallets by interacting with a smart contract. This reduces the risk of exchange-level hacks,
but also makes the regulation of financial transactions against things like fraud, corruption, money
laundering, and terrorist financing more difficult to enforce.
2.6. Not all DEXs are created equal
Traders interact with smart contracts on the blockchain to use DEXs. There are three main types of
decentralized exchanges, including: order book DEXs, automated market makers (AMMs) and DEX
aggregators (see Figure 4).
On-Chain
Order Book DEX
(OBDEX)
Decentralized
Exchanges (DEX)
Automated
Market Makers
(AMM)
Off-Chain
Aggregators
(DEXAG)
Figure 4: Decentralized Exchanges
Order-book DEXs (OBDEX) were one of the first initiatives in the development of decentralized
exchanges. As with the CEX model discussed previously, all open orders of currency pairings are found
in the order-book, with the exchange of assets resulting from the crossing of these orders. OBDEXs,
however, can be off-chain or on-chain. Off-chain refers to DEX platforms which hold their order books
off the blockchain, instead operating a centralized limit orderbook, with only the settlement of trades
occurring on the blockchain. On the other hand, on-chain order books execute all limit order entry,
amendment, and cancellations on-chain while users’ funds remain in their wallets. With an average
target block time of 14 seconds (Ethereum), on-chain DEXs have a ‘matching engine’ which operates
at a relative disadvantage in terms of speed. On-chain operations also come with a gas fee, making
the initial examples of fully on-chain DEXs relatively slow, costly, and ultimately unpopular. Examples
of order book DEXs include IDEX, Serum, and MDEX. At present, OBDEX is the least popular form of
exchange due largely to liquidity issues (Aspris et al., 2020). Since their operating model is directly
comparable to CEXs, the higher fees associated with transacting on the blockchain, and smart-contract
related risks associated with off-chain solutions have limited their market share.
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Box 8. Most Popular DEX Protocols
Protocol Name
EtherDelta
AirSwap
Uniswap
Balancer
Curve
Kyber Network
1inch
Protocol Type
Exchange
P2P / OTC
AMM
AMM
Hybrid AMM
Reserve aggregator
Aggregator
Price Discovery
Off-chain order book
P2P negotiation
Smart contract
Smart contract
Smart contract
Proposal by maker
Smart Contract
2.6.1. Automated Market Makers (AMM)
The growth in native digital assets has fostered a desire to create better functioning and more efficient
methods of exchange that are fit for execution on the blockchain. Digital securities are typically viewed
as intrinsically more complex than traditional instruments. As a result, investors face a range of
conventional trading problems, such as an underlying lack of liquidity and slower price discovery. In
this search for better models of exchange, Automated Market Makers (AMM), through smart contract
systems, have become important building blocks, or ‘primitives’ for decentralized finance. AMMs are
protocols for providing liquidity and conducting price operations. They encourage passive market
participants - likely to hold their assets for long periods - to “deposit” their digital assets to liquidity
pools (reserves). Traders may execute orders to trade between these two assets at prices determined
by the constant product formula, for a fixed fee yield (Angeris et al., 2020).
An AMM is an automated process that allows for the exchange of digital assets according to a fixed
formula. Constant formula market makers (CFMM), as a class of AMMs, link the reserves of two or
more different assets dynamically, relying on a constant function with specific properties. The
constant function is a reference to the value of a certain reserve that must remain unchanged during
any transaction. The proliferation of CFMMs is associated with a desire to transact in an autonomous,
atomistic, and decentralized way - whilst simultaneously resolving liquidity and price discovery
problems that hinder alternative models of exchange. Several prominent AMMs include Uniswap’s
constant product AMM, Balancer’s constant average AMM, and Curve’s hybrid model.
AMMs rely on liquidity pools and liquidity providers to function. A liquidity pool is a cryptocurrency
reserve used to facilitate future trades. Liquidity providers can create new pools or supply existing
pools with liquidity, which allows traders to exchange between two assets. The funds provided
(staked) by liquidity providers are processed, protected, and are ‘held’ by smart contracts, allowing
AMMs to be non-custodial for those who use them to swap between assets. For every liquidity pool
that is created, a new smart contract is created on the blockchain. Unlike traditional asset markets
where market-making activities are undertaken only by the most sophisticated market participants
(for example, Citadel or Virtu), anyone in an AMM can be a liquidity provider and earn fee revenue for
the supply of liquidity. 20 The fee is a reward for inventory and adverse selection costs faced by the
liquidity provider and therefore commensurate with the bid-ask spread set by traditional market
20
For more information on the importance of sophistication in liquidity provision see Chen et al. (2017).
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makers. 21 Liquidity providers typically earn a share of the fees levied on trades (‘swaps’) by liquidity
demanders, which is distributed proportionately to their share of liquidity provided to the pool of
reserve assets.
Figure 5 illustrates the operational nature of an AMM. In this figure, liquidity providers contribute
specific quantities of token X and token Y to the liquidity pool (smart contract). Traders can swap token
X for token Y in a particular ratio (the price) that is determined by a pricing protocol. This protocol is
the AMM and trader interaction is with the smart contract and not directly with a counterparty, as
would be the case in a limit order book environment. In exchange for the risk that liquidity providers
take in committing liquidity, a transaction fee is paid by traders, which is embedded into the price.
Protocol reward schemes may provide an addition stream of income to liquidity providers, in return
for providing liquidity on currency pairs considered desirable by the protocol, similar to the way that
companies may directly incentivize market makers in a traditional stock exchange. 22
AMM
Liquidity Pool
Deposit X and
Y token
Liquidity
Providers
Token X
Token Y
Swap X and Y
token
Pay
transaction
Fees
Earn Fees
(+ rewards)
Traders
Figure 5: Automated Market Makers (AMM)
2.6.1.1. “Constant” Models of Exchange:
Automated market makers apply functions to price swaps based on the number of tokens (liquidity)
they have. There are several popular implementations of constant function models, all of which hold
constant (𝑘𝑘) the product, sum, or mean (average), of all trading pair groups. In their simplest form,
assuming a two token environment (𝑥𝑥 and 𝑦𝑦), the price mechanisms can be expressed as follows:
•
•
•
•
Constant Product Market Maker (CPMM) – where : 𝑥𝑥 × 𝑦𝑦 = 𝑘𝑘;
Constant Sum Market Maker (CSUMM) – where: 𝑥𝑥 + 𝑦𝑦 = 𝑘𝑘;
Constant Mean Market Maker (CMMM) 23 - where: 𝑥𝑥𝑤𝑤1 + 𝑦𝑦𝑤𝑤2 = 𝑘𝑘
Constant Hybrid Market Makers (CHMM) – where some function of 𝑥𝑥 and 𝑦𝑦 is held constant
A key difference, however, is that this fee is fixed as opposed to the bid-ask spread set by market makers
which can be adjusted depending on the arrival of information or any prevailing liquidity imbalances. For a more
detailed discussion of the rewards to liquidity providers in AMMs see Foley, O’Neill and Putnins (2022).
22
For further information on ‘yield farming’ in AMM protocols, see Han et al. (2021).
23
w1 and w2 represent the proportion of tokens in the capital pool such that w1+w2 = 1. The Balancer exchange
function allows for multiples tokens in the pool, where w is the normalized weight of the token such that the
sum of all normalized weights is equal to 1.
21
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2.6.1.2. Constant Product Market Makers (CPMM)
In a generalized CPMM, the product of the quantity of two tokens in a liquidity pool is constant. This
is popularly expressed as follows: 𝑥𝑥 × 𝑦𝑦 = 𝑘𝑘, where 𝑥𝑥 and 𝑦𝑦 refer to the quantities (reserves) of two
tokens, A and B, and 𝑘𝑘 is the product of these initial quantities. The value of 𝑘𝑘 is known as the invariant
because there is a constant balance of assets used to determine the price of tokens in the liquidity
pool. In a two-token liquidity pool (e.g., ETH-BTC), where one asset is purchased, its price will rise in
line with the shrinking supply, thereby maintaining the constant state of balance. This can be visualized
with the aid of Figure 6 below. The curve in this figure represents different states of constant balance
within the liquidity pool. Trades (or asset swaps) can happen anywhere along this curve. When a trader
purchases 𝑥𝑥, this involves removing ∆𝑥𝑥 = 𝑥𝑥 − 𝑥𝑥′ from the AMM and adding ∆𝑦𝑦 = 𝑦𝑦′ − 𝑦𝑦 preserving
the constant 𝑘𝑘, 𝑥𝑥 × 𝑦𝑦 = 𝑘𝑘 = (∆𝑥𝑥 + 𝑥𝑥 ′ )(𝑦𝑦 ′ − ∆𝑦𝑦). As more of 𝑥𝑥 is acquired (and therefore withdrawn
from the pool), the price of 𝑥𝑥 increases relative to 𝑦𝑦. 24
Figure 6: Constant Product Market Makers (CPMM)
It is important to consider that this function does not scale linearly – it is an asymptotic function,
meaning that larger purchases (withdrawals) will result in larger price impact (slippage). It can be
observed from the pricing curve in Figure 7 that larger trades (relative to their pool size) move the
market, meaning that in order to avoid significant price slippage, both the swap and pool size warrant
consideration.
For a more detailed discussion of the bonding curve and its impacts for price discovery of cryptocurrency
assets see Lehar and Parlour (2021).
24
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Among the first and most popular implementations of this model is Uniswap 25, which was established
in 2018, supporting only ETH-ERC20 trading pairs. Multiple iterations (v2 and v3) have resulted in
improved liquidity (ERC20-ERC20 pairs), enhanced functionality (trades, flash swaps, range orders),
and better capital efficiency (𝑥𝑥 × 𝑦𝑦 = 𝑘𝑘 locally in a price range depending on liquidity √𝑘𝑘 within that
range).
Figure 7: CPMM - Price Impact
Box 9. Uniswap Model
The primary example of a constant product market maker is Uniswap. The exchange rate in this
market is based on the relative size of asset reserves and the amount by which an incoming trade
changes this ratio.
To further conceptualize this, consider a pool that has 5 ETH tokens (𝑥𝑥) and 10,000 USDT tokens
(𝑦𝑦). Using the function 𝑥𝑥 × 𝑦𝑦 = 𝑘𝑘, this yields 𝑘𝑘 = 50,000:
5 𝐸𝐸𝐸𝐸𝐸𝐸 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 (𝑥𝑥) × 10,000 𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 (𝑦𝑦) = 50,000 = 𝑘𝑘
The Uniswap AMM protocol was developed in Solidity on less than 500 lines of code. Its current code is
organized in 4 smart contracts and divided into a core and periphery section. The core (pair, factory, ERC20) is
for storing tokens and contains functions for adding tokens, swapping tokens, as well as minting and burning
functions. The periphery is for interacting with the core. The v3-core code can be found at:
https://github.com/Uniswap/v3-core
25
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This product of the two token quantities must remain constant when transactions occur. However,
it increases or decreases k when LP’s add or remove liquidity.
Now suppose trader A wants to purchase 1 ETH. The swap would reduce the number of ETH in the
pool to 4 ETH. Assuming no trading fees in this simplified example, how many USDT must be paid
(added) to the pool so that the constant 𝑘𝑘 is maintained?
To calculate this:
(𝑥𝑥 − ∆𝑥𝑥)(𝑦𝑦 + ∆𝑦𝑦) = 𝑘𝑘
∆𝑦𝑦 =
∆𝑦𝑦 =
𝑘𝑘
− 𝑦𝑦
𝑥𝑥 − ∆𝑥𝑥
50,000
− 10,000
(5 − 1)
∆𝑦𝑦 = 2,500
This results in 2,500 USDT, which is the amount that would need to be deposited to acquire 1 ETH.
It implies a trade price of $2,500 per ETH. The calculated price ensures that the invariant is satisfied
(4 𝐸𝐸𝐸𝐸𝐸𝐸 × 12,50 𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈 = 50,000) after the exchange and the price of the trade is:
∆𝑦𝑦
𝑝𝑝𝑎𝑎 =
= $2,500 𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈/𝐸𝐸𝐸𝐸𝐸𝐸
∆𝑥𝑥
If buying 1 ETH will cost $2,500, this can be thought of as the ask price (𝑝𝑝𝑎𝑎 ) since it is the price at
which the AMM sells 1 unit of ETH to the trader. What about the bid price (𝑝𝑝𝑏𝑏 ) at which a trader
could sell 1 ETH? Repeating the calculation for a 1 ETH sell order, we get:
(𝑥𝑥 + ∆𝑥𝑥)(𝑦𝑦 − ∆𝑦𝑦) = 𝑘𝑘
∆𝑦𝑦 = 𝑦𝑦 −
𝑘𝑘
𝑥𝑥 + ∆𝑥𝑥
∆𝑦𝑦 = 10,000 −
𝑝𝑝𝑏𝑏 =
50,000
(5 + 1)
∆𝑦𝑦 = 1,666.66
∆𝑦𝑦
= $1,666.66 𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈/𝐸𝐸𝐸𝐸𝐸𝐸
∆𝑥𝑥
So, we have an implied bid/ask of $1,666.66 / $2,550 for a trade size of 1 ETH.
From these implied bid and ask prices we can compute an implied bid-ask spread for an assumed 1
ETH trade size: ($2,500-$1,666) / (($2,500+$1,666)/2) = 40%.
While a 40% bid-ask spread may seem large, that is because we consider a large trade relative to
the amount of liquidity in the AMM: the trade consumes 20% of the total ETH liquidity. What if we
considered a smaller trade? What if there were more tokens (liquidity) in the AMM, i.e., a lager 𝑘𝑘?
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If we repeat the process above, but this time with the trader trading only 0.01 ETH the bid and ask
prices equate to $999 and $1001, respectively, implying a bid-ask spread of
($1001-$999) / (($1001+$999)/2) = 0.20%
We can see from this example that the size of trades (relative to the size of the pool), increases the
cost of transacting. This design feature of making it infinitely expensive to consume the whole
amount of a certain coin has the intended effect of preserving the liquidity of the pool.
2.6.1.3. Alternative Models
Constant Mean Market Maker (CMMM)
This is a variation of the constant product model designed to allow liquidity pools with more than two
tokens and non-standard weights. An example of a CMMM implementation is the Balancer AMM. 26
Constant Sum Market Maker (CSMM)
In this variant, the multiplication of the constant product is replaced with an additive function: x +
y = k. In other words, liquidity in the pool is equal to the total value of Asset X and Y. An example of
this implementation is the mStable protocol. 27 Such implementations result in a linear price curve,
rather than an asymptotic price. This is predominantly used for assets whose value is not expected to
vary relative to each other (i.e., USDT vs USDC).
Hybrid CFMM
A hybrid constant function allows for any number of unique parameters in the pool. A hybrid function
could for example include a combination of constant product and constant sum or an entirely new
expression. Curve 28 is an exchange liquidity pool on Ethereum that adopts a hybrid function. Such
implementations typically allow for a constant sum (i.e., linear) pricing when the pool is relatively
evenly populated by the two assets, moving towards a constant product (i.e., asymptotic) pricing when
the pool becomes unbalanced. Such implementations were critical in the de-pegging event of the UST
stablecoin during 2022. When the USDC/UST pools were relatively equivalent (because both had a
value of $1 USD) a constant sum (linear) pricing was applied. As the de-pegging event led traders to
dump the devaluing UST in favor of USDC, a constant product (asymptotic) pricing became dominant,
ensuring that the price of UST would rapidly fall towards zero.
Box 10. Risks of Liquidity Provision – Impermanent Loss: Liquidity providers face the potential of
value loss, often referred to as “impermanent loss” by participating in AMM liquidity pools. In
simple terms, impermanent loss can be thought of as the ‘loss’ to investors when assets are locked
into a liquidity pool instead of being held (or lent/staked). The impermanent part of this phrase
alludes to the fact that this loss is not permanent, because, under the mean reversion assumption,
price will return to its equilibrium value – therefore, a loss in only realized if investors withdraw
from the liquidity pool before this point is reached. This loss depends on the degree of correlation
between the assets in the pool as well as its size, with less correlated assets (e.g., stablecoins) in
Whitepaper - https://balancer.fi/whitepaper.pdf
https://mstable.org/
28
https://curve.fi/
26
27
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larger pools (or pools where the ratio of their locked funds is not equal) mitigating the potential for
such loss. Further, different protocols and mechanisms may moderate such loss, with impermanent
loss potentially greater under a constant sum rule relative to a constant product rule.
2.6.2. Key Insights about AMMs: A Summary
•
•
•
•
•
•
•
•
Trades are conducted via swaps in liquidity pools. There is no order-book.
Smaller traders typically face lower slippage costs under an AMM mechanism relative to an
order-book mechanism.
Price is determined by a mathematical function and is not the ‘last price’ as in the order book.
Trading pairs found on centralized exchange exist as individual liquidity pools in AMMs.
There are no dedicated market makers in liquidity pools, any participant can provide liquidity.
Liquidity providers earn fees (and potentially protocol token rewards) for providing liquidity
but face risks such as impermanent loss.
Investors obtain immediate liquidity from liquidity pools without exchange counterparties.
Due to the decentralized nature of AMMs, any ERC-20 token can be permissionlessly listed on
a decentralized protocol.
Box 11. How to Provide Liquidity in Uniswap
In Uniswap v3, liquidity providers go through four key steps to provide liquidity. The first step
involves selecting a pair of tokens they wish to provide liquidity to. This can be any pair of ERC-20
tokens, and where there is no current pool, liquidity providers can create a new market. The second
step involves reviewing the fee tier. Default fee tiers align with the type of token, stablecoin fees
set at a lower level as compared to exotic pairs where liquidity providers take on higher levels of
price risk. The third step in this process, which is distinct from Uniswap v2, involves setting a price
range in which to provide liquidity. In the former iteration, all users provided liquidity across the
entire price curve, however, in its current form liquidity providers specify a price range within which
they are willing to provide liquidity. Liquidity providers then formalize this by deciding how much
capital to contribute to this position and deposit proportional amounts of the token pair. Once this
transaction is approved, liquidity providers need to action the transfer of tokens from their wallet
to the smart contract.
2.7. DEX Aggregators
Aggregators have emerged to address the growing problem of liquidity fragmentation and execution
quality across numerous available decentralized exchanges. 29 Decentralized exchange aggregators are
blockchain-based applications with cross-chain functionality that enable users to access liquidity pools
from multiple DEXs. DEX aggregators provide search convenience and improved quality of execution,
with the latter aided through the optimization of exchange rates, token pricing, and slippage.
Aggregators in decentralized markets are conceptually similar to smart order routing (SOR) technology
employed by exchanges and brokers in traditional financial markets. SORs automate the process of
handling orders by identifying opportunities to optimize execution quality across fragmented markets,
as discussed in detail in Foucault and Menkveld (2008). Like smart order routers, DEX aggregators can
exhibit different levels of performance based on factors such as quoted price accuracy, gas usage,
reversion rates, response times and preferences associated with order splitting through algorithmic
29
Similar issues have been experienced and addressed in equity markets. See for example Aitken et al. (2017).
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optimization. As at the end of January 2022, nearly $US19bn worth of crypto trading volume was
transacted through DEX aggregators with the leading aggregators 1inch and Matcha responsible for
over 80% of this activity.
Despite some clear benefits from pooling liquidity sources in fragmented markets, it should be noted
that at present most trading activity is concentrated in a small handful of DEXs, which limits the
effectiveness of these aggregators. Furthermore, whilst aggregators help to address transactional
slippage, they are not designed to deal with slippage issues associated with the practice of miner
extractable value (MEV). 30 MEV is a practice linked to decentralized finance where miners (or
validators under proof of stake environment) manipulate order transactions to extract profits – similar
to front-running or trading on order flow documented in traditional equity markets (i.e. Van Kervel
and Menkveld (2019). MEV typically arises from structural arbitrage trading strategies, with miners
indirectly profiting from trader transaction fees (MEV ‘bots’ vie for the opportunity to front-run orders
by diverting an increasing share of the profits to miners). Nevertheless, despite these issues,
aggregators hold a unique position in the DeFi market that appeals to a variety of user groups.
Box 12. 1inch (DEX aggregator) – 1inch is a leading DEX aggregator that emerged from an ETH
hackathon in 2019. Founded by Sergej Kunz and Anton Bukov, 1inch has grown to cover over 50
DEXs across 8 blockchain networks, including Ethereum, Polygon, and BNB chain. 1inch uses a
proprietary API called Pathfinder which contains a discovery and routing algorithm that is designed
to ensure the most favorable outcome for traders expressed in terms of overall execution quality.
3. Data
Our analysis includes data from a wide variety of sources. We extract DEX/AMM data directly from
the Ethereum blockchain. We run our own full historical node, and then parse transactions relating to
various protocols. This identifies the assets traded within a swap (i.e., Number of Asset A sold, and
Number of Asset B received), block number, date, and time (of block confirmation), as well as the
individual user ‘trading’ with the protocol. The ratio of Asset A traded for Asset B provides us with an
implicit ‘price’ for each transaction.
We extract centralized cryptocurrency exchange data directly from Tardis.dev and examine three of
the largest markets by total trading volume: Binance, Kraken, and Coinbase. We sourced tokenized
equity trades on the FTX exchange (prior to its collapse) from Tardis.dev. Tardis provides the
timestamp on each trade (to the millisecond), as well as the direction of the trade (buyer or seller
initiated), price, and volume. We also source the best-bid and ask quotes from these markets, which
are updated every time there is a quote update.
Equity market data (used for comparison with tokenized equities) is downloaded from Refinitiv, a
Thompson Reuters product, for all securities which had tokenized representations on FTX. Our primary
analysis examines June 2020 to May 2021. This sample allows us to capture the periods through which
both DEX and AMM markets have considerable market share. With the introduction of Uniswap V2 in
May 2020, DEX volumes peaked around August 2020, and were rapidly replaced by utilization of the
Uniswap V2 AMM.
30
For more information on the causes and effects of MEV see Daian et al. (2020).
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This sample also covers good examples of both bull and bear markets, periods of extreme volatility
and relative calm, which can be evidence from the price graph below. Figure 8 shows the price for the
two major cryptocurrency assets (Ethereum and Bitcoin) which together account for more than 60%
of the overall market capitalization of the cryptocurrency space alongside the S&P500 Index.
Figure 8: ETH-BTC versus S&P500
3.1. Construction of transactions cost metrics
In markets that utilize traditional limit orderbook structures (such as US Equity markets, tokenized
securities traded on FTX, and centralized cryptocurrency exchanges), it is possible to compute
standard measures of transactions costs, including effective spread, realized spread, and price
impact. 31
Effective spreads are calculated as the difference between the trade price and the prevailing Best Bid
and Offer (BBO) midpoint and reflect the implicit transaction cost for small round-trip trades at the
best quotes. As there is no national aggregator of quotes on centralized cryptocurrency exchanges,
we use the prevailing quotes on each exchange respectively.
Realized spreads compare trade prices with the BBO midpoint prevailing at a specified reference time
after the trade, as a proxy for the profits earned by liquidity providers. Following Conrad et al. (2015),
realized spreads are calculated at a horizon of thirty seconds after each trade. Price impact, which is
a measure of adverse selection risk, is computed as the difference between the midpoint at a
reference time after the trade and the prevailing midpoint at the time of the trade. At the trade level
(𝑡𝑡), the three measures are:
31
For further information on the construction of standard measures of market quality see Foley et al. (2016).
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𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡 = 2𝐷𝐷𝑡𝑡
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡 = 2𝐷𝐷𝑡𝑡
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝑡𝑡 = 2𝐷𝐷𝑡𝑡
(𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡 −𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑡𝑡 )
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑡𝑡
10,000
(𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡 −𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑡𝑡+30𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 )
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑡𝑡
(𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑡𝑡+30𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 −𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑡𝑡 )
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑡𝑡
(1)
10,000
10,000
(2)
(3)
where 𝐷𝐷𝑡𝑡 is the direction of the trade, taking a value of +1 (-1) for buyer (seller) initiated trades. These
metrics are in basis points. We aggregate them from trade-level measures to a measure per day (𝑑𝑑)
and asset pair (𝑖𝑖) by taking a volume-weighted average across the trades.
Unlike centralized exchanges, AMMs do not display quotes. Therefore, to approximate the above
measures for AMMs and other decentralized exchanges, we use the prevailing best quotes on the
largest centralized exchange, Binance, for the respective symbols to calculate the 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑡𝑡 input to
the formulas. We do have the other inputs for AMMs: (i) a price for each trade in an AMM taken from
blockchain data, and (ii) AMM trade initiators are visible, making it possible to uniquely identify each
transaction as buyer initiated (D = +1) or seller initiated (D = -1).
4. How well do the different markets facilitate trade?
4.1. An overview of liquidity
To better understand the differences between the markets used, we first construct descriptive
statistics for each of the markets. Table 1 and Table 2 document the average price, trade size, daily
$Volume, number of trades, volatility, transactions costs and depth for the 26 equities that were also
traded in tokenized form.
The differences between the two are immediately apparent. While the average prices of the assets
traded across both exchanges are approximately equal, which is to be expected since they represent
the same US-listed assets over the same period, the tokenized securities exhibit significantly lower
levels of trade activity. While the mean (median) equity trade size is $13,918 ($8782), tokenized
security trades are an order of magnitude smaller - $579 ($120). The number of trades per securityday is also significantly lower for the tokenized exchange – where the tokenized securities average 33
trades per day, their equity market counterparts average 151,000 daily trades. The smaller number of
trades, combined with the smaller value of trades results in significantly lower average traded
$Volume - $25,000 in tokenized securities vs $3bn for equity markets.
Trading costs are also significantly higher for the tokenized securities: quoted spreads average 83bps
– over 10 times higher than the 8bps in their equity market counterparts. Similar differences in
magnitudes are observed for the effective spread, realized spread and price impact measures.
While quoted depth is much higher in the tokenized equities ($28,000 vs $2,000) this is reflective of
the significantly wider quoted spreads observed – larger depths are to be expected if the cost of
trading at those depth levels is over 10 times larger.
23
Electronic copy available at: https://ssrn.com/abstract=4301258
Table 1: Summary Statistics - Tokenized Securities (TKN). The table shows summary statistics for tokenized equity securities.
The price is the traded price of the symbols traded on the venue. The trade size is in USD. The volume is the total daily traded
volume in USD. The number of trades counts the number of daily trades by symbol. Volatility (high-low) is the difference
between the 30-minute high-low trade price over the high-low midpoint. The 30-minute metric is then averaged by symbol
date. The volatility (midpoint) metric is the daily standard deviation of 30-minute midpoint returns. Quoted spread is the
difference between the best ask and bid relative to the midpoint in basis points, time-weighted. The depth at best is the
available volume at the best prices in USD, time-weighted. The effective spread, realized spread and price impact are volume
weighted and in basis points. The realized spread and price impacts use a horizon of 30 seconds.
n
Mean
Median
StdDev
Min
Max
Price
4,288
342.201
125.755
644.975
3.811
3,340.931
Trade Size
4,288
579.368
120.526
1,469.409
0.340
15,550.660
Volume (USD)
4,288
25,333.466
1,091.931
114,685.821
0.952
1,964,238
No of Trades
4,288
33.646
8.000
147.048
1.000
3,551
Volatility (High-Low)
4,288
0.004
0.001
0.012
0.000
0.193
Volatility (Midpoint - Std)
4,288
72.474
48.262
90.906
2.593
1,451.438
Quoted Spread (bps)
4,288
82.214
60.833
81.218
3.594
901.186
Depth at Best (USD)
4,288
28,895
15,905
34,516
77.244
234,606
Effective Spread (bps)
4,288
73.891
44.822
108.590
0.354
1,796.706
Realized Spread (bps)
4,288
40.341
26.740
96.623
-712.971
1,283.967
Price Impact (bps)
4,288
33.649
13.208
61.109
-43.986
751.624
Table 2: Summary Statistics - Equity Securities (EQX). The table shows summary statistics for traditional equity securities.
The price is the traded price of the symbols traded on the venue. The trade size is in USD. The volume is the total daily traded
volume in USD. The number of trades counts the number of daily trades by symbol. Volatility (high-low) is the difference
between the 30-minute high-low trade price over the high-low midpoint. The 30-minute metric is then averaged by symbol
date. The volatility (midpoint) metric is the daily standard deviation of 30-minute midpoint returns. Quoted spread is the
difference between the best ask and bid relative to the midpoint in basis points, time-weighted. The depth at best is the
available volume at the best prices in USD, time-weighted. The effective spread, realized spread and price impact are volume
weighted and in basis points. The realized spread and price impacts use a horizon of 30 seconds.
n
Mean
Median
StdDev
Min
Max
Price
9,490
268.789
84.960
563.620
1.828
3,408.408
Trade Size
9,490
13,918.102
8,782.802
14,035.102
756.748
75,410.224
9,490
3,002,644,460
836,489,655
5,828,049,124
344,977
40,977,729,065
No of Trades
9,490
151,686
86,569.000
203,079.982
255.000
1,598,213
Volatility (High-Low)
9,490
0.014
0.011
0.012
0.002
0.169
Volatility (Midpoint - Std)
9,490
0.007
0.006
0.006
0.001
0.055
Quoted Spread (bps)
9,072
8.044
4.533
9.017
0.244
62.795
Depth at Best (USD)
9,490
2,583.68
1,016.06
4,764.32
57.11
40,566.34
Effective Spread (bps)
9,072
7.515
4.410
7.206
0.676
41.964
Realized Spread (bps)
9,072
-1.832
-0.665
4.808
-31.877
11.151
Price Impact (bps)
9,072
9.356
4.937
10.511
-1.084
69.647
Volume (USD)
24
Electronic copy available at: https://ssrn.com/abstract=4301258
We next present summary statistics for our centralized exchange sample in Table 3. The wide
dispersion observed in prices is consistent with the nature of cryptocurrency assets. The maximum
trade price recorded ($57,130) belongs to bitcoin, while the minimum of $0.003 reflects the smaller
‘meme’ assets in our sample, such as dogecoin. The disparity is further evidenced in the difference
between the mean ($2002) and median ($5.899) price. Trade sizes average $839, comparable to the
traded values observed in tokenized equities – consistent with their similar clientele (i.e., crypto
traders). Daily $Volumes exhibit similar skews, with a few currencies (i.e., Ethereum and Bitcoin)
dominating trading. This results in a mean daily $Volume of $21M, whilst the median is only $1M.
Transaction costs are higher than equities but lower than tokenized equities, consistent with their
higher levels of trading activity. Traders consuming liquidity pay, on average, 31bps.
Table 3: Summary Statistics - Centralized Exchanges (CEX). The table shows the summary statistics of a variety of variables
by symbol (equities, tokenized equities, or cryptocurrencies) date for each of the market structures. The price is the traded
price of the symbols traded on the venue. The trade size is in USD. The volume is the total daily traded volume in USD. The
number of trades counts the number of daily trades by symbol. Volatility (high-low) is the difference between the 30minute high-low trade price over the high-low midpoint. The 30-minute metric is then averaged by symbol date. The
volatility (midpoint) metric is the daily standard deviation of 30-minute midpoint returns. Quoted spread is the difference
between the best ask and bid relative to the midpoint in basis points, time-weighted. The depth at best is the available
volume at the best prices in USD, time-weighted. The effective spread, realized spread and price impact are volume
weighted and in basis points. The realized spread and price impacts use a horizon of 30 seconds.
n
Mean
Median
StdDev
Min
Max
Price
84,059
2,002.510
5.899
7,732.279
0.003
57,130.459
Trade Size
84,059
839.476
577.644
916.033
42.724
11,618.149
Daily Volume (USD)
85,268
21,832,018
1,007,053
151,175,214
0.000
4,193,611,537
No of Trades
85,268
14,898
1,761
67,260
0.000
1,514,527
Volatility (High-Low)
84,059
0.013
0.011
0.010
0.000
0.086
Volatility (Midpoint - Std)
83,930
107.810
88.122
74.425
1.048
594.261
Quoted Spread (bps)
85,134
26.492
16.154
42.979
0.022
711.303
Depth at Best (USD)
85,134
12,538.32
3,274.32
68,110.22
295.72
1881880.53
Effective Spread (bps)
83,987
31.714
18.543
47.599
0.371
957.380
Realized Spread (bps)
83,987
15.224
5.139
34.661
-117.655
493.055
Price Impact (bps)
83,987
13.909
9.122
22.553
-15.604
882.453
Decentralized exchanges are more limited in their scale of activity as shown in Table 4. Our sample
period contains only 477 stock-days on which trading activity occurs in our selected symbols. With this
relatively sparse activity, trade sizes average around $500. Relative higher level of volatility, and higher
effective spreads are indicative of a low-liquidity market. The large price impact (218bps, or over 2%)
and negative realized spreads are consistent with DEX’s containing ‘stale trades’ which are ‘picked off’
by opportunistic arbitrageurs. Given the off-chain nature of the limit-orderbook for DEXs and AMMs,
we are not able to construct measures of quoted spread or depth.
25
Electronic copy available at: https://ssrn.com/abstract=4301258
Table 4: Summary Statistics – Decentralized (Order Book) Exchanges (DEX). The table shows summary statistics
decentralized exchange securities. The price is the traded price of the symbols traded on the venue. The trade size is in USD.
The volume is the total daily traded volume in USD. The number of trades counts the number of daily trades by symbol.
Volatility (high-low) is the difference between the 30-minute high-low trade price over the high-low midpoint. The 30-minute
metric is then averaged by symbol date. The effective spread, realized spread and price impact are volume weighted and in
basis points. The realized spread and price impacts use a horizon of 30 seconds.
N
Mean
Median
StdDev
Min
Max
Price
477
160.138
29.887
167.356
0.040
869.565
Trade Size
477
480.314
329.572
630.403
48.926
10,494.194
Volume (USD)
477
4,140.93
2,461.22
5,227.42
689.80
56,087.39
No of Trades
477
9.038
7.000
5.835
3.000
44.000
Volatility (High-Low)
477
0.005
0.001
0.009
0.000
0.037
Effective Spread (bps)
477
66.300
9.072
121.804
0.000
957.380
Realized Spread (bps)
477
-52.547
-54.895
109.173
-276.589
159.488
Price Impact (bps)
477
218.409
233.550
145.691
6.915
1,116.970
Finally, we turn to automated market makers, represented by UniSwap V2. The results are presented
in Table 5. Given that the UniSwap protocol exists on the Ethereum network, there is a lack of nonEthereum assets (i.e., Bitcoin and other native cryptocurrency assets). AMM volumes are approaching
that of CEXs, with AMM ‘pools’ trading on average over $12m per day, compared to the $21m for
CEXs. The number of trades is significantly lower than their CEX counterparts, averaging just under
1,700 trades per day (compared to 15,000 on the CEX). However, the less frequent number of trades
belies a larger average trade size in the AMMs ($4,000 vs $839 in the CEX). The larger trade size is
likely a function of the ‘fixed cost’ of settlement required via gas fees (which averages around $30 per
trade in our sample). 32 Effective spreads on the AMM are the highest across the various market
structures analyzed, at over 129 basis points. This reflects not only the costs of ‘slippage’ (walking the
AMM bonding curve), but also the potential for disintermediation activity with on-chain trading – for
example, conduct such as front-running or ‘sandwich attacks’, as well as the potential delay in
confirming transactions.
Felez-Vinas et al. (2021) provide a detailed discussion of the returns to miners from transactions in the
Ethereum Network.
32
26
Electronic copy available at: https://ssrn.com/abstract=4301258
Table 5: Summary Statistics - Decentralized (AMM) Exchanges. The table shows the summary statistics AMM securities. The
price is the traded price of the symbols traded on the venue. The trade size is in USD. The volume is the total daily traded
volume in USD. The number of trades counts the number of daily trades by symbol. Volatility (high-low) is the difference
between the 30-minute high-low trade price over the high-low midpoint. The 30-minute metric is then averaged by symbol
date. The effective spread, realized spread and price impact are volume weighted and in basis points. The realized spread
and price impacts use a horizon of 30 seconds.
n
Mean
Median
StdDev
Min
Max
Price
3,268
223.395
7.674
462.489
0.040
1,886.755
Trade Size
3,268
3,927.677
2,311.263
4,115.153
0.217
19,275.043
Volume (USD)
3,268
12,039,489
799,706
25,314,689
0.217
289,361,584
No of Trades
3,268
1,699.205
305.000
2,872.393
1.000
16,413.000
Volatility (High-Low)
3,268
0.011
0.010
0.007
0.000
0.066
Effective Spread (bps)
3,268
129.988
81.309
148.929
0.000
957.380
Realized Spread (bps)
3,268
14.156
22.950
31.909
-656.746
153.021
Price Impact (bps)
3,268
121.525
64.527
168.644
0.812
1,116.970
4.1.1. Liquidity and Market adoption
To better understand the difference in transaction costs and liquidity between the two markets, we
first examine the liquidity gap. The liquidity gap is the difference in liquidity (Effective spread, realized
spread or price impact) between matched token pairs on different markets (AMM versus CEX and TKN
versus EQX).
4.1.2. Tokenized Stocks vs Equity Market Liquidity
Figure 9 shows the liquidity gap (effective spread, realized spread, price impact) between tokenized
stocks and their matched underlying equities over the sample period. The figures reveal that as
relative volume (blue) in the tokenized assets rises, the effective spread (red), or cost of demanding
liquidity, falls. Both realized spread (the reward for providing liquidity) and price impact (the extent to
which a trade permanently moves the prices of the underlying assets) are both significantly higher for
tokenized equities but decrease over time as the relative volume traded in the tokenized venue
increases. This indicates that it may, in the future, be possible for the transaction costs to compress
further, albeit such a result would require a significant increase in the relative volume of tokenized
equity trading. Despite the increases in tokenized volume share during our sample period, relative
trading volumes of tokenized equities remain incredibly low – around 1/5000th of the volume traded
on the US equity market venues. Notwithstanding this increase in volume, the estimated effective,
realized and quoted spreads exhibit a significant amount of noise, and a slight down-trending pattern.
This is likely driven by the noise inherent in the infrequent trading activity of the tokenized equities.
27
Electronic copy available at: https://ssrn.com/abstract=4301258
Figure 9: Liquidity Gap and Market Share (Tokenized Equities versus Equity Securities)
We next examine the relative differences in transaction costs between tokenized equities and their
publicly listed counterparts on traditional exchanges (in this case, all equities are US listed on either
NASDAQ or NYSE) in a multivariate setting. In both market settings, traditional combined limit order
book market structures are employed. However, as previously observed, there were considerably
lower levels of trading activity in tokenized equities compared to public markets. This can be
attributed to the infancy of these tokenized liquidity markets, the fact that almost all securities that
were traded on FTX were chosen as those stocks that have the highest retail (and overall) liquidity,
and the lower number of natural market participants, including liquidity providers, in the tokenized
equity exchange.33 Our initial pairwise regression takes the form:
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑦𝑦𝑖𝑖,𝑑𝑑 = 𝛼𝛼 + 𝛽𝛽1 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑒𝑒𝑖𝑖,𝑑𝑑 + 𝛽𝛽2 $𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑒𝑒𝑖𝑖,𝑑𝑑 + 𝛽𝛽3 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑦𝑦𝑖𝑖,𝑑𝑑 + 𝛽𝛽4 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝜀𝜀𝑖𝑖,𝑑𝑑
(4)
where 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑦𝑦𝑖𝑖,𝑑𝑑 is a measure of transactions costs (effective spread, realized spread, or
price impact) for each asset pair 𝑖𝑖 on day 𝑑𝑑; 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑒𝑒𝑖𝑖,𝑑𝑑 is the average daily price (in USD) of the traded
asset, $𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑒𝑒𝑖𝑖,𝑑𝑑 is the total daily traded dollar volume, 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑦𝑦𝑖𝑖,𝑑𝑑 is the high-low price range
scaled by the average of the high and low prices; and 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 is a dummy variable that takes a
value of 1 for tokenized stocks and 0 for those traded on traditional venues NYSE and NASDAQ.
The results presented in Table 6 show that after accounting for factors known to influence
transactions costs, tokenized equities are significantly more expensive to trade than traditional
equities. Traders in tokenized stocks pay around 140 basis points more than traditional equities when
liquidity is demanded. Liquidity providers are compensated with approximately 70 basis points more
33
Boehmer et al. (2021) identify the role of retail traders in US markets, and how to quantify their trading.
28
Electronic copy available at: https://ssrn.com/abstract=4301258
in realized spread, and the price impact of trades is over 69 basis points higher for tokenized assets,
indicating that these trades ‘chase’ the fundamental value, likely representative of the fact that
primary equity markets ‘lead’ price discovery. Given the mean effective spread for the equities which
have been tokenized is 7 basis points, this indicates that trading the tokenized versions of these
securities is over 20x more expensive than trading the underlying asset.
Table 6: Regression Analysis 1 - Market Quality (Equity Securities v Tokenized Equity).Market Quality is
a measure of transactions costs (effective spread, realized spread or price impact); price is the average daily
price (in USD) of the traded asset, $Volume is the total daily traded dollar volume, Volatility is the high-low price
range scaled by the average of the high and low prices; and Tokenized is a dummy variable that takes a value of
1 for tokenized stocks and 0 for those traded on traditional venues NYSE and NASDAQ.
Intercept
Price
$Volume
Volatility
Tokenized
Fixed Effects
Adjusted R2
Observations
Effective Spread
-130.61***
(-14.95)
-0.00
(-1.50)
6.28***
(16.17)
55.65
(1.26)
140.13***
(23.37)
Symbol, Date
47.81%
13,359
Realized Spread
-67.02***
(-8.28)
-0.00
(-0.86)
3.24***
(8.77)
-38.98
(-0.84)
70.11***
(12.62)
Symbol, Date
27.66%
13,359
Price Impact
-60.78***
(-10.16)
-0.00
(-0.40)
2.88***
(10.85)
110.95***
(3.07)
68.65***
(17.49)
Symbol, Date
32.99%
13,359
Traditional equity markets in the U.S. are amongst the most liquid in the world, with thousands of
participants and billions of dollars traded per day. They have also benefitted from over a century of
continuous development and regulation. The markets for tokenized equities by contrast are young. It
is thus possible that this fledgling market has not yet reached maturity, and as it attracts more traders
will see liquidity improved.
To better understand the interaction between changes in trade activity and liquidity we perform a
further regression analysis to include not only a dummy variable for the venue in which a trade occurs,
but also an interaction term capturing the proportion of combined dollar volume traded on the
tokenized exchange. Our pairwise regression takes the following form:
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑦𝑦𝑖𝑖,𝑑𝑑 = 𝛼𝛼 + 𝛽𝛽1 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑒𝑒𝑖𝑖,𝑑𝑑 + 𝛽𝛽2 $𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑒𝑒𝑖𝑖,𝑑𝑑 + 𝛽𝛽3 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑦𝑦𝑖𝑖,𝑑𝑑 + 𝛽𝛽4 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 +
(5)
𝛽𝛽5 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × %𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖,𝑑𝑑 + 𝜀𝜀𝑖𝑖,𝑑𝑑
where all variables are as previously defined, and %𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖,𝑑𝑑 is the dollar volume traded
in tokenized stocks as a proportion of total traded volume (Tokenized + Traditional markets).
Table 7: Regression Analysis 2 - Market Quality (Equity Securities v Tokenized Equity). Market Quality is
a measure of transactions costs (effective spread, realized spread or price impact); price is the average daily
price (in USD) of the traded asset, $Volume is the total daily traded dollar volume, Volatility is the high-low price
range scaled by the average of the high and low prices; and Tokenized is a dummy variable that takes a value of
1 for tokenized stocks and 0 for those traded on traditional venues NYSE and NASDAQ.
29
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Intercept
Price
$Volume
Volatility
Tokenized
Tokenized ×
%TokenizedVolume
Fixed Effects
Adjusted R2
Observations
Effective Spread
Realized Spread
Price Impact
-216.89***
(-17.69)
-0.01***
(-3.76)
10.45***
(18.49)
-11.79
(-0.26)
239.89***
(19.03)
-156.32***
(-13.76)
-0.01***
(-3.27)
7.55***
(14.20)
-108.79**
(-2.19)
173.37***
(14.81)
-58.19***
(-7.35)
-0.00
(-0.28)
2.75***
(7.56)
112.97***
(3.00)
65.66***
(8.24)
-5.84***
-6.04***
0.17
(-8.39)
Symbol, Date
48.53%
13,359
(-9.57)
Symbol, Date
28.76%
13,359
(0.39)
Symbol, Date
32.99%
13,359
While the tokenized exchange remains significantly more expensive to trade than traditional equity
markets, the key finding in Table 7 is that as the relative volume traded in the tokenized exchange
increases, the transactions costs in this exchange reduce significantly. This evidence highlights the
potential for tokenized equity venues to become cheaper as they become more mature, and their
relative volume share increases.
4.1.3. AMM vs CEX liquidity
We next turn our attention to the difference in transactions costs between the Automated Market
Makers (AMMs) and Centralized Exchanges (CEXs). As in our analysis of tokenized securities, Figure 10
shows the liquidity gap (effective spread, realized spread, price impact) for tokens traded on the CEX
and AMM. To get a sense of the relationship between the liquidity gap (red) and overall adoption of
the AMM (blue), the right-hand side axis, the relative AMM volume share is plotted.
Effective spreads measure the cost of trading when an order is executed. The effective spreads show
a clear declining pattern, reducing from around 75-125bps in June 2020 to less than 50bps in April
2021. Across this time, the volumes in AMMs have increased by over 400%. Realized spreads measure
the rewards to liquidity provision, from the prospective of a liquidity provider. We can see that realized
spreads also decline, from around 20bps at the start of the sample to less than 10bps towards the end
of the sample. Finally, price impact measures the permanent price impact generated by a trade. These
declined from 60-110bps in June 2020 to around 40bps by the end of our sample. Consistent with the
other two graphs, AMM utilization over this period experiences a significant increase.
Figure 10: Liquidity Gap and Market Share (Centralized Exchange versus Automated Market Maker)
30
Electronic copy available at: https://ssrn.com/abstract=4301258
We next compare the raw transactions costs for assets where trading for tokens is observed in the
two market structures across the same sample horizon. Our pairwise regression takes the form:
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑦𝑦𝑖𝑖,𝑑𝑑 = 𝛼𝛼 + 𝛽𝛽1 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑒𝑒𝑖𝑖,𝑑𝑑 + 𝛽𝛽2 $𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑒𝑒𝑖𝑖,𝑑𝑑 + 𝛽𝛽3 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑦𝑦𝑖𝑖,𝑑𝑑 + 𝛽𝛽4 𝐴𝐴𝐴𝐴𝐴𝐴𝑖𝑖 + 𝜀𝜀𝑖𝑖,𝑑𝑑 (6)
where 𝑀𝑀𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑦𝑦𝑖𝑖,𝑑𝑑 is one of our measure of transactions costs (effective spread, realized
spread, or price impact) for asset 𝑖𝑖 on day 𝑑𝑑; 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑒𝑒𝑖𝑖,𝑑𝑑 is the average daily price (in USD) of the traded
asset, $𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑒𝑒𝑖𝑖,𝑑𝑑 is the total daily traded dollar volume, 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑦𝑦𝑖𝑖,𝑑𝑑 is the high-low price range
scaled by the average of the high and low prices; and 𝐴𝐴𝐴𝐴𝐴𝐴𝑖𝑖 is a dummy variable that takes a value of
1 for stocks traded on the UniSwap V2 AMM and 0 for those traded on traditional centralized
exchanges (Coinbase, Kraken, and Binance).
The results presented in Table 8 show that demanding liquidity in an AMM costs approximately 67
basis points more than trading in a centralized exchange. Liquidity providers in the AMM earn 13 basis
points on average more than their centralized counterparts, and the price impact of trades on AMMs
is around 83 basis points higher.
Keeping in mind that the effective spread has two components – the realized spread and price impact
– it quickly becomes obvious that the higher cost of trading on the AMM is driven not by the required
returns of liquidity providers, but rather by the significantly higher price impact. This higher price
impact is consistent with the fact that the ‘quotes’ on AMMs are uninformed – that is, prices can only
be moved by trades. Trades are required to ensure that AMM prices are equivalent to those observed
on centralized exchanges. As such, arbitrageurs frequently execute trades at ‘stale’ prices on the
AMM, unwinding them on CEXs. This leads to a very high difference in execution costs driven by the
permanent price impact of the trades executed on AMMs.
31
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Table 8: Regression Analysis 3 - Market Quality (AMM versus CEX). Market Quality is a measure of
transactions costs (effective spread, realized spread or price impact); price is the average daily price (in USD)
of the traded asset, $Volume is the total daily traded dollar volume, Volatility is the high-low price range scaled
by the average of the high and low prices; and AMM is a dummy variable that takes a value of 1 for stocks traded
on the UniSwap V2 AMM and 0 for those traded on traditional centralized exchanges (Coinbase, Kraken, and
Binance).
Intercept
Price
$Volume
Volatility
AMM
Fixed Effects
Adjusted R2
Observations
Effective Spread
101.28***
(16.56)
-0.00
(-0.50)
-7.45***
(-19.04)
1309.62***
(27.07)
66.97***
(42.43)
Symbol, Date
59.42%
42,664
Realized Spread
53.44***
(13.47)
-0.00***
(-4.45)
-3.71***
(-18.27)
488.91***
(19.55)
-12.99***
(-16.89)
Symbol, Date
35.95%
42,664
Price Impact
45.03***
(11.99)
0.00
(0.21)
-3.39***
(-12.53)
687.48***
(21.66)
82.92***
(65.35)
Symbol, Date
58.86%
42,664
To further examine the relationship between AMM volume share and transactions costs, we construct
a regression specification which includes not only a dummy variable for the venue in which a trade
occurs, but also an interaction term capturing the proportion of combined dollar volume traded on
the AMM. Our pairwise regression takes the following form:
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑦𝑦𝑖𝑖,𝑑𝑑 = 𝛼𝛼 + 𝛽𝛽1 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑒𝑒𝑖𝑖,𝑑𝑑 + 𝛽𝛽2 $𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑒𝑒𝑖𝑖,𝑑𝑑 + 𝛽𝛽3 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑦𝑦𝑖𝑖,𝑑𝑑 + 𝛽𝛽4 𝐴𝐴𝑀𝑀𝑀𝑀𝑖𝑖
+𝛽𝛽5 𝐴𝐴𝐴𝐴𝐴𝐴𝑖𝑖 × %𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑖𝑖,𝑑𝑑 + 𝜀𝜀𝑖𝑖,𝑑𝑑
(7)
where all variables are as previously defined, and %𝐴𝐴𝐴𝐴𝐴𝐴𝑖𝑖,𝑑𝑑 is the dollar volume traded on UniSwap
V2 as a proportion of total traded volume (AMM + CEX markets).
Consistent with our previous findings, our results in Table 9 show that effective spreads and price
impacts are higher in AMMs than on centralized exchanges. As the volume share of AMMs increases,
this difference significantly decreases. Interestingly, we find that realized spreads (or the return for
liquidity provision) on the AMM is lower than on the centralized exchanges. As the volume traded on
the AMM increases, the returns for liquidity provision increase. This is consistent with the nature of
AMMs – more uninformed orderflow countervails the impact of arbitrageurs, resulting in a positive
effect of liquidity provision as volume share migrates to the AMM. These results indicate that there is
a potential for AMMs to ‘catch up’ to centralized exchanges. That is, with sufficient volume, the
transactions costs on these venues may equilibrate to the cost of transacting in a CEX, and - with
sufficient volume – may even become cheaper than their centralized counterparts.
Table 9: Regression Analysis 4 - Market Quality (AMM versus CEX). Market Quality is a measure of
transactions costs (effective spread, realized spread or price impact); price is the average daily price (in USD)
of the traded asset, $Volume is the total daily traded dollar volume, Volatility is the high-low price range scaled
32
Electronic copy available at: https://ssrn.com/abstract=4301258
by the average of the high and low prices; and AMM is a dummy variable that takes a value of 1 for stocks traded
on the UniSwap V2 AMM and 0 for those traded on traditional centralized exchanges (Coinbase, Kraken, and
Binance). %AMM Volume is the dollar volume traded on UniSwap V2 as a proportion of total traded volume
(AMM + CEX markets).
Intercept
Price
$Volume
Volatility
AMM
AMM × %AMM
Volume
Fixed Effects
Adjusted R2
Observations
Effective Spread
86.59***
(14.31)
-0.00
(-0.42)
-6.36***
(-16.34)
1299.91***
(26.95)
128.20***
(14.00)
Realized Spread
78.28***
(20.08)
-0.00***
(-4.13)
-5.55***
(-28.19)
505.33***
(20.33)
-116.50***
(-32.04)
Price Impact
0.30
(0.09)
0.00
(0.45)
-0.08
(-0.32)
657.92***
(21.41)
269.29***
(43.29)
-4.44***
7.50***
-13.51***
(-7.43)
Symbol, Date
59.68%
42,664
(32.37)
Symbol, Date
38.55%
42,664
(-32.70)
Symbol, Date
64.32%
42,664
4.1.4. Cost of Settlement
While traditional exchanges undertake settlement internally on their own database infrastructure
(similar to traditional equity markets), decentralized markets such as AMMs require participants to
have their transactions validated by the blockchain. Effectively, the ‘matching engine’ is the blockchain
on which the underlying AMM operates. In our analysis, we examine the operations of the Uniswap
V2 blockchain, which requires approximately 165,000 units of ‘gas’ to execute a swap between two
assets (i.e. – see Barbonne and Ronaldo, 2022). To better understand the costs of settlement in these
AMM marketplaces, we collect the mean gas fee required to undertake such a transaction for every
block in our sample period. We can further compute the $USD value of settlement by multiplying the
required amount of gas by the gas price (measured in Ethereum), and then further multiplying by the
daily price of Ethereum. Our analysis is shown in Figure 11, which indicates that the vast majority of
Uniswap transactions cost between $10-20 (Mean/median settlement costs are $18.8/$15.2) to settle
to the blockchain, with extreme cases costing over $100 during periods of network congestion. 34
Figure 11: Cost of Settlement - Gas Fees
34
For a thorough discussion of the Ethereum mempool and the effects of congestion see Spain et al. (2020).
33
Electronic copy available at: https://ssrn.com/abstract=4301258
4.2. Trade Size Analysis
4.2.1. Distribution of Trade Sizes
To further understand the costs of trading using these alternative mechanisms, we undertake a tradesize analysis, breaking individual trade pairs up into their component parts, and then compare the
transactions costs for individual trades. In these comparisons, it is important to correctly identify
individual trades, particularly in non-AMM markets (AMM ‘market orders’ are inherently observable,
making their identification unambiguous). For example, an incoming market order interacting with
five resting limit orders will typically output five trade reports. To deal with this issue, we follow the
standard convention used in the literature. For example, in equity markets we aggregate trade reports
with the same direction (buy vs sell) and same millisecond remainder as being part of the same market
order, following Jurkatis (2022). In centralized cryptocurrency exchanges, there is significant
heterogeneity in the speed of matching engines, meaning that many end up processing the individual
limit order components of an incoming market order across multiple milliseconds. For the centralized
exchanges considered, we follow the batching mechanisms suggested by Foley, Krekel, Mollica and
Svec (2022).
Figure 12 shows the relative size of trades in our four exchange types. What is immediately obvious is
that trades in tokenized stocks are significantly smaller than trades in their equity market
counterparts. This differential is so marked that we constrain our analysis to the region in which we
observe trades in the tokenized assets - $0-$150,000. While we note that many equity trades
significantly exceed this value, a fair comparison of trading costs cannot be considered outside of the
range for which we empirically observe trades in the tokenized equities.
For cryptocurrency assets, we observe most AMM trades between $0-$5M, where centralized
exchanges experience a significant number of trades both in the $0-$5M range and also between $5$20M, consistent with their more established presence in this asset class.
Figure 12: Trade Size Distribution
34
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4.2.2. Trading Costs for Different Trade Sizes
Our analysis of transactions costs so far has dealt with asset-day averages. This has the potential to
overweight days in which few trades occur at relatively high transactions costs, as all asset-days are
given equal weight. There is also the potential issue that smaller trades may execute at better prices,
while large trades may ‘walk the book’, resulting in large effective spreads and price impacts. When
these are volume-weighted, it is possible to introduce biases into the computed asset-day
observations. Importantly, some exchange structures (such as AMMs) with less ‘fleeting’ liquidity may
35
Electronic copy available at: https://ssrn.com/abstract=4301258
provide benefits for large trades that are not evident for the large number of small trades executed
on the venue. To better understand these effects, we undertake regressions at the trade level. That
is, each individual market order generates its own observation of effective spread and price impact.
We then run a simple regression of the following form:
(8)
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑦𝑦𝑡𝑡 = 𝛼𝛼 + 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑡𝑡 + 𝜀𝜀𝑡𝑡
(9)
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑦𝑦𝑡𝑡 = 𝛼𝛼 + 𝐴𝐴𝐴𝐴𝑀𝑀𝑡𝑡 + 𝜀𝜀𝑡𝑡
where 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑦𝑦𝑡𝑡 is either the effective spread or price impact for each trade, 𝑡𝑡, 𝛼𝛼 is a constant
and 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑡𝑡 is a dummy variable which takes a value of 1 for trades in tokenized equities, and 0
for trades occurring in the traditional NYSE/NASDAQ markets. Similarly, 𝐴𝐴𝐴𝐴𝑀𝑀𝑡𝑡 is a dummy variable
taking a value of 1 for asset pairs traded in the AMM, and 0 for asset pairs traded in the CEX.
Before estimating these regressions, we partition our trades into four buckets based on the dollar
value of the trade. We then estimate the regressions separately for trades whose value is between
$0-$1k, $1k-$10k, $10k-$25k, and $25k-$150k. Given the lack of tokenized equity trades outside of
the $150k range (our maximum trade size is slightly less than $150,000) in the interest of a
representative comparison, we exclude all equity market trades which exceed $150,000 in size.
Table 10 reports the results for the comparison between tokenized assets and equity trades. For
effective spreads, or the cost of consuming liquidity, we observe that the transactions costs for
tokenized equities are consistently higher than those of their centralized exchange counterparts. Small
trades are around 63bps more expensive in tokenized stocks, with this higher cost increasing with the
size of the trade. In the extreme, large trades of $25-$150k cost on average 128bps (or 1.28%) more
than their traditional equity-market counterparts.
Table 10: Tokenized Securities - Trade Size Analysis. Tokenized Equity is a dummy variable which takes a value
of 1 for trades in the FTX tokenized equities, and 0 for trades occurring in the traditional NYSE/NASDAQ markets.
Effective Spread
Price Impact
$0-$1k
$1k-$10k
$10k $25k
$25k $150k
$0-$1k
$1k-$10k
$10k $25k
$25k $150k
63.37***
91.01***
118.41***
128.84***
97.28***
109.73***
88.52***
82.70***
(10.89)
(10.77)
(7.41)
(32.21)
(13.34)
(30.54)
(20.46)
(6.49)
10.87***
6.01***
4.77***
4.39***
0.33***
1.44***
2.21***
3.28***
(0.01)
(0.00)
(0.00)
(0.00)
(0.01)
(0.01)
(0.00)
(0.00)
Fixed effects
Hour of
day
Hour of
day
Hour of
day
Hour of day
Hour of
day
Hour of
day
Hour of
day
Hour of day
Observations
7,585,182
6,887,613
3,067,626
3,852,999
7,578,791
6,879,808
3,064,944
3,849,801
R-squared
0.00
0.01
0.02
0.01
0.00
0.00
0.00
0.00
Tokenized
Equity
Constant
While tokenized equities also experience higher price impact than their equity-market counterparts,
a slightly different pattern emerges, with small trades experiencing 97bps of permanent price impact,
and large trades ‘impacting’ the market less severely. This could be due to the high amounts of depth
observed in the tokenized exchanges – albeit at significantly wider quoted spreads.
36
Electronic copy available at: https://ssrn.com/abstract=4301258
We next examine the differences in trades occurring on Centralized Exchanges and AMMs. While our
method of analysis remains unchanged, we use different trade-size buckets, in keeping with the
differing market microstructure of the two markets. In this setting, we compare trades in five buckets:
$0-$1k; $1k-$10k; $10k - $100k; $100k - $1M and trades greater than $1M.
Table 11 reports the results of the AMM trade size analysis. Consistent with our asset-day analysis,
AMMs have significantly higher transactions costs for trades of all sizes. Whilst these are slightly
decreasing from small to medium sized trades (67-66bps), they increase significantly for trades of over
$1m, being 253bps more expensive, or almost 2.2%. This large increase over CEXs is likely reflective
of the large opportunity such trades show for extractive industries such as front-running and sandwich
attacks. Permanent price impacts are also monotonically decreasing in trade sizes between $0 - $1m,
reducing from 33bps to 30bps. However, similar to our effective spread analysis, for trades greater
than $1m this increases over 3x to 125bps.
Table 11: AMM - Trade Size Analysis. AMM is a dummy variable taking a value of 1 for asset pairs traded in the
AMM, and 0 for asset pairs traded in the CEX.
Trade Size
$0-$1k
Effective Spread
$10k $100k $1k-$10k
$100k
$1M
>$1m
$0-$1k
Price Impact
$10k $1k-$10k
$100k
AMM
67.62***
67.40***
66.24***
68.00***
220.2***
34.56***
32.66***
30.80***
29.20***
103.3***
(0.523)
(0.422)
(0.580)
(4.040)
(2.786)
(0.322)
(0.252)
(0.338)
(1.930)
(3.387)
0.776***
1.114***
1.596***
4.545***
48.14***
0.252***
2.158***
3.540***
5.745***
26.84***
(0.00227)
(0.00984)
(0.0198)
(0.256)
(0.382)
(0.00140)
(0.00587)
(0.0115)
(0.122)
(0.464)
Observations
3,829,713
1,377,807
286,137
10,071
73
3,829,713
1,377,802
286,133
10,069
73
R-squared
0.708
0.721
0.683
0.491
0.969
0.013
0.049
0.054
0.074
0.810
Constant
$100k $1M
>$1m
These results challenge the commonly held perception that AMMs provide a more cost-effective
means of transacting compared to centralized exchange alternatives. Our results reveal that they are
not particularly well suited to larger size transactions.
4.2.3. Price Impact Functions for the Different Markets
Price impact is a measure of the permanent change in price that is generated by a trade. In general,
larger trades are expected to generate higher levels of price impact given their increased demand for
liquidity. Higher price impact results in inferior prices for the liquidity demander, and effectively serves
as compensation for the liquidity provider. As a result, the ability of a given market to absorb the price
impact of a trade will typically be a function of its liquidity. Due to the large depth typically provided
by AMMs, it is often claimed that AMMs provide better execution quality to very large trades. To test
this conjecture, we construct price impact curves for the various assets considered.
37
Electronic copy available at: https://ssrn.com/abstract=4301258
For each market, we select one of the most liquid traded instruments and analyze price impact at the
trade-by-trade level during a one-week period (March 8, 2021 to March 14, 2021).35 We aggregate
trades that originate from a single marketable order by summing their volumes and retaining the last
price in the trade sequence.
For each market separately, we estimate the price impact curve as follows. First, for each trade 𝑡𝑡, we
compute the signed dollar volume of the trade:
𝑉𝑉𝑡𝑡 = 𝐷𝐷𝑡𝑡 𝑄𝑄𝑡𝑡 𝑃𝑃𝑡𝑡
(10)
where 𝐷𝐷𝑡𝑡 is the trade direction (-1 for sells and +1 for buys), 𝑄𝑄𝑡𝑡 is the trade volume in shares, and 𝑃𝑃𝑡𝑡
is the trade price in dollars. We also compute each trade’s total price impact - 𝑃𝑃𝑃𝑃𝑡𝑡 - (including
temporary and permanent components) as:
(11)
𝑃𝑃𝑃𝑃𝑡𝑡 = 10,000[ln (𝑃𝑃𝑡𝑡 ) − ln (𝑀𝑀𝑡𝑡−1 )]
where 𝑃𝑃𝑡𝑡 is the trade price and 𝑀𝑀𝑡𝑡−1 is the midquote that was prevailing immediately before the
trade. 36 This price impact measure is the log ‘return’ from the market midquote prior to the trade,
compared to the trade price, expressed in basis points.
Second, because many empirical studies consistently document that price impacts are non-linear in
volume, we construct a non-linear signed dollar volume term. Based on the recent empirical literature
that characterises the functional form for price impact functions, we use a power law functional form,
raising dollar volume to a power, 𝛿𝛿:
𝑉𝑉𝑡𝑡∗ = 𝐷𝐷𝑡𝑡 . (𝑄𝑄𝑡𝑡 𝑃𝑃𝑡𝑡 )𝛿𝛿
(15)
The empirical literature finds that the optimal exponent 𝛿𝛿 when fitting price impact curves is in the
range 0.5 to 0.7. Several notable studies use exponents close to 0.5 implying the specific case of a
square-root impact law, and several empirical studies find exponents around 2/3 (0.67).37 Based on
this empirical evidence we fit price impact curves using 𝛿𝛿 = 0.7 for all markets except AMMs. For
AMMs, the price impact functional form is determined by the constant product rule rather than the
limit order book dynamics as is the case in all other markets. The constant product rule implies a price
impact curve that is asymmetric: diminishing marginal impacts for sells (𝛿𝛿 < 1), meaning a sell order
of 10 ETH will have less than 10 times the price impact of a sell order for 1 ETH, but increasing marginal
impacts for buys (𝛿𝛿 > 1) meaning a buy order of 10 ETH will have more than 10 times the price impact
of a buy order for 1 ETH. We, therefore, separately fit price impact curves for AMM buys using 𝛿𝛿 =
1.8 and sells using 𝛿𝛿 = 0.8.
Third, we calibrate the price impact curve for each market, estimating the following regression:
∗
𝑃𝑃𝑃𝑃𝑡𝑡 = 𝛽𝛽̂ 𝑉𝑉𝑡𝑡∗ + 𝛾𝛾�𝑉𝑉𝑡𝑡−1
+ 𝜀𝜀𝑡𝑡
(16)
For AMMs, we use the ETH-USDT pair. Correspondingly, for CEX, we select Binance and use the ETH-USDT
pair. For tokenised equities, we select GME (GameStop) due to its high trading activity, and correspondingly, for
equities we also consider GME for comparison.
36
The midquote is the average of the best bid and best ask in the market at the time. For AMMs, the midquote
is taken from the CEX.
37
Square-root impact laws have been used in industry models of price impact functions (Torre, 1997) and various
price impact studies (e.g., Gabaix et al. (2003, 2006) and Hopman (2007)). Exponents around 2/3 have been
documented by Almgren et al. (2005), Bershova and Rakhlin (2013), and Zhou (2012), among others. Several
studies illustrate the universality of price impact functional forms across different assets and market types
underpinned by common theoretical basis (e.g., Gabaix et al. 2003, 2006; Lillo et al., 2003; Zhou, 2012).
35
38
Electronic copy available at: https://ssrn.com/abstract=4301258
∗
where 𝑉𝑉𝑡𝑡−1
is included as a control variable due to serial correlation in price impacts. Non-linearity is
captured through the terms 𝑉𝑉𝑡𝑡∗ which are signed powers of dollar volume.
Fourth, we plot the calibrated price impact curves in the above model, using the estimated values of
𝛽𝛽̂. The results are in Figures 13-15 below.
Figure 13 compares the two markets that trade equities – Panel A is the traditional equities market
(NYSE, Nasdaq), whereas Panel B is for tokenized equities. In both cases we obtain a very “standard”
price impact curve - with buys pushing prices up and sells pushing prices down, but at a decreasing
marginal rate as the trade volume increases. The scales of the vertical axes reveal a substantial
difference in liquidity. The traditional equity markets can handle much larger trades for a given price
impact than can the tokenized equities market which is currently far less liquid. For example, a
$100,000 buy is estimated to have a price impact of around 10 bps in the traditional equities market,
whereas in the market for tokenized stocks, the price impact of such a trade is estimated as closer to
600 bps.
Panel A: Total price impact curve for stocks
Panel B: Total price impact curve for tokenized stocks
Figure 13: Calibrated empirical price impact curves for markets that trade equities. The figure shows the
estimated total price impact in basis points (vertical axis) for different trade sizes (horizontal axis), based on the
calibrated price impact model given in equation (4). Negative signed dollar volumes are sells and positive values
are buys. For example, -$50,000 on the horizontal axis is a sell with trade value $50,000. Panel A is the traditional
equities market (NYSE, Nasdaq), whereas Panel B is for tokenized equities. Note that the vertical axis scale is
different in the two plots. The models are calibrated using a week of trade-by-trade data in March 2021.
Figure 14 compares the two markets that trade cryptocurrencies – Panel A is a centralized exchange
(Binance), whereas Panel B is a decentralized automated market maker, AMM (UniSwap). The
calibrated price impact curve for the CEX, like equities, has a very “standard” shape - with decreasing
marginal price impacts as the trade volume increases. The CEX appears to be more liquid as it has a
smaller price impact for a given trade size.
In contrast, the price impact curve for the AMM is not like standard price impact curves – it is
asymmetric and because of the constant pricing function, price impact increases at an accelerating
rate for buys (increasing marginal impact) but increasing at a decelerating rate for sells (decreasing
marginal impact). Note also that these are calibrated empirical curves with price impact measured
relative to the CEX midpoint, as opposed to theoretical price impact curves inferred from the AMM
39
Electronic copy available at: https://ssrn.com/abstract=4301258
pricing function. The AMM price impact curve also shows that the AMM tends to be a relatively lowcost venue for executing small buy trades, compared to executing sells. For example, a $50,000 buy in
the AMM is estimated to have a price impact of 2 bps above the CEX midpoint, whereas a $50,000 sell
in the AMM is estimated to have a price impact of 30 bps below the CEX midpoint. 38
Comparing scales between Panels A and B of Figure 14, the AMM is less liquid than the CEX as it tends
to have significantly larger price impacts overall. Particularly, with respect to large buys, the
accelerating price impact of the AMM renders it an expensive venue in comparison to the CEX. For
example, a $200,000 buy is estimated to have a price impact of around 30 bps in the AMM, whereas
in the CEX, the price impact of such a trade is estimated at a mere 3 bps.
Panel A: Total price impact curve for CEX
Panel B: Total price impact curve for AMMs
Figure 14: Calibrated empirical price impact curves for markets that trade cryptocurrencies. The figure shows
the estimated log total price impact in basis points (vertical axis) for different trade sizes (horizontal axis), based
on the calibrated price impact model given in equation (4). Negative signed dollar volumes are sells and positive
values are buys. For example, -$50,000 on the horizontal axis is a sell with trade value $50,000. Panel A is a
centralized exchange (Binance), whereas Panel B is a decentralized automated market maker, AMM (UniSwap).
Note that the vertical axis scale is different in the two plots. The models are calibrated using a week of trade-bytrade data in March 2021 for the asset pair ETH-USDT.
Figure 15 aggregates the price impact curves of the four markets on a single plot with the same axis
scale to give a better perspective of the differences in liquidity. The figure shows that tokenized stocks
are a clear outlier with the steepest price impact curves (least liquidity). Tokenized equities are
followed by AMMs in terms of liquidity, with CEX and traditional equities being the most liquid markets
with comparatively flat price impact curves.
This asymmetry may be a function of the specific period chosen for the analysis and the average price
differential between the AMM and CEX during that period.
38
40
Electronic copy available at: https://ssrn.com/abstract=4301258
Figure 15: Calibrated empirical price impact curves for all markets. The figure shows the estimated log total price
impact in basis points (vertical axis) for different trade sizes (horizontal axis), based on the calibrated price
impact model given in equation (4). Negative signed dollar volumes are sells and positive values are buys. For
example, -$50,000 on the horizontal axis is a sell with trade value $50,000. The models are calibrated using a
week of trade-by-trade data in March 2021.
4.3. Can AMMs become competitive with Centralized Exchanges?
Our analysis so far has identified that trading costs for digital assets traded using this the new market
infrastructure provided by AMMs significantly exceed those of their existing market counterparts.
Further, we have shown that as the market share in AMMs increases, the costs of transacting falls. A
natural question then arises: how much activity would need to be present on the AMMs to bring their
trading costs down to levels observed in the Centralized Exchanges?
We empirically address this question by estimating quoted and effective spreads as a function of the
venue in which they trade, and an interaction term for the relative proportion of volume traded in the
AMM. Using the parameter estimates, we are then able to project future levels of AMM trading
activity that would result in comparable costs with the CEX. 39
The results presented in Figure 16 indicate that the AMM effective spread falls to approximately 30bps
(our sample mean for CEXs) when relative activity reaches 165% of the CEX. Similarly, AMM volume
would need to reach approximately 150% of the current CEX volumes to match the 13.9bps sample
mean price impact for CEXs. Given the significant growth rates in AMM usage and adoption as
documented in Aspris et al. (2021), AMM activity increasing by 150% could feasibly occur within the
span of a single year, implying AMMs may shortly become cost competitive with traditional market
structures, which trade cryptocurrencies.
Due to the incredibly small market share of tokenized equities that were traded on FTX (less than 0.1%
of combined trading volume) we cannot reliably estimate any reasonable volume for which
39
Noting that the current relative market share used in our estimates is approximately 35%.
41
Electronic copy available at: https://ssrn.com/abstract=4301258
transactions costs may become equivalent to their equity market counterparts, suggesting that
significant development of this market would be necessary before it could become cost competitive.
140
120
100
Basis Points
80
60
40
20
-20
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
105%
110%
115%
120%
125%
130%
135%
140%
145%
150%
155%
160%
165%
170%
175%
180%
185%
190%
195%
200%
0
-40
-60
AMM Effective Spread
AMM Price Impact
Figure 16: Projected AMM Transaction Costs
5. Conclusion
The emergence of blockchain technology has seen the creation and digitization of new,
cryptographically secured digital assets. These include cryptocurrencies such as Bitcoin and Ethereum
as well as digital tokens reflecting ownership of both traditional assets (e.g., equities, fiat currencies)
and more recent asset types (e.g., governance tokens, art NFTs). Recent innovations have allowed
traditional securities and financial instruments to be tokenized and thus stored and transferred on
public blockchains. This innovation in tokenization of assets has spurred further advances in the way
assets are traded and settled, generating entire new paradigms in markets such as decentralized
exchanges and automated market makers.
While these innovations have generated much fanfare and future promise, research about these
market types to date is limited. This research report provides the first rigorous analysis of trading costs
associated with these new markets for digital assets.
We first compare traditional equity exchanges (NYSE/NASDAQ) and their tokenized counterparts. Our
findings show that the market for tokenized equities is in its infancy: implicit transactions costs such
as effective spreads are 10 times higher than in traditional equities markets, with the explicit costs of
trading (exchange fees) more than 2 times as large. While tokenized equities present some potential
benefits – fractionalized shares, 24-hour trading, global accessibility, instant riskless settlement –
these have yet to attract sufficient interest to generate a competitive and active marketplace.
Next we analyze the trading of cryptocurrencies and tokens on their blockchains, such as stablecoins
and utility tokens. We examine three market types: (i) Centralized Exchanges (CEX) operating central
limit order books (Coinbase, Binance, and Kraken); (ii) Decentralized Exchanges (DEX) that offer limit
42
Electronic copy available at: https://ssrn.com/abstract=4301258
order books; and (iii) Automated Market Makers that use liquidity pools and bonding curves to
facilitate transactions.
Trading costs in all cryptocurrency trading venues exceed those in traditional equity markets. Among
the cryptocurrency trading venues, centralized exchanges are the cheapest, with transaction costs
averaging 32bps (approximately 4 times more expensive than trading equities). DEXs are
approximately 2 times more expensive than CEXs, with AMMs being the most expensive with trading
costs averaging approximately 130bps. Exchange fees are also significantly more expensive in these
alternative asset classes. CEXs charge traders between 2-26bps. This wide variance is driven by the
‘tiered’ nature of fees – exchanges such as Kraken charge 26bps for traders with volumes less than
$50,000 per month, while Binance reduces its trading fees to 2bps for traders who exceed $4billion in
a single month. The EtherDelta DEX charges 30bps to fund the protocol, which is similar to popular
AMMs such as Uniswap V2 and Sushiswap. While not analysed in this paper, Uniswap V3 allows
different liquidity pools to be established with different exchange fees – with tiers ranging from 1bp
to 100bps.
A summary of our key findings is in Table 12, contrasting the structure, costs, risks, and performance
of the different market types.
Table 12: Summary of Findings
Feature
Equity Exchanges
Tokenized
Equities
CEX
DEX
AMM
Market Maker
Electronic liquidity
providers (ELP)
ELP
ELP
ELP/Arbitrageur
Liquidity pool
7.5bps
74bps
32bps
66bps
130bps
<1bps
Clearinghouse
1-2bps
2-7bps
Internal
Free
2-26bps
Internal
Free
Settlement Speed
2-3 days
Instant
Instant
Exchange Speed
Counterparty Risk
KYC/AML
Fast
Low
Strong
Fast
High
Medium
Fast
High
Medium
30bps
Eth Blockchain
Gas Cost ($5-$50)
Variable
(10sec-1min)
Slow
None
None
1-100bps
Eth Blockchain
Gas Cost ($5-$50)
Variable
(10sec-1min)
Slow
None
None
Implicit Transactions
Costs
Explicit Exchange Costs
Settlement Method
Settlement Cost
While cryptocurrencies and tokenization of assets are in the early stages of development, particularly
compared to traditional equity markets, their advantages such as real-time riskless settlement and
new methods of trading hold significant promise for improving market efficiency, reducing risks, and
reducing overall costs of market infrastructure. While there are many impediments to tokenizing
traditional assets now, including significantly less liquidity, leading to higher trading costs, we show
that these costs tend to fall as adoption increases. Given tokenized assets enable distributed markets
that are truly borderless, with reduced barriers to entry and conducive to rapid innovation, it is likely
that these tokenized assets, and their exchange market structures, are here to stay.
43
Electronic copy available at: https://ssrn.com/abstract=4301258
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Appendix A
Sample selection – asset pairs considered in our primary analysis.
Matched Pair List (Symbols)
Equities – Tokenized Securities (EXQ-TKN)
Centralized Exchanges – Automated Market
Makers (CEX-AMM)
(Count = 36)
(Count = 15)
AAPL-USD
AAVE-ETH
AMC-USD
BAT-ETH
AMD-USD
BAT-USDC
AMZN-USD
ETH-DAI
ARKK-USD
ETH-USDC
BABA-USD
ETH-USDT
BB-USD
GRT-ETH
BILI-USD
KNC-ETH
BNTX-USD
LINK-ETH
BYND-USD
LINK-USDT
CRON-USD
MANA-ETH
FB-USD
REP-ETH
GDX-USD
STORJ-ETH
GDXJ-USD
UNI-BTC
GLD-USD
USDC-USDT
GME-USD
GOOGL-USD
MRNA-USD
MSTR-USD
NFLX-USD
NIO-USD
NOK-USD
NVDA-USD
PENN-USD
PFE-USD
PYPL-USD
SLV-USD
SPY-USD
SQ-USD
TLRY-USD
TSLA-USD
TSM-USD
TWTR-USD
UBER-USD
USO-USD
ZM-USD
47
Electronic copy available at: https://ssrn.com/abstract=4301258
Centralized Exchanges
Symbol List (Universe)
AMM
AAVE-BTC, AAVE-ETH, AAVE-EUR, AAVE-GBP
AAVE-USD, ADA-BTC, ADA-ETH, ADA-EUR
ADA-USDT, ALGO-BTC, ALGO-EUR, ALGO-USD
ATOM-BTC, ATOM-USD, BAL-BTC, BAL-USD
BAND-BTC, BAT-BTC, BAT-ETH, BAT-USDC
BCH-BTC, BCH-EUR, BCH-GBP, BCH-USD
BCH-USDT, BNT-BTC, BTC-AUD, BTC-DAI
BTC-EUR, BTC-GBP, BTC-USD, BTC-USDC
BTC-USDT, COMP-BTC, COMP-USD, CRV-BTC
DAI-USD, DASH-BTC, DASH-USD, DOT-BTC
DOT-EUR, DOT-USDT, EOS-BTC, EOS-ETH
EOS-EUR, EOS-USD, EOS-USDT, ETC-BTC
ETC-ETH, ETC-EUR, ETC-USD, ETH-AUD
ETH-BTC, ETH-DAI, ETH-EUR, ETH-GBP
ETH-USD, ETH-USDC, ETH-USDT, FIL-BTC
FIL-EUR, FIL-USD, GRT-BTC, GRT-ETH
GRT-EUR, GRT-USD, ICX-BTC, ICX-ETH
KAVA-BTC, KNC-BTC, KNC-ETH, KNC-USD
KSM-BTC, LINK-BTC, LINK-ETH, LINK-EUR
LINK-USD, LINK-USDT, LRC-BTC, LSK-BTC
LSK-ETH, LTC-BTC, LTC-ETH, LTC-EUR
LTC-GBP, LTC-USD, LTC-USDT, MANA-BTC
MANA-ETH, MKR-BTC, NANO-BTC, NANO-ETH
NMR-BTC, OMG-BTC, OMG-ETH, OMG-EUR
OMG-USD, OXT-BTC, OXT-USD, PAXG-BTC
QTUM-BTC, QTUM-ETH, REN-BTC, REP-BTC
REP-ETH, REP-USD, SC-BTC, SC-ETH
SNX-BTC, SNX-EUR, SNX-USD, STORJ-BTC
STORJ-ETH, TRX-BTC, TRX-ETH, UMA-BTC
UNI-BTC, UNI-USD, USDC-USDT, WAVES-BTC
WAVES-ETH, WBTC-BTC, XLM-BTC, XLM-EUR
XLM-USD, XMR-BTC, XRP-AUD, XRP-BTC
XRP-ETH, XRP-EUR, XRP-GBP, XRP-USD
XRP-USDT, XTZ-BTC, XTZ-EUR, XTZ-USD
YFI-BTC, YFI-EUR, YFI-USD, ZEC-BTC
ZEC-USD, ZEC-USDC, ZRX-BTC
AAVE-ETH
BAT-ETH
BAT-USDC
ETH-DAI
ETH-USDC
ETH-USDT
GRT-ETH
KNC-ETH
LINK-ETH
LINK-USDC
LINK-USDT
MANA-ETH
REP-ETH
STORJ-ETH
UNI-BTC
UNI-USDT
USDC-USDT
Equities
AAPL
ABNB
AMC
AMD
AMZN
ARKK
BABA
BB
BILI
BNTX
BYND
CGC
CRON
FB
GDX
GDXJ
GLD
GLXY
GME
GOOGL
MRNA
MSTR
NFLX
NIO
NOK
NVDA
PENN
PFE
PYPL
SLV
SPY
SQ
TLRY
TSLA
TSM
TWTR
UBER
USO
ZM
48
Electronic copy available at: https://ssrn.com/abstract=4301258
Tokenized
Equities
AAPL-USD
ABNB-USD
ACB-USD
AMC-USD
AMD-USD
AMZN-USD
APHA-USD
ARKK-USD
BABA-USD
BB-USD
BILI-USD
BITW-USD
BNTX-USD
BYND-USD
CGC-USD
CRON-USD
ETHE-USD
FB-USD
GBTC-USD
GDX-USD
GDXJ-USD
GLD-USD
GLXY-USD
GME-USD
GOOGL-USD
MRNA-USD
MSTR-USD
NFLX-USD
NIO-USD
NOK-USD
NVDA-USD
PENN-USD
PFE-USD
PYPL-USD
SLV-USD
SPY-USD
SQ-USD
TLRY-USD
TSLA-USD
TSM-USD
TWTR-USD
UBER-USD
USO-USD
ZM-USD