Cryptocurrencies

Yield Farming

∗

Patrick Augustin,

†

Roy Chen-Zhang,

‡

and Donghwa Shin

First draft: October 15, 2021

This draft: September 24, 2022 (Download the latest version here)

Abstract

We characterize the risk and return characteristics of yield farming investment strategies

on PancakeSwap, one of the largest automated market makers among the emerging ecosys-

tem of decentralized ﬁnancial services. PancakeSwap provides opportunities for earning

passive income by pledging pairs of cryptocurrency tokens in liquidity pools and harvesting

governance tokens in yield farms, a practice called ‘yield farming.’ Yield farming gener-

ates performance through several components related to capital gains, trading fee revenue

and farm yields, and is exposed to impermanent losses that are driven non-linearly by dif-

ferential return performance in the underlying cryptocurrency token pairs. We ﬁnd that

yield farming delivers positive Sharpe ratios that are comparable to those of other cryp-

tocurrency investments and the S&P 500 index. However, investment performance declines

signiﬁcantly after accounting for transaction costs and price impact that is largest for farms

with the highest headline yields. leading possibly to negative risk-adjusted returns. We

furthermore ﬁnd that ﬂows to high-yield farms chase past performance and high yields and

predict negative future returns. These patterns are similar to investment behavior and

risk-return characteristics observed in traditional markets, despite the absence of ﬁnancial

intermediaries. Since yield farming is easily accessible to retail investors, our analysis has

important implications for the current debate about the regulation of decentralized ﬁnancial

services.

JEL Classiﬁcation Codes: G12, G13, G14, O33, Y80

Keywords: blockchain, consumer protection, cryptocurrencies, decentralized ﬁnance, ﬁn-

tech, household ﬁnance, yield farming

∗

Preliminary Draft. No guarantee for accuracy or sense, comments welcome. As for helpful comments,

we thank Greg Brown, Mikhail Chernov, William Cong, Darrell Duﬃe, Christian Lundblad, Paige Ouimet,

Neil Pearson, Cameron Peng (discussant), Daniel Rabetti (discussant), Adam Reed, Alessio Saretto, and

participants at the 2022 Active Management Research Symposium organized by UNC Institute of Private

Capital, 2022 Boulder Summer Conference, 2022 Greater China Area Finance Conference, themed “Finance

Research in the Era of Big Data”, 2022 International Risk Management Conference, 15th Annual Risk

Management Conference at National University of Singapore, 2022 UBRI Connect at UCL, 2022 Canadian

Derivatives Institute Annual Conferenece, a ﬁnance seminar at UNC Kenan-Flagler Business School. We

also thank Wei Yang for excellent research assistance. Augustin acknowledges ﬁnancial support from the

Canadian Derivatives Institute. Shin acknowledges ﬁnancial support from the Kenan Institute.

†

McGill University and Canadian Derivatives Institute; [email protected].

‡

University of North Carolina at Chapel Hill; Roy Chen-Zhang@kenan-ﬂagler.unc.edu.

University of North Carolina at Chapel Hill; Donghwa Shin@kenan-ﬂagler.unc.edu.

Electronic copy available at: https://ssrn.com/abstract=4063228

“Right now, we just don’t have enough investor protection in crypto. Frankly, at this time,

it’s more like the Wild West.”

Chair Gary Gensler, Securities and Exchange Commission

1 Introduction

Decentralized ﬁnance (DeFi) is a rapidly growing segment of the emerging cryptocurrency

ecosystem. By operating through applications built on blockchains and executed through

smart contracts, DeFi intends to eliminate the inﬂuence of central ﬁnancial intermediaries.

Figure 1 illustrates that the total value locked, a measure of aggregate capital investments

into DeFi applications, has been growing at an exponential pace over the last 2 years,

having recently surpassed $200 billion. Harvey, Ramachandran, and Santoro (2021) discuss

the implications of DeFi for the future of our ﬁnancial system.

We study yield farming, a novel decentralized ﬁnancial service that is accessible to both retail

and institutional investors. Yield farming is a modern version of securities lending whereby

investors earn passive income from the provision of digital liquidity. This investment activity

has gathered signiﬁcant interest in the popular press because of the scale of promised returns.

Advertised interest rates are often several hundred percent and can be as high as as several

thousand percent (e.g., Oliver, 2021). Yield farming has also attracted regulatory interest

from the Securities and Exchange Commission, who consider it to be an unregulated and

complex investment strategy with hidden risks to unsophisticated investors (e.g., Gensler,

2021).

We provide the ﬁrst assessment of yield farming performance using a novel hand-collected

data set sourced from Binance Smart Chain (BSC). BSC is a public blockchain launched

by Binance with the purpose of providing a centralized exchange that features high trade

execution speeds, lower congestion risks and lower trading fees than other comparable smart

contract applications. On BSC, Binance Coin (BNB) is the main medium of exchange for

trading purposes and for the payment of transaction costs that are known as gas fees.

Our data contains daily information on a cross-section of 219 yield farms that are active

on PancakeSwap between September 23, 2020 and September 5, 2021. PancakeSwap is

one of the most popular automated market makers, next to other similar platforms like

Uniswap and Sushiswap. It is also one of the largest automated market makers with 435,130

active users on October 24, 2021, compared to 47,730 active users recorded on Uniswap.

PancakeSwap is particularly useful for studying yield farming since it is one of the platforms

that lists yield farms in addition to liquidity pools. Studying yield farms is the centrepiece

of our work. Moreover, the number of active users in relation to total value locked suggests

that the yield farming space is populated by many retail investors, thereby emphasizing the

importance for investor protection.

Electronic copy available at: https://ssrn.com/abstract=4063228

We ﬁrst characterize the risk and return characteristics of yield farming strategies. Yield

farming is a mechanism for passively earning income by supplying digital liquidity. The

overall performance is earned through a chain of transactions that, taken together, form a

complex investment product.

Yield farmers ﬁrst pledge pairs of cryptocurrency tokens in equal amounts to associated

liquidity pools for which they are rewarded with liquidity tokens. These liquidity tokens

certify the liquidity provision and represent a claim to a fraction of the aggregate liquidity

in the pool. When the liquidity tokens are redeemed, the fractional ownership of the pool

may change in value due to the constant product technology hardwired into the automated

market maker system. Thus, liquidity miners may face capital gains or losses, in addition

to fee revenue from the trading activity of third party investors in exchange for the liquidity

provision. Liquidity miners also face signiﬁcant downside risk through impermanent losses.

This is realized as a loss function that is driven non-linearly by return diﬀerences among

the pair of cryptocurrency tokens associated with a pool.

Another key component of yield farming is the staking of liquidity tokens that are rewarded

for liquidity provision into yield farms. Each liquidity pool is associated with a unique yield

farm that promises an interest rate often exceeding several hundred percent. Yield farmers

earn that rate in proportion to the aggregate liquidity locked in a yield farm, which is paid

using PancakeSwap’s governance token Cake. This ultimately exposes yield farmers further

to exchange rate risk stemming from the variation in the value of Cake relative to the USD.

We explicitly show that yield farming is subject to non-trivial price impacts that are non-

linearly related to the amount of liquidity invested into a yield farming strategy. We for-

malize the price impact function and show that it is concave in the investment amount.

Besides the price impact, we also provide information on the magnitude and time variation

of gas fees charged for round trip costs in yield farming.

As a second step, we assess the empirical return performance of yield farming strategies and

compare them to other benchmark strategies in cryptocurrency markets and the S&P500

index. We take the perspective of U.S. investor who needs to buy digital assets using

the USD as a base currency and exchange all farm yields back to its local currency at

the prevailing exchange rates. We ﬁnd that yield farming strategies appear to generate

attractive returns, with Sharpe ratios between 2 and 3. While such Sharpe ratios appear

extraordinarily large, they are similar to those for investments into the S&P500 index,

Bitcoin or Ethereum, and are partially explained by the extraordinary bull run in most

asset markets during our sample period.

Yield farming also generates Sharpe ratios that are larger than those of simple buy-and-

hold trading strategies in the underlying pairs of cryptocurrency tokens. It also generates

superior performance to a strategy that considers liquidity mining without yield farming.

Even though the joint investment activity is a strictly dominating strategy, not all investors

appear to stake their liquidity tokens into yield farms. This is suggestive evidence of investor

inertia and lack of investor sophistication.

Electronic copy available at: https://ssrn.com/abstract=4063228

While we uncover positive investment performance without the consideration of transaction

costs, the performance becomes signiﬁcantly weaker when we account for trading costs

(a.k.a. gas fees) and price impact. While gas fees shift the return performance linearly

downward for all yield farms, price impact is especially important for farms that advertise

large headline yields. This motivates our additional analysis on the relation between ﬂows

and performance in yield farms.

As a last step, we study the relation between yield farming ﬂows and performance. We

follow the mutual fund literature and deﬁne farm ﬂows as the change in total value locked,

after accounting for growth in liquidity associated with return performance. We scale ﬂows

by total value locked to make them comparable across yield farms. We ﬁnd that farms

with high headline yields attract more ﬂows and that positive return performance predicts

future ﬂows. Moreover, we ﬁnd that new ﬂows are negatively correlated with future farm

performance.

Overall, our evidence is consistent with evidence from other asset markets that reﬂects re-

turn chasing behavior, whereby ﬂows chase positive past performance. Our ﬁndings also

provide supportive evidence for patterns that are associated with reaching for yield. We

consider these ﬁndings to be intriguing since they typically arise in a setting with ﬁnan-

cial intermediaries, while yield farming is implemented in a decentralized market without

ﬁnancial intermediaries.

Given the risks to retail investors associated with obfuscated investment strategies and

complex ﬁnancial products, we believe that our evidence has important policy implications

for regulatory disclosure and investor protection.

2 Literature

Our work is most closely related to the emerging literature on decentralized ﬁnance. In Table

1, we compare a select number of studies that examine decentralized exchanges(DEX). To

our knowledge, this is the ﬁrst empirical study of the risk and return characteristics of yield

farming strategies based on a novel hand collected data set.

In contrast to earlier studies, we focus on PancakeSwap, a smart contract platform operating

on the Binance Smart chain (BSC). BSC charges comparatively lower transaction costs

than Ethereum, the supporting blockchain for Uniswap and SushiSwap. Hence, yield farms

operating on BSC are more easily accessible to retail investors.

Several studies characterize the theoretical properties of automated market makers (AMM)

with the constant product model that has been adopted by major decentralized exchanges

(Angeris, Kao, Chiang, Noyes, and Chitra, 2019; Aoyagi, 2021). Lehar and Parlour (2021),

Park (2021) further examine strategic trading and liquidity provision in decentralized ex-

changes. Capponi and Jia (2021) underscore the investor trade-oﬀs arising from the personal

Electronic copy available at: https://ssrn.com/abstract=4063228

beneﬁts of token investments and loss exposure associated with high token exchange rate

volatility. Relatedly, we explicitly characterize the impermanent-loss and price-impact func-

tions implicit in liquidity mining and yield farming. Han, Huang, and Zhong (2021) suggest

that trading on DEXs are informative about the decentralized consensus of cryptocurrency

value. Li and Mayer (2021) study the safe asset properties of stablecoins.

Yield farming is a complex and opaque investment strategy. Thus, we also relate to the lit-

erature on complex structured ﬁnance. For example, Henderson and Pearson (2011) suggest

that highly popular structured retail products (SRPs) deliver subpar performance for retail

investors in spite of high promised returns. Supply-based theories explain the popularity of

SRPs among retail investors by arguing that intermediaries exploit investors’ lack of ﬁnan-

cial sophistication (e.g. C´el´erier and Vall´ee, 2017; Egan, 2019; Ghent, Torous, and Valkanov,

2019; Henderson, Pearson, and Wang, 2020). Shin (2021) advocates a demand-based ex-

planation whereby investors extrapolate and aggressively chase past performance. In a

signiﬁcant departure from that work, we study complex ﬁnancial products oﬀered through

smart contracts operating on a blockchain without centralized ﬁnancial intermediaries who

may drive the security design or beneﬁt from sales.

Yield farms promise passive income at impressive headline rates. This connects our work

to the literature on “reaching for yield,” i.e., investors’ propensity to buy riskier assets

to achieve higher yields. That phenomenon has been documented in the corporate bond

(Becker and Ivashina, 2015; Chen and Choi, 2021) and mutual fund market (Choi and

Kronlund, 2018). Bordalo, Gennaioli, and Shleifer (2016) show how investors’ salience bias

can lead to reaching-for-yield behavior when ﬁrms compete for consumer attention. Our

evidence suggests that reaching for yield may also exist in decentralized exchanges even in

the absence of ﬁnancial intermediaries and related agency conﬂicts.

Our work adds to the developing literature of cryptocurrencies and blockchain technologies

(Harvey, 2016; Yermack, 2017; Biais, Bisiere, Bouvard, and Casamatta, 2019; Saleh, 2021;

Easley, O’Hara, and Basu, 2019), including initial coin oﬀerings (e.g., Howell, Niessner,

and Yermack, 2020; Hu, Parlour, and Rajan, 2019; Lee, Li, and Shin, 2022), price ma-

nipulations(Gandal, Hamrick, Moore, and Oberman, 2018; Griﬃn and Shams, 2020; Cong,

Li, Tang, and Yang, 2021; Li, Shin, and Wang, 2021) and illegal activity (Foley, Karlsen,

and Putnins, 2019), equilibrium pricing of bitcoin (Biais, Bisiere, Bouvard, Casamatta, and

Menkveld, 2020; Pagnotta and Buraschi, 2018) and its adoption (Hinzen, John, and Saleh,

2020), and cryptocurrency valuation (Cong and He, 2019; Cong, Li, and Wang, 2021; Sockin

and Xiong, 2020).

Makarov and Schoar (2019, 2020) document arbitrage opportunities across centralized cryp-

tocurrency exchanges. The apparent price dispersions have been related to explanations

including noise traders (Kr¨uckeberg and Scholz, 2020; Dyhrberg, 2020), liquidity frictions

(Kroeger and Sarkar, 2017), settlement latency (Hautsch, Scheuch, and Voigt, 2019), risk

premiums (Borri and Shaknov, 2021), restrictions to cross-border capital ﬂows (Yu and

Zhang, 2018; Choi, Lehar, and Stauﬀer, 2018). Augustin, Rubtsov, and Shin (2021) docu-

ment an increase in bitcoin’s price eﬃciency following the introduction of bitcoin futures.

Electronic copy available at: https://ssrn.com/abstract=4063228

3 Institutional background

We ﬁrst provide background information on decentralized ﬁnance, yield farming, the Bi-

nance Smart Chain, and PancakeSwap. We then discuss why PancakeSwap is especially

useful for the study of yield farming.

3.1 Decentralized ﬁnance and cryptocurrency yield farming

Decentralized ﬁnance (DeFi) corresponds to an emerging ecosystem of protocols and ﬁ-

nancial applications built on blockchain technology with programmable capacities, such

as Ethereum and Binance Smart Chain. Smart contracts on the blockchain execute all

transactions automatically, without third-party intervention.

According to DeFi Llama

, a public dashboard which provides data on DeFi, the total

dollar value locked (TVL) in decentralized ﬁnancial services is $205.76 billion as of October

11, 2021. This represents a dramatic increase from less than $1 billion in February 2020.

Yield farming is a way of earning income as compensation for providing liquidity to liquidity

pools. Holders of cryptocurrency tokens earn rewards by locking tokens up in liquidity pools,

which issue claims to the pledged tokens. These new claims, called ‘LP tokens’ or ‘ﬂip

tokens’, can be pledged to yield farms that promise yield enhancements. That additional

passive income is paid to yield farming investors using the platform’s governance token.

To an extent, yield farming is a decentralized variant of securities lending, although the chain

of transactions is more complex. The main reason underlying its popularity is the critical

need for platform owners to incentivize liquidity provision to ensure a platform’s long-term

success. In a decentralized exchange, a more liquid pool implies a smaller price impact per

trade, which is desirable for traders. In a lending pool, a larger amount of liquidity in a pool

may drive down the borrowing interest rate, which could attract larger groups of borrowers.

Yield farming is a useful tool to encourage the injection of such liquidity.

Headline rates and promised investment rates in yield farms can be large. Annual yields

north of 100% are commonly observed. There exists, however, signiﬁcant cross-sectional

heterogeneity in promised yields across the farms, as we show in Figure 2.

Yield farming strategies appear to be complex. The total return performance from yield

farming has four components: the realized yield, capital gains from pairs of cryptocurrencies,

fees from trading volume in liquidity pools and yield farms, and impermanent losses driven

by the relative price change of cryptocurrency pairs locked in liquidity pools. Thus, the

complexity of yield farming strategies resembles obfuscated investment strategies observed

https://deﬁllama.com/home. See also Figure 1.

Electronic copy available at: https://ssrn.com/abstract=4063228

in complex structured derivative products (e.g. Henderson and Pearson, 2011; C´el´erier and

Vall´ee, 2017; Egan, 2019; Henderson, Pearson, and Wang, 2020; Shin, 2021).

We focus our analysis on yield farms listed on PancakeSwap, a popular automated market

maker that ranks second in the league tables of decentralized exchanges oﬀering cryptocur-

rency lending services. Transaction costs in PancakeSwap are signiﬁcantly lower than in

other popular decentralized exchanges like Uniswap. This lowers the barriers to entry for

retail investors, who are active investors in yield farms .

The combination of low barriers to entry, a large number of service providers, and complex

investment strategies promising high returns with signiﬁcant downside risk raises concerns

about the protection of retail investors in cryptocurrency markets. These concerns are

underscored by the aggressive stance recently taken by the U.S. Securities and Exchange

Commission, who have become increasingly vocal about enhanced regulatory scrutiny of

decentralized ﬁnancial services. Our work is intended to inform this ongoing debate by

means of assessing the risk and return characteristics of yield farming strategies.

3.2 Binance Smart Chain

Binance Chain was launched by Binance in April 2019. Its main goal is to allow for faster

decentralized trading. The largest and most well-known decentralized application on the

Binance Chain is Binance DEX. Despite its success in DEX trading, Binance DEX embeds

several limitations that limit its ﬂexibility. For example, to guarantee high throughput, the

application does not support smart contracts, which require excess computational resources.

This can, therefore, easily congest the entire network.

Binance Smart Chain (BSC) is a public blockchain running in parallel to the Binance Chain.

Distinctive features of BSC include smart contract functionality and compatibility with the

Ethereum Virtual Machine (EVM). BSC was launched with the purpose of maintaining

the high throughput of Binance Chain while still allowing for smart contracts within the

ecosystem.

In the BSC ecosystem, Binance Coin (BNB) is used as the basic medium of exchange,

similar to the role played by Ether (ETH) in the Ethereum network. End users pay their

transaction fees in BNB and use BNB to trade cryptocurrencies on the many decentralized

exchanges deployed on BSC.

The primary advantages of BSC are its high throughput rate and low transaction fees. BSC

updates its blocks approximately every 3 seconds, using a variant of the Proof-of-Stake

consensus algorithm. More speciﬁcally, it employs Proof-of-Staked Authority (or PoSA), in

which participants stake BNB to become validators of the blocks. As of September 5, 2021,

the platform’s 21 active validators play an important role in keeping the network running.

Electronic copy available at: https://ssrn.com/abstract=4063228

According to the CEO of Binance, Changpeng Zhao

, BSC allows for a maximum of 300

transactions per second. In contrast, Ethereum processes up to a maximum of 16 transac-

tions per second. The current version of BSC is thus about 20 times faster than Ethereum.

BSC transaction fees are also cheaper than those of Ethereum. As of September 5, 2021,

the average transaction fee charged by BSC is $0.399, whereas the average transaction fee

charged by Ethereum is $5.842. In fact, the diﬀerence in fees widens signiﬁcantly when the

Ethereum network becomes congested. For example, the average Ethereum transaction fee

was $71.72 on May 19, 2021, whereas the maxium daily average transaction fee of BSC was

$1.08 on May 11, 2021.

These advantages make BSC one of the strongest competitors to Ethereum. As of October

9, 2021, total transactions on BSC have outpaced those on Ethereum, despite Ethereum pre-

ceding BSC by almost 4 years.

Binance Coin is currently the third largest cryptocurrency

in terms of market capitalization, following Bitcoin and Ethereum.

Another important feature of the BSC is its EVM-compatibility. This implies that the

chain can beneﬁt from the rich universe of Ethereum tools and DApps. For example,

project developers can easily transition their projects between Ethereum and BSC. The

growth of PancakeSwap is in part spurred by the popularity of Uniswap, which is built on

the Ethereum blockchain. This is because a signiﬁcant part of Uniswap’s source code was

directly ported to BSC to build an initial version of PancakeSwap.

3.3 PancakeSwap

PancakeSwap is the largest decentralized exchange built on the Binance Smart Chain. Un-

like traditional ﬁnancial markets employing market-maker systems based on limit order

books, PancakeSwap employs a new system called automated market maker (AMM), im-

plemented through smart contracts. For details on the mechanism of AMMs and their

pricing schedules, see, for example, Lehar and Parlour (2021).

In PancakeSwap, multiple liquidity pools are deployed to facilitate trading of pairs of cryp-

tocurrencies. Investors deposit an equal dollar amount of two cryptocurrencies into a liq-

uidity pool, and thereby become liquidity providers. In exchange for the liquidity provision,

the liquidity provider receives LP tokens to certify their liquidity provision. In return for

their liquidity provision, liquidity providers receive a ﬁxed proportion of trading volume

registered in a pool. Third-party trades on PancakeSwap are charged a fee proportional to

0.25% of the trading volume, of which 0.17% is added to the liquidity pool associated with

the corresponding cryptocurrency pair.

https://twitter.com/cz_binance/status/1361596039698944000.

https://ycharts.com/indicators/ethereum_average_transaction_fee and https://ycharts.com/

indicators/binance_smart_chain_average_transaction_fee_es

Ethereum launched on July 2015, whereas Binance Smart Chain launched on April 2019.

Electronic copy available at: https://ssrn.com/abstract=4063228

In addition to the income generated from trading fees, liquidity providers can earn additional

passive income if the liquidity pool has a corresponding yield farm. Such income, called

farm yield, is earned by staking the LP tokens to the corresponding yield farm. Farm yields

are paid in PancakeSwap’s governance token.

PancakeSwap migrated from version 1 (v1) to version 2 (v2) on April 24, 2021. This

transition was implemented to enhance the platform’s technological and security features.

Both versions have co-existed since then. We study yield farming for both versions.

In PancakeSwap, the CAKE token serves as the governance token for the Decentralized

Autonomous Organization (DAO), where token holders can cast votes to inﬂuence the

future development of the platform.

3.4 PancakeSwap as an ideal laboratory to study yield farming

Numerous decentralized trading venues oﬀer passive income opportunities through yield

farming. Among many DeFi platforms, Uniswap and PancakeSwap consistently lead the

league ranks in terms of their trading activity. The key diﬀerence between these two plat-

forms is that Uniswap runs on the Ethereum blockchain, while PancakeSwap runs on the

Binance Smart Chain.

Several features of PancakeSwap make it particularly appealing for the study of yield farm-

ing. First, and most importantly, Uniswap does not oﬀer yield farms: Liquidity providers

in Uniswap liquidity protocols receive a ﬁxed fraction of trading volume as their passive

income. However, liquidity providers cannot stake their LP tokens in farms in Uniswap to

earn additional income through yield farming.

Second, PancakeSwap is one of the largest decentralized exchanges. In Table 2, we report the

daily trading volume for the ten largest decentralized exchanges as of October 9, 2021. The

largest DEX is dYdX, which is specialized in derivatives trading. Augustin, Rubtsov, and

Shin (2021) discuss the market for regulated and unregulated cryptocurrency derivatives.

The second largest DEX is PancakeSwap (v2) with a 24-hour trading volume of $1,185.34 on

October 9, 2021. PancakeSwap (v2) is followed by Uniswap (v3), 1inch Liquidity Protocol,

Uniswap (v2), and SushiSwap. The trading volume on PancakeSwap (v2) is comparable to

the combined trading volumes of Uniswap (v3) and Uniswap (v2). While the rank tables

vary over time, PancakeSwap is among the leading DEXs focused on spot trading.

Third, the low transaction cost and high transaction speed of Binance Smart Chain make

PancakeSwap easily accessible to retail investors. As discussed in Section 3.2, transaction

costs of the Binance Smart Chain are an order of magnitude lower than those of Ethereum.

Yet, the transaction speed of Binance Smart Chain is faster than that of Ethereum. Ac-

cording to DappRadar

, PancakeSwap registered 435,130 active users on October 24, 2021,

DappRadar: https://dappradar.com/rankings

Electronic copy available at: https://ssrn.com/abstract=4063228

in contrast to 47,730 active users recorded for Uniswap. The number of active users is high-

est for PancakeSwap among all decentralized applications built on all blockchains tracked

by DappRadar. In light of the growing concern about the risks of complex yield farming

strategies for retail investors, our study has policy implications for investor protection.

Fourth, PancakeSwap features a large cross-section of yield farms. This provides important

variation to help understand the risk and return characteristics of yield farms. We study

219 unique yield farms created as of September 5, 2021.

4 Conceptual framework

Yield farming enables investors to earn passive income oﬀ their cryptocurrency holdings by

making tokens available for trading in decentralized markets called farms. Conceptually,

this is akin to a modern version of securities lending with the distinctive feature that

smart contracts operating on permissionless blockchains automatically execute transactions

without involvement of ﬁnancial intermediaries. In practice, the yield farming process is

more complex than traditional securities lending and involves a chain of transactions that,

linked together, deliver returns from “farming for yields.”

Formally, yield farming involves two independent investment decisions. First, an investor

can earn passive income by providing liquidity to a liquidity pool. There is a large menu

of liquidity pools that operate within a decentralized trading platform like PancakeSwap.

Liquidity providers receive liquidity tokens (a.k.a. LP tokens or ﬂip tokens) in exchange for

their liquidity provision.

Second investors can stake LP tokens into a yield farm to earn additional passive income.

That income is paid in the form of the cryptocurrency token that makes up the base currency

of the initial liquidity pool.

The total yield farming return between day t and t + h, R

t,t+h

, is thus equal to:

t,t+h

= R

t,t+h

+ R

t,t+h

, (1)

where R

t,t+h

and R

t,t+h

deﬁne the returns from liquidity provision and the staking of LP

tokens into a yield farm, respectively.

4.1 Liquidity Provision

Liquidity pools are deﬁned in terms of pairs of cryptocurrency tokens. For example, one of

the most popular liquidity pools on PancakeSwap is an automated market for buying and

selling ETH and the cryptocurrency token BNB. To provide liquidity to the ETH/BNB

Electronic copy available at: https://ssrn.com/abstract=4063228

pool, a liquidity provider needs to deposit ETH and BNB in equal amounts, taking into

account their current market prices. For example, if the price of one ETH corresponds to

10 BNB, an investor would need to deposit 10 BNBs for each unit of ETH.

The pools’ aggregate liquidity L

is characterized by the aggregate token valuation, de-

ﬁned by the number of ETH and BNB tokens, α

and α

, and their prices, P

and P

respectively:

= α

· P

+ α

· P

. (2)

Returns to liquidity provision are derived from two sources: growth in the value of the

liquidity pool and fee revenue earned from third party trading activity in the pool, that is:

t,t+h

t+h

+ T rading F ee Return

t,t+h

t+h

· P

t+h

+ α

t+h

· P

t+h

· P

+ α

· P

+ T rading F ee Return

t,t+h

(3)

Intuitively, growth in the value of the liquidity pool is similar to a traditional price return.

The key diﬀerence is that the number of shares α

is neither constant nor based on the

initial investment. Instead, it is time-varying and determined by the trading activity in the

liquidity pool. This feature arises because of the constant-product technology hardwired

into liquidity pools. See Lehar and Parlour (2021) for details.

In exchange for their liquidity provision, investors receive LP tokens to certify their partial

ownership in the pool. While the fractional ownership stays constant over time, the pool’s

liquidity value may change when end users independently buy and sell ETH and BNB. The

terms of trade for end users are such that the product of the quantities available in the pool

is equal to a constant k:

k = α

= α

t+h

. (4)

This implies that the fractional claim to the liquidity pool is constant over time. However,

the number of units of ETH and BNB represented by this claim will change as a result of

variation in the pool’s composition arising from trading activity by end users. Thus, when

a liquidity provider decides to redeem their liquidity tokens in exchange for ETH and BNB,

the number of tokens they receive from redemption may diﬀer from those initially deposited

(i.e., α

t+1

6= α

) despite the same fractional claim to the liquidity pool.

A second feature of the constant-product technology is that the products of price and

quantity have to equalize across assets, that is, for all t:

= α

. (5)

A consequence of the constant-product technology is that the returns to liquidity provision

have two distinct components. Investors are exposed to capital gains/losses resulting from

joint changes in the tokens’ prices and in the pool’s liquidity, since this leads to ﬂuctuations

in the composition of tokens that an investor can claim using the liquidity token. In addition,

Electronic copy available at: https://ssrn.com/abstract=4063228

investors are exposed to impermanent losses, which depend on the relative returns of both

ETH and BNB (i.e., changes in the ratio of token prices). To formalize our discussion, the

return from liquidity growth can be expressed as:

t+h



t,t+h



| {z }

capital gain

−



t,t+h

−

t,t+h



| {z }

impermanent loss

, (6)

where R

t,t+h

= P

t+h

and R

t,t+h

= P

t+h

denote the gross returns of tokens A and

B, corresponding to ETH and BNB in our example. In Appendix B.1, we explicitly show

how the above expression is obtained from the initial liquidity provision that starts with a

nominal dollar investment.

Intuitively, the impermanent loss corresponds to the diﬀerence between the return from

liquidity provision and the return from a buy-and-hold strategy (without pledging the

cryptocurrency tokens to a liquidity pool). Impermanent losses depend non-linearly on

the relative diﬀerence in token returns. Importantly, they are strictly negative and expose

investors to signiﬁcant upside and downside risk analogous to a short volatility exposure

(Aigner and Dhaliwal, 2021). See Appendix B.1 for additional discussion.

The total return from liquidity provision may nonetheless exceed that of a simple buy-

and-hold strategy due to the additional income generated from trading fees. As of August

14, 2021, PancakeSwap charges a trading cost equivalent to 25 basis points (bp) of trading

volume. Part of that (17bp) is passed on to liquidity providers as a fraction c of total trading

volume V

t,t+h

observed over two consecutive time periods t and t + h and proportional to

the initial fractional dollar investment I

in the liquidity pool. Since the return from

trading fees depends on the initial investment, the total fee return is characterized as

T rading F ee Return

t,t+h

= c · ((I

t,t+h

) /I

= c · V

t,t+h

. (7)

4.2 Yield farming

A second passive source of income is generated by staking the liquidity tokens in yield farms

which promise a yield y

. That income is paid in terms of the platforms’s governance token,

which corresponds to Cake in the case of PancakeSwap.

The annualized yield is implicitly deﬁned through a complicated function that depends

on (a) the number of Cake tokens created through the validation of a new block on the

blockchain; (b) the total number of Cake tokens redistributed for staking M

; (c) a farm-

speciﬁc multiplier m

which deﬁnes the number of Cake tokens allocated to the farm with

the creation of a new block; (d) the total liquidity staked to the farm L

staked

; and (e) the

price of Cake P

Cake

The creation of new Cake tokens through blockchain validation corresponds to a rate of

approximately 40 Cake tokens for each three second period. Thus, assuming that 28,800

Electronic copy available at: https://ssrn.com/abstract=4063228

blocks are created each day, the annualized promised yield from staking liquidity tokens to

a yield farm is given by:



365 × 28, 800 × 40 × m



Cake

staked



. (8)

Cake tokens may be allocated to other purposes than yield farming. Therefore, the aggregate

multiplier does not have to correspond to the sum of all multipliers across yield farms on a

platform like PancakeSwap, i.e., M 6=

, where k corresponds to the number of farms.

Note that we explicitly write out the price of the Cake reward for yield farming, P

Cake

because one of the token pair in the liquidity pools does not have to be Cake. Realized

farm yield between t and t + h is thus deﬁned as

Cake

t+h

n=1

t+n−1

Cake

t+n−1



365



. (9)

4.3 Aggregation

Aggregating across all components allows us to decompose the total (h −period) return to

yield farming strategies into four components associated with token capital gains, imper-

manent losses, revenues from trading fees, and realized farm yields:

t,t+h



t,t+h



| {z }

capital gain

−



t,t+h

−

t,t+h



| {z }

impermanent loss

+ c · V

t,t+h

| {z }

trading fee revenue

+ P

Cake

t+h

n=1

t+n−1

Cake

t+n−1



365



| {z }

realized farm yield

. (10)

4.4 Impact of trading frictions

In practice, yield farming involves a chain of transactions that, taken together, may involve

sizable transaction costs. Table A.1 breaks down the chain of transactions for a hypothetical

yield farming strategy. We provide additional details in Appendix B.2.

Harvesting yields at PancakeSwap involves a chain of 12 transactions (excluding step 1 and

14 in Table A.1 that are unrelated to the yield farmer’s transactions). A full round-trip

transaction involves three types of costs associated with gas fees, trading fees, and price

impact. These costs may signiﬁcantly lower the returns from yield farming.

Gas fees correspond to transaction costs associated with the use of BSC’s computational

resources for trade execution. Among the set of 12 transactions, yield farmers have to

Electronic copy available at: https://ssrn.com/abstract=4063228

pay gas fees for 10 of them. The average gas fee for a round-trip of an yield farming in

PancakeSwap is estimated to be $3.28 in our sample period.

Gas fees are especially detrimental to smaller retail investors since the ﬂat fee is more costly

for small stake investments and frequent rebalancing. In addition, since the gas fee applies

to each yield farm, it reduces the beneﬁts of diversifying systematic risk across several yield

farms. An initial $1,000 investment will thus lose about 33 bps in a round-trip transaction

due to gas fees alone, and 33 bps per week for weekly rebalancing. That consideration

is important for retail investors who have a tendency to rebalance too frequently Odean

(1999). A diversiﬁcation strategy across 10 farms would incur a per period cost of 10×3.28

= $32.8, which, for a $1,000 investment, is more than the typical performance fee owed to

a hedge fund, excluding any consideration for hurdle fees or water marks.

Gas fees thus encourage larger and more concentrated investments, which may not be

appropriate for ﬁnancially unsophisticated investors. In our analysis, we consider investment

sizes of $5,000, $10,000, $100,000 and $1,000,000. This allows us to consider cases where

gas fees do not wash out all potential yield farm returns.

Investors also incur trading fees. PancakeSwap charges a fee of 0.25% (proportional to

trading volume) for each transaction. Since yield farmers need to buy and sell tokens in

intermediate steps, they will lose at least an additional 0.50% of their initial investment for

a round-trip transaction. See Appendix B.2 for more details.

The third transaction cost arises through price impact. To quantify price impact, we assume

that yield farmers invest an amount I

corresponding to a constant fraction f of the liquidity

pool value L

, i.e. I

= f ·L

. Equation (6) provides the return to liquidity provision without

frictions. With price impact and ignoring trading fees, the return to liquidity provision is

impacted as follows:

λ(f)



t,t+h



−



t,t+h

−

t,t+h





, (11)

where λ(f) is the price impact function. We illustrate in Panels (a) to (c) of Figure 3 how

price impact relates to investment size. Considering both trading fees and price impact, the

return to liquidity provision reduces to:

(1 − 0.0050)λ(f)



t,t+h



−



t,t+h

−

t,t+h





We emphasize another indirect channel through which yield farming performance is nega-

tively aﬀected. Equation (8) suggests a negative relation between the aggregate liquidity

in a yield farm and the oﬀered farm yield. We provide empirical support for that pattern

in Figure 4. Since liquidity provision increases the size of a farm, it mechanically decreases

the oﬀered farm yield. Hence, too much liquidity provision can be a self-defeating strategy.

Electronic copy available at: https://ssrn.com/abstract=4063228

4.5 Yield farm ﬂows

In our analysis, we examine ﬂows into yield farms. To measure net inﬂows of liquidity,

we, therefore, follow the mutual fund literature (e.g., Sirri and Tufano, 1998; Coval and

Staﬀord, 2007) and deﬁne the measure f low

t,t+h

over an h-period trading horizon

F low

t,t+h

t+h

− L

× R

∗

t,t+h

, (12)

where R

∗

t,t+h

corresponds to the yield farm return deﬁned in Equation (10) net of the realized

farm yield, that is R

∗

t,t+h



t,t+h



−



t,t+h

−

t,t+h



+ c ·V

t,t+h

We exclude the realized farm yield term in our ﬂow deﬁnition because it does not aﬀect the

size of next period’s liquidity pool, unlike capital gains, impermanent losses and trading fees.

The reason is that the farm yield is paid in Cake rather than using the base cryptocurrency

of th liquidity pool or yield farm.

5 Data

We assemble a novel data set of historical yield farm data, including token prices, liquidity

staked to liquidity pools/yield farms and the corresponding token shares, the time-varying

value of liquidity tokens that represent claims to token shares, as well as the yield farm

multipliers. We obtain these data by tracing all transactions on the Binance smart chain,

which forms the underlying plumbing of the PancakeSwap trading platform. We combine the

yield farm data with price and volume data from Binance Smart Chain and cryptocurrency

return factors constructed as in Liu, Tsyvinski, and Wu (2019).

5.1 Farm data

We collect information on all yield farms stored in PancakeSwap’s main staking contract

from the beginning of its existence on September 23, 2020 to September 5, 2021. We ﬁrst

extract from the main staking contract the contract addresses of all liquidity pools that

have a yield farm associated with them. We then reconstruct from the blockchain the time

series of each yield farm’s multiplier at a daily frequency.

An important consideration in our study is the migration from PancakeSwap v1 to Pan-

cakeSwap v2 on April 24, 2021, when the platform upgraded the technological and security

features of its smart contract design. At the time of the switch, liquidity providers in ver-

sion 1 were encouraged to withdraw their liquidity and redeposit it in the corresponding

liquidity pool that was transitioned to version 2. Migrating one’s liquidity was considered

to be a dominant strategy since the new version would pay higher rewards, and failure to

Electronic copy available at: https://ssrn.com/abstract=4063228

migrate could lead to higher transaction costs. Both versions have co-existed since then.

Interestingly, we observe that not all liquidity providers have migrated to the new version.

Since each liquidity pool is uniquely linked to one pair of cryptocurrency tokens, we could

easily identify the contract address of each matching liquidity pool in PancakeSwap v2.

To measure a farm’s yield, we use information on the cryptocurrency shares provided to

each liquidity pool (α

), the aggregate liquidity in each pool (L

), and the total amount of

liquidity tokens staked in each farm (L

staked

). We collect information on cryptocurrency

shares using the tokens’ balances in each pool. Given the tokens’ prices, a pool’s aggregate

liquidity is computed as the aggregate dollar value of a token pair, say, L

= P

We further collect each pool’s aggregate supply of liquidity tokens and the number of such

tokens staked to the yield farms. The aggregate liquidity staked to a farm is then given

by a pool’s aggregate liquidity times the fraction of liquidity tokens that have been staked,

staked

= (# staked LP tokens/Aggregate # of LP tokens) · L

Given the novelty of our yield farm data and the lack of reliable information providers, we

implement several accuracy checks to vet the data reliability. The most important input to

our study is the farm yield described in Equation (8). We veriﬁed its accuracy by collecting

oﬀered farm yields from PancakeSwap’s homepage

at midnight Greenwich Meridian Time

(GMT) on October 11, 2021. We manually veriﬁed that the multipliers collected from the

main staking contract are identical to those advertised on PancakeSwap’s web interface.

Then, we veriﬁed that our imputed farm yields align with those that are publicly listed.

In Figure A.3, we report the relation between our imputed farm yields based on Equation

(8) on the y-axis and those listed by PancakeSwap on the x-axis. All observations are nearly

perfectly aligned with the (red dashed) 45-degree line. A linear projection of the imputed

farm yields on the listed farm yields obtains a slope coeﬃcient of 1.002 with an R

of 1.00.

This is strong supportive evidence for the validity of our data building procedure.

5.2 Price, trade, and gas fee data

We obtain daily price (P

) and trading volume (V

t,t+h

) information for each farm. We source

gas fee data from a proprietary data provider specialized in blockchain data services covering

Bitcoin, Ethereum, Binance Smart Chain, among others. For a pair of cryptocurrency

tokens in a liquidity pool, one typically serves as the numeraire, while the other is considered

a token of interest. For example, in the ETH-BNB pool, ETH is the token of interest and

BNB is the numeraire. In each liquidity pool, the price of the token of interest (e.g. ETH)

is taken to be the most recent end-of-day price in GMT, where the price is expressed in

terms of the numeraire token (e.g. BNB).

To ﬁnd the prices of the numeraire tokens, we proceed in several steps. Table A.2 lists

all numeraire tokens in the 219 liquidity pools and yield farms in our study. Among the

https://pancakeswap.ﬁnance/farms

Electronic copy available at: https://ssrn.com/abstract=4063228

10 numeraire tokens, 4 are stablecoins pegged to the U.S. dollar: Binance USD (BUSD),

TerraUSD (UST), Binance-Peg Tether (USDT), and Binance-Peg USD Coin (USDC). We

collect their prices from CoinMarketCap for conversion. We infer the U.S. dollar value of the

remaining numeraire tokens (e.g., Binance-Peg Ethereum (ETH)) from related token pairs

of other liquidity pools in PancakeSwap. For example, we obtain the price of Binance-Peg

Ethereum (ETH) in terms of Binance Coin (BNB) as numeraire, and the price of Binance

Coin (BNB) in terms of Binance USD (BUSD) as numeraire. Using this approach, we can

back out the price of Binance-Peg Ethereum (ETH) in Binance USD (BUSD) and convert

it to U.S. dollars using the price of Binance USD in U.S. dollars from CoinMarketCap.

If there are no transactions on a given day, we use price information from the previous

trading day instead. The daily trading volume of a pool is deﬁned as the daily sum of

trades across all cryptocurrencies in a given pool, measured in U.S. dollars.

We consider the impact of gas fees on the performance of yield farming strategies. Diﬀerent

functions executed by smart contracts incur diﬀerent gas fees. To accurately impute the

gas fees in the yield farming process, we ﬁrst identify the chain of transactions that incur

gas fees in a round-trip cost (see Table A.1). We then compute the average daily gas fee

in U.S. dollars for each transaction in the chain. In a last step, we compute the gas fee for

one round-trip cost by summing the average gas fee across all corresponding transactions.

5.3 Yield farmers data

We collect transaction data for each of the LP tokens through BscScan

, a freely-accessible

utility for searching data on the BSC. From these transaction logs, we then reconstruct the

holding information of each wallet for each token. Transactions in which a user deposits

cryptocurrency into a certain liquidity pool and receive LP tokens are represented as a LP

token transfer from the null address to the wallet address of the user. Transactions in which

a user stakes/unstakes their LP tokens in a yield farm are represented as a token transfer

to/from the main staking contract. Transactions in which a user redeems their LP tokens

at a liquidity pool in exchange for underlying tokens are represented in the data as a LP

token transfer to the address of the LP token itself.

After collecting the above transaction data for all farms on PancakeSwap, we further re-

ﬁne the scope of our data in a few ways. First, we restrict our attention only to the

accounts active in our sample period. Second, we eliminate wallet addresses belonging to

non-PancakeSwap smart contracts, which may be a yield aggregator or an automated passive

strategy. Finally, we omit wallet addresses that have transacted LP tokens with other, non-

PancakeSwap smart contracts. These addresses employ staking on PancakeSwap as part

of multi-platform investment strategies, which are beyond the scope of our current study.

With the above reﬁnements, we are left with 1,957,867 transactions made by 252,490 unique

https://bscscan.com/

Electronic copy available at: https://ssrn.com/abstract=4063228

wallets active on PancakeSwap throughout our sample period. For accounts with a positive

LP token balance at the end of our sample period, we make the standard assumption that

these positions are exited on the last day of our sample. For each transaction, we match

the price and oﬀered yield of the LP token to the nearest end-of-day price by block height

diﬀerence.

We compute several farmer-level measures of yield farming behavior. First, we compute

No. Farms, the number of liquidity pools that each wallet interacts with. Second, we

deﬁne Eﬃciency as Time Staked/Time in Liquidity Pool where Time Staked and Time in

Liquidity Pool refer to the length of time for which the user has staked their LP tokens in

a yield farm and the length of time for which the user has provided liquidity, respectively.

We average this measure across liquidity pools. Third, we deﬁne Staked Balance and LP

Balance as the time-weighted average balance for staking and liquidity provision. The

prices used in these calculations are the nearest end-of-day price from the beginning of each

holding period, and the weights are the length of each holding period. Finally, we deﬁne

Oﬀered Farm Yield of an yield farmer, as the time-weighted average of the oﬀered yield at

the beginning of each holding period. In order to guarantee that our results are not driven

by very small investors, we choose farmers whose LP Balance is larger than $10. With this

restriction, we are left with 207,699 unique farmers.

One caveat is that yield farmers may own and use multiple wallets. Hence, measures such

as No. Farms, Staked Balance, and LP Balance could be underestimated. We believe that

it is unlikely for yield farmers to systematically use multiple wallets for yield farming: there

are no monetary beneﬁts of doing this, and managing multiple wallets may add additional

eﬀort costs towards implementing yield farming strategies. We are also in the process of

applying several wallet clustering algorithms to our sample in order to allay this concern.

5.4 Cryptocurrrency factors

Liu, Tsyvinski, and Wu (2019) document that a three-factor model using the cryptocurrency

equivalents of the market, size and momentum factors are useful for explaining the cross

section of expected cryptocurrency returns. We replicate these factors using their approach.

We obtain the cross-section of daily closing prices for cryptocurrencies from Coinmarketcap’s

historical API endpoint. For each cryptocurrency, prices are calculated using a volume-

weighted average of prices reported from each of the markets for which Coinmarketcap has

data. Our risk-free rate is from the St. Louis Fed’s one-month constant maturity rate.

We exclude from our sample coins without trading volume data, coins with less than $1

million in market capitalization at the time of portfolio formation, and coins without price

data for the following day. To control for potential outliers, we winsorize the market capi-

talization at the 1st and 99th percentiles during portfolio formulation.

Electronic copy available at: https://ssrn.com/abstract=4063228

For all three factors, we form portfolios at the end of the prior day and consider a one-day

holding period before re-balancing at the end of the day. All returns are measured in terms

of U.S. dollars. The excess cryptocurrency market return is constructed for a value-weighted

portfolio of all coins with data on the portfolio formation day (prior to applying the ﬁlters),

minus the risk-free rate at a daily frequency.

The excess cryptocurrency size factor is constructed as a zero-investment, long-short strat-

egy with a long position deﬁned as the value-weighted portfolio of coins in the bottom

quintile of market capitalizations on the portfolio formation day, and a short position in

the respective top quintile. For the cryptocurrency momentum factor, we further exclude

coins for which the three-week price history is unavailable. The momentum factor is then

constructed as a zero-investment, long-short strategy with a long position deﬁned as the

value-weighted portfolio of coins in the top quintile of three-week momentum on the port-

folio formation day, and a short position in the respective bottom quintile.

In Appendix C.1, we describe our successful replication of Liu, Tsyvinski, and Wu (2019),

suggesting that our cryptocurrency factors are reliably estimated.

6 Evidence

We ﬁrst provide an overview of the data. We then describe the trading behavior of yield

farmers and examine the risk and return characteristics of yield farming strategies. We end

with a discussion on the interpretation of the evidence and the limitations of our analysis.

6.1 Descriptive overview

We illustrate in Panel (a) of Figure 5 the number of active farms during our sample period.

We consider a farm to be active if the farm yield multiplier is nonzero, which means that

liquidity providers staking LP tokens in the farm earn non-negative passive income.

We identify 219 unique active yield farms during our sample period, among which 110 farms

co-exist both in both versions of PancakeSwap. The remaining 109 farms are active in only

one of both versions. The total number of active farms at any period increases quickly from

inception of PancakeSwap to a peak of 160 farms in July 2021.

In Panel (b) of Figure 5, we plot the the Total Value Locked (TVL) in all active farms,

i.e., the aggregate amount of liquidity deposited for yield farming. Yield farming at Pan-

cakeSwap has experienced extraordinary growth, with TVL surpassing $7 billion in May

2021. Analogously to the boom and bust cycles experienced by Bitcoin and other cryp-

tocurrency markets, TVL dropped sharply following its peak and experienced renewed mo-

mentum after the drop in aggregate liquidity.

Electronic copy available at: https://ssrn.com/abstract=4063228

In Figure 6, we provide a histogram of yield farm duration. We deﬁne the duration of a

yield farm to be the period during which the farm oﬀers a non-negative passive income to

yield farmers, that is, the farm’s multiplier is strictly positive. We ﬁnd a signiﬁcant amount

of heterogeneity for the life span of yield farms. The mean (median) duration is 130.22

(111) days with a standard deviation of 84.88 days. Some farms have very short durations.

Each yield farm features a unique pair of cryptocurrency tokens. We report in Table 3 the

ten largest yield farms in terms of their TVL as of September 5, 2021. The largest farm

is associated with CAKE-BNB and recorded TVL of $931.72 million in its pool. The 10th

largest farm is associated with USDC-USDT, which started on June 28, 2021, and recorded

TVL of $103.29 million by the end of our sample period.

There is a signiﬁcant amount of heterogeneity in the yields that are oﬀered by the ten largest

farms reported in Table 3, ranging from 5.82% for USDC-BUSD to 34.90% for CAKE-BNB.

These headline yields look attractive on an annualized basis.

In Panel (a) of Figure 2, we plot the time-variation in the median farm yield together with

its cross-sectional distribution. In Panel (b), we report the same evidence from November

1, 2020 onwards, due to extreme yields oﬀered during the initial phases of yield farming.

These ﬁgures highlight signiﬁcant ﬂuctuations in the median farm yield, which is often

higher than 100%. In addition, there is signiﬁcant variation in dispersion of farm yields, as

is underscored by the ﬂuctuations in the interquartile range of the yield farm distribution.

Such rich variation in yields across farms and across time provides an opportunity to better

understand the drivers of cross sectional variation in the risk and return characteristics of

yield farming strategies and the performance of liquidity provision.

In Table 4, we report the summary statistics of the return performance associated with

yield farming strategies. In Panel A, we focus on annualized returns computed for a daily

trading horizon. The average (median) return to yield farming is 147.7% (193.16%) during

our sample period. This is the average return across the 219 unique yield farms, which

have a duration that is about 129 days, on average. Returns to yield farming are volatile

with a standard deviation that is on average 125.89%. Yield farming generates a return

performance that is negatively skewed (-0.3061), fat-tailed (7.6484) and weakly negatively

serially correlated with a ﬁrst-order autocorrelation coeﬃcient of -0.0999.

In Panel B of Table 4, we provide the same statistics for a weekly trading horizon. the

average yield farm has a duration of 20 weeks. The key diﬀerence at the weekly frequency

is that yield farming performance is weakly positively serially correlated (AC1 coeﬃcient of

0.0407), less negatively serially correlated and less fat tailed.

We also provide information about the returns to liquidity provision that excludes the

staking of liquidity tokens into yield farms (liquidity mining). The returns to liquidity

mining alone are signiﬁcantly smaller with average (median) annualized returns of 19.44%

and 6.30% (57.53% and 53.48%) at the daily and weekly frequency, respectively.

Electronic copy available at: https://ssrn.com/abstract=4063228

Another useful comparison is the return performance of a simple buy-and-hold strategy

that invests into the pair of cryptocurrency tokens associated with a pool. This comparison

is useful because investors face a choice of directly investing into a pair of cryptocurrency

tokens or stake them to a liquidity pool. At the daily (weekly) frequency, a buy-and-hold

strategy earned on average 49.10% (37.59%) on an annualized basis during our sample pe-

riod. Thus, buy-and-hold strategies earn on average about a third of the return performance

of a yield farming strategy, before considering the costs associated with each strategy.

The returns to yield farming may seem extraordinarily large at ﬁrst. This is driven by

our sample period that overlaps with a strong bull market in asset markets in general, and

for cryptocurrencies in particular. We illustrate this by comparing the return performance

of yield farming strategies to other well-known strategies and list that information under

“benchmark strategies” in Table 4.

During the same period, Bitcoin and Ethereum earned an average of 168.72% and 266.41%

on an annualized basis for a daily trading horizon. In comparison, the cryptocurrency

market factor of Liu, Tsyvinski, and Wu (2019) earned 186.27% at the daily frequency,

and the S&P 500 index recorded a performance of 31.70%.

We also ﬁnd that the average

return for MVIS CryptoCompare Digital Assets 10 (100) index is 227.95% (219.20%) on an

annualized basis for a daily trading horizon.

6.2 Evidence of lack of investor sophistication

6.2.1 Evidence from yield farmers data

Several features of the yield farming infrastructure at PancakeSwap enable us to infer infor-

mation about the activities of its participants. In this subsection, we provide some evidence

consistent with cross-sectional variation in sophistication across yield farmers.

First, PancakeSwap migrated to a new version on April 24, 2021 when it upgraded the

technological and security features of its smart contract design. Since then, liquidity pools

and yield farms associated with a particular pair of cryptocurrency tokens have coexisted on

both old and new platforms. Liquidity providers were strongly encouraged to switch their

liquidity provision from version 1 to version 2, but had to trigger the switch themselves.

In Figure 7, we show that a signiﬁcant amount of liquidity remains in the liquidity pools

associated with the old version. This is puzzling since the switch to the new version is

considered to be a strictly dominant investor strategy. Migrating liquidity to the new

version delivers higher rewards for staking the same tokens as in version 1, alongside lower

transaction costs. This is likely a sign of investor inertia or inattention.

We present detailed statistics for the construction of all cryptocurrency factors of Liu, Tsyvinski, and

Wu (2019) in Tables A.3 and A.4.

Electronic copy available at: https://ssrn.com/abstract=4063228

Second, returns to yield farming involve several independent transactions. Investors ﬁrst

need to provide liquidity to liquidity pools. The liquidity tokens that certify the liquidity

provision then need to be independently staked to a yield farm. Combining both transac-

tions is a strictly dominant strategy compared to liquidity provision alone. However, we

show in Figure 8 that the number of LP tokens staked in yield farms is signiﬁcantly lower

than the aggregate amount of LP tokens minted to certify liquidity provision.

We would expect the staking ratio to be equal to one at all times. However, the median

ratio is below one most of the time. The 10th (25th) percentile of the distribution even

drops to as low as 30% (85%). This is further evidence that supports the lack of investor

sophistication in this market. However, we caveat this interpretation with the possibility of

investors staking their LP tokens in third-party yield farm aggregators. While we currently

do not have access to this information, we are in the process of collecting it.

In order to better understand this phenomenon of forgoing farming opportunities, we look to

the trading data for individual yield farmers. Table 7 Panel A shows farmer-level summary

statistics. The average yield farmer invests in 1.81 farms and provides $6,959 of liquidity.

However, Staked Balance, the dollar value of LP tokens staked in yield farms, is substan-

tially lower than LP Balance, the provided liquidity. This suggests that a signiﬁcant proﬁt

generated from farming is lost for investors who miss the farming opportunities possibly due

to the complex nature of trading strategies. Consistent with this ﬁnding, Eﬃciency is 0.82,

which implies that the length of time that the average yield farmer keeps his/her LP tokens

in a farm is signiﬁcantly lower than the length of time that he/she keeps corresponding

liquidity in a liquidity pool.

In Panel B of Table 7, we decompose the farmers into two groups depending on Eﬃciency

using 0.98 as a threshold. Interestingly, we ﬁnd that a large number of farmers do not meet

this eﬃciency requirement. 60,514 farmers’ Eﬃciency measures are less than or equal to

0.98. Although the average LP Balance of the low eﬃciency group is lower than that of the

high eﬃciency group, we ﬁnd that average LP Balance of the low eﬃciency group remains

economically signiﬁcant ($3,099). Their average eﬃciency is also remarkably low (0.40),

and their Oﬀered Farm Yield is relatively high (140%). Overall, the results suggest that a

large number of yield farmers miss a substantial amount of revenue from farming.

In Panel C, we decompose the farmers into quintiles based on their average LP Balance. We

observe that LP Balance is positively correlated with Eﬃciency, suggesting that smaller

yield farmers are more likely to miss their farm yields, which range from 131% to 153%

across quintiles. Nevertheless, we still observe a signiﬁcant fraction of yield farmers missing

farm yields, even in the top quintile. Another interesting observation is that diﬀerences in

average LP Balance are substantial across quintiles. For instance, the average LP Balance

of quintile 1 is only $25.55, whereas that of quintile 5 is $33709. This suggests that there

exists signiﬁcant cross-sectional dispersion in average investment sizes among users of Pan-

cakeSwap. Both very large and small investment sizes could be concerning because they

may generate sub-optimal performance, as illustrated in Section 6.4.

Electronic copy available at: https://ssrn.com/abstract=4063228

6.2.2 Additional suggestive evidence

There exists additional evidence suggesting that a signiﬁcant fraction of yield farmers are

not sophisticated. First, there is suggestive evidence that many investors in PancakeSwap

are small retail investors. According to DappRadar

, PancakeSwap registered 435,130 active

users on October 24, 2021, in contrast to 47,730 active users recorded for Uniswap. The

number of active users on PancakeSwap is the largest among all decentralized applications

built on all blockchains tracked by DappRadar. The trading volume in PancakeSwap was

about $1.2B on October 24, which implies that the average yield farmer in PancakeSwap

traded $2,757.

In addition, survey results suggest that a signiﬁcant fraction of yield farmers are not sophis-

ticated. CoinGecko, a major cryptocurrency data provider, surveyed 1,347 cryptocurrency

investors regarding yield farming in August 2020. (CoinGecko, 2020) Interestingly, a sig-

niﬁcant fraction of yield farmers seem to be overconﬁdent and unsophisticated. According

to the survey, 79% of yield farmers claim to understand the associated risks and rewards of

yield farming to a reasonable extent. However, about 40% of yield farmers report that they

could not read smart contracts to verify potential vulnerabilties or scams of the yield farms.

In addition, 33% of yield farmers do not know what the impermanent loss is, implying that

they are taking risks that they are unaware of.

6.3 Performance of yield farming strategies without transaction costs

In Table 5, we decompose yield farming returns into their four components: capital gains,

impermanent losses, trading fees, and farm yields. We ﬁrst focus on the full sample results.

Farm yields contribute the most to yield farming performance, with an average daily log

return of 153.92%. Capital gains are the second largest contributor, with an annualized

daily log return that is 38.29% on average. This is comparable to the return performance

of the S&P500 index during that period.

We note that capital gains are signiﬁcantly more volatile than farm yields, and that they

have more extreme negative and positive outcomes. The annualized standard deviation

is 124.73%, compared with 3.08% for farm yields, and the wider interquartile range for

capital gains reﬂects the greater kurtosis of 7.72, compared to a a distribution that is much

less fat-tailed for farm yields. The persistence of returns is also diﬀerent across these two

components. While capital gains exhibit weak negative serial correlations, farm yields are

persistent with a ﬁrst order autocorrelation coeﬃcient of 0.7625.

The annualized daily impermanent loss is −41.08% on average. In addition, the distribution

is negatively skewed and exhibits the largest excess kurtosis among all four components, a

DappRadar: https://dappradar.com/rankings

Electronic copy available at: https://ssrn.com/abstract=4063228

value of 49.48. This reﬂects investors’ negative exposure to correlation risk, since imper-

manent losses are exponentially sensitive to the return divergence between the underlying

pairs of cryptocurrency tokens.

The annualized daily trading fee is 11.36%, on average, making it the least important

contributor to yield farming performance. Despite the lower volatility (standard deviation

of 0.72%), trading fees can become important, as demonstrated by the positive skewness

(2.9542) and kurtosis (18.4164).

In Table 5, we report similar statistics for yield farms, sorted into terciles by the magnitude

of their average in-sample oﬀered yield. This sorting exercise reveals a negative relationship

between the headline yields and capital gains performance.

In farms with low headline yields (Tercile 1), capital gains are signiﬁcantly larger than farm

yields (152.12% vs. 51.20%). On the other hand, in farms with high headline yields, capital

gains are highly negative, on average (−84.18%), while farm yields deliver an annualized

daily return of 271.96%. Trading fees and impermanent losses appear similar across all

three terciles.

In Panel B of Table 5, we report the decomposed annualized return performance for weekly

trading horizons. The patterns are broadly similar to those of daily trading horizons.

In Table 6, we perform a variance decomposition. This helps better understand the pro-

portion of variation in the aggregate return series explained by each of the four return

components arising from capital gains, impermanent losses, trading fees, and farm yields.

For the variance decomposition, we split the covariance terms equally for each component.

We report the variance decomposition for the overall population, and for each tercile of the

population sorted by their average oﬀered yield throughout the sample period.

Consistent with the large standard deviations observed for capital gains in Table 5, capital

gains dominate the overall variation of the raw yield farming performance. The proportion

of variation explained by capital gains is close to 100%. This is true at both the daily and

weekly trading horizons.

We assess the value-weighted performance of yield farming strategies in Table 8, using the

pools’ aggregate liquidity as weighting factors. We take the perspective of a U.S. investor

who starts from an initial hypothetical $1 USD investment and ignore all transaction costs.

We compute returns in excess of the three-month U.S. Treasury bill secondary market rate.

We focus on the daily trading frequency in Panel A.

We ﬁnd that, without transaction costs, yield farming was highly proﬁtable during our

sample period. The average value-weighted excess return delivered an annualized return of

237.12%. This is signiﬁcantly larger than the returns to a strategy that focuses only on

liquidity mining (185.98%), and larger than a buy-and-hold strategy in the same pairs of

Electronic copy available at: https://ssrn.com/abstract=4063228

cryptocurrency tokens associated with the liquidity pools (196.28%). All three strategies

deliver negatively skewed performances, with a non-trivial amount of excess kurtosis.

To assess risk-return trade-oﬀs, we standardize the return performance by the annualized

standard deviations and compute Sharpe ratios for all investment strategies. These mea-

sures suggest a lucrative risk-return trade-oﬀ, with values ranging from 2.38 for buy-and-

hold strategies to 2.89 for yield farming.

While Sharpe ratios may appear extraordinarily large, they are comparable to similar mag-

nitudes recorded during our sample period for benchmark trading strategies. For example,

an investment in the S&P 500 Index delivered a Sharpe ratio of 2.37 during the same period.

Sharpe ratios for other comparable investments range from 1.97 for the cryptocurrency mar-

ket factor of Liu, Tsyvinski, and Wu (2019) to 2.41 for an investment in Ethereum. It is

important to note that, for reasons of simplicity and clarity, we do not account for autocor-

relation in our annualization of return volatility. At a weekly measurement frequency, for

instance, yield farming strategies have large and positive autocorrelation coeﬃcients. Cor-

recting for them will increase the annualized standard deviation, and thereby decrease our

reported Sharpe ratios for yield farming strategies. Since these coeﬃcients are much larger

for yield-farming strategies at a weekly frequency compared to our benchmarks, the overall

eﬀect of the correction will worsen the relative performance of yield farming strategies.

We also report alphas estimated using the three-factor cryptocurrency return model of Liu,

Tsyvinski, and Wu (2019). Their framework suggests that a three-factor model with cryp-

tocurrency market, size, and momentum factors can price the cross-section of cryptocur-

rency returns. Thus, we assess the risk-adjusted performance of yield farming performance

relative to this three-factor cryptocurrency benchmark. We ﬁnd that the alpha for yield

farming investments is on average 137.78%. Because of the short and volatile sample period,

this alpha is estimated with a t-statistic of only 1.86.

6.4 Performance of yield farming strategies with transaction costs

The evidence suggests that yield farming delivers attractive returns, with high risk adjusted

returns and Sharpe ratios. We question whether these returns are realistically attainable,

despite the positive bull run observed during our sample period. An important insight of

our study is the careful examination of trading fees and the price impact implicit in staking

cryptocurrency pairs to liquidity pools and in harvesting farm yields.

In Table 9, we document the performance of yield farming strategies, accounting for gas

fees, trading fees and price impact. We then compare these results to the frictionless

benchmark. We add the information ratio using the best ﬁt from the three-factor model of

Liu, Tsyvinski, and Wu (2019) as a benchmark portfolio to compute tracking errors.

Despite the signiﬁcantly lower transaction costs recorded on BSC compared to Ethereum,

gas fees signiﬁcantly lower the return performance. This is because the multiplicity of

Electronic copy available at: https://ssrn.com/abstract=4063228

transactions that are needed for a round-trip transaction can accumulate to non-trivial

amounts, especially with frequent rebalancing.

In Panel A of Table 9, we show the performance of yield farming strategies after accounting

for transaction cots. We consider initial investments ranging from $5,000 to $1,000,000.

The impact of gas fees and trading costs is especially harmful for small size investments,

since they are based on ﬂat dollar amounts. When the investment size is too small, the ﬁxed

transaction costs reﬂect a large proportion of the investment so that they absorb a large

fraction of the positive return performance. This incentivizes larger investment amounts to

reduce the dollar cost basis. However, amounts of $100,000 or more may not be an option

for unsophisticated retail investors and we ﬁnd that a large proportion of investors invest

less than $1,000 in farms in Section 6.2.

On the other hand, when the investment size is too large, there is too much capital relative to

the liquidity provision ability of a pool. Thus, when swapping to get the tokens, the slippage

from illiquidity is too high. We previously discussed that larger investments endogenously

also lead to lower farm yields, thereby putting further downward pressure on the investment

performance. Across the board, we notice that the risk-adjusted performance becomes

negative, as suggested by the negative alphas and information ratios, regardless of the

investment size.

These observations also have implications for diversiﬁcation. A portfolio of fewer yield

farms would save more on ﬁxed transaction costs, but would be more exposed to illiquidity

(slippage) when opening/closing positions, due to higher idiosyncratic risk. In contrast,

holding a more diversiﬁed portfolio of farms would cost more but would lower potential

losses from illiquidity (slippage) when opening/closing positions.

To shed more light on the precise mechanism of these trade-oﬀs, we plot in Figure 10 the

hypothetical return performance of two diversiﬁed yield-farming investment strategies as

a function of investment size. We consider both a value-weighted and an equal-weighted

strategy, whereby the value-weighted (equal-weighted) portfolio consists of all yield farm

returns, beginning on October 20, 2020 and re-balancing every seven days thereafter until

September 5, 2021.

In Panels (a.1), (a.2) and (a.3), we observe a non-monotonic relation between investment size

and return performance in PancakeSwap. For small investment sizes, returns are negative

and volatile, leading to negative Sharpe ratios. The same phenomenon appears for larger

investments sizes close to $10 million. Maximum Sharpe ratios are attained for investment

amounts ranging between $100,000 and $1 million for value-weighted and equal-weighted

portfolios, respectively.

Note that the average return may be less than -100% because the average return is computed based on

log rather than arithmetic returns.

Electronic copy available at: https://ssrn.com/abstract=4063228

Our analysis in Table 9 shows that, besides the drop in yield farming performance, the

impact on performance is dependent on the farm yield distribution. In particular, we

observe the greatest reduction in yield farm performance for farms that oﬀer the highest

headline yields (tercile 3). That impact is especially pronounced for large investments

such as $100,000 and $1,000,000. This important observation leads us to further assess

the relation between ﬂow and performance, since there is important evidence from other

asset markets that suggest investors reach for yield (e.g., Becker and Ivashina, 2015; Choi

and Kronlund, 2018; Chen and Choi, 2021; Bordalo, Gennaioli, and Shleifer, 2016) and

consequentially pursue investment strategies with large headline rates (e.g., Henderson and

Pearson, 2011; C´el´erier and Vall´ee, 2017; Egan, 2019; Henderson, Pearson, and Wang, 2020;

Shin, 2021).

In Panel B of Table 9, we report the yield farming performance when we account for trading

frictions at a weekly trading horizon. The impact on performance is naturally less dramatic,

since portfolio re-balancing happens seven times less frequently. However, we observe the

same pattern in that the biggest price impact is suﬀered by the farms with the highest

headline rates and for large investments. Most importantly, we observe that Sharpe ratios

are in general lower than those of benchmark indexes such as the S&P 500 Index and MVIS

10 Index.

Since we study yield farming at PancakeSwap, we believe our results to be conservative.

We show in Figure 9 the average gas fee incurred in yield farming at PancakeSwap and at

SushiSwap, one of the largest DEX yield farms in Ethereum as of September 5, 2021. For

PancakeSwap, the average cost to enter (exit) yield farming over all days is $1.39 ($1.89).

For SushiSwap, the average cost to enter (exit) over all days is $109.12 ($164.34). Thus,

any impact from transaction costs will likely be ampliﬁed for alternative studies based on

SushiSwap.

We go through the similar data collection process to construct the performance of SushiSwap-

based yield farming strategies. Consistent with our intuition, in Panel (b) of Figure 10, we

ﬁnd that the performance of yield farming strategies in SushiSwap is poor. Both maximum

average return and maximum Sharpe ratio of SushiSwap-based yield farming strategies are

signiﬁcantly lower than those of PancakeSwap-based strategies. For example, the maxi-

mum Sharpe ratio is lower than 1.5 and the Sharpe ratio is particularly low when the size

of investment is low due to high gas cost. The maximum Sharpe ratio is attained at the

investment size of $4-5 million and even at this size of investment, the Sharpe ratio is lower

than that of S&P 500 (2.4).

6.5 The relation between farm ﬂows and performance

In light of the observation that price impact is largest for farms with high headline yields, we

assess the relation between farm ﬂows and performance. To compute farm ﬂows, we closely

follow the mutual fund literature and estimate them using the time series variation in each

Electronic copy available at: https://ssrn.com/abstract=4063228

pool’s aggregate liquidity L

and the per period farm growth due to return performance

t,t+h

(e.g., Sirri and Tufano, 1998; Coval and Staﬀord, 2007). We provide a detailed

description in Section 4. We aggregate ﬂows at the daily frequency to obtain weekly ﬂows.

In Table 10, we report the results from a regression of farm ﬂows on oﬀered farm yield (y

lagged farm ﬂows, and past performance of a yield farming strategy. Speciﬁcally, we regress

F low

t,t+7

= a+by

k=1

·F low

t−7k,t−7(k−1)

h=1

t−7h,t−7(h−1)

+ε

, (13)

including pool ﬁxed-eﬀects and common crypto market factors X

as control variables.

The ﬁrst notable observation is that yield farmers seem to reach for high yields. The

coeﬃcients for Oﬀered Farm Yield are about 0.0149 in columns (1) and (3), both of which

are statistically signiﬁcant at the 5% level. The magnitude is economically signiﬁcant as

well. A one-standard-deviation increase in Oﬀered Farm Yield is associated with a 0.012

(1.2%) increase in one-week ahead Flow. The eﬀect becomes even more signiﬁcant, both

statistically and economically, once we add farm ﬁxed eﬀects to control for farm-speciﬁc

characteristics, such as underlying tokens in the pool. The coeﬃcient is 0.0973 (0.114) in

column (4) ((6)) and it is statistically signiﬁcant at the 1% level. Under these speciﬁcations,

a one-standard-deviation increase in Oﬀered Farm Yield is associated with 0.077-0.091

(7.7% - 9.1%) increase in Flow. This is an economically signiﬁcant magnitude.

High yield seeking behavior is observed in many other ﬁnancial markets (Henderson and

Pearson, 2011; Becker and Ivashina, 2015; Bordalo, Gennaioli, and Shleifer, 2016; C´el´erier

and Vall´ee, 2017; Choi and Kronlund, 2018). A vast majority of this line of research em-

phasizes the role of intermediaries as the source of the reaching-for-yield phenomenon. In

contrast, yield farming operates through smart contracts on decentralized markets without

ﬁnancial intermediation. Our evidence suggests that reaching for yield may also exist in

decentralized ﬁnance. This is of interest since our results imply that reaching for yield

can arise even in the absence of ﬁnancial intermediaries and related agency conﬂicts or

competing incentives.

Another important ﬁnding is that yield farmers chase past performances of yield farming

strategies. The one-week ahead Log return is a strong predictor of next week’s Flow, similar

to what is observed for mutual funds (e.g. Brown, Harlow, and Starks, 1996; Chevalier and

Ellison, 1997; Berk and Green, 2004; Sirri and Tufano, 1998). This is similarly intriguing in

the absence of ﬁnancial intermediation and agency frictions, since ﬁnancial intermediaries

are often cited as important drivers of the positive relation between ﬂows and past returns

(e.g. Chevalier and Ellison (1997); Berk and Green (2004)).

Finally, Figure 11 highlights a notable relationship between past F low and future perfor-

mance of yield farming strategies. Although superior past returns and high oﬀered yields

can generate high inﬂows of liquidity, high inﬂows do not lead to better performance of yield

farming strategies. In fact, higher inﬂows predict lower returns from yield farming strategies

Electronic copy available at: https://ssrn.com/abstract=4063228

in the next 2-3 weeks. This explains a lack of persistence in yield farming returns.

Berk

and Green (2004) propose a model with rational learning and decreasing returns-to-scale

to justify the lack of persistence. In this model, to generate decreasing return-to-scale, it

is crucial to assume that the cost of managing a fund of a certain size is increasing, convex

function with respect to the size of the fund. In yield farming, while higher Flow does not

increase any managial costs, it mechanically drives down oﬀered farm yields, due to the

logic implemented in a smart contract, which can eventually lead to under-performance in

the long run.

7 Conclusion

We provide the ﬁrst characterization of yield farming, a novel decentralized ﬁnancial service

available to retail investors in the cryptocurrency ecosystem. Using a novel hand-collected

data set on 219 yield farms from PancakeSwap, an automated market maker operating on

the Binance Smart Chain, we also assess the yield farming return performance and describe

the associated risks.

While yield farming appears to deliver positive investment performances during our sam-

ple period that is comparable to other standard investment strategies, Sharpe ratios are

signiﬁcantly reduced after accounting for transaction fees and price impact. With daily re-

balancing, risk-adjusted returns become negative. Investors are also exposed to large losses

that are driven by the return diﬀerential of underlying cryptocurrency pairs associated with

yield farms.

We uncover a non-monotonic trade-oﬀ between investment size and return performance.

Small trades are penalized by high nominal transaction costs and low liquidity is associated

with volatile returns. Large trades are less penalized by excessive gas fees, but too much

liquidity provision may lead to price impact and slippage that hurts investors and ampliﬁes

volatility. We ﬁnd that maximum and non-negative Sharpe ratios arise for investment sizes

between $100,000 and $1 million. Thus positive yield farming performance may not be

attainable to small retail investments.

Importantly, we ﬁnd that the price impact is larger for farms that oﬀer higher yields. Our

analysis suggests that this is because ﬂows into farms chase past positive performance.

However, this leads to greater price impact that ultimately lowers excess returns.

Our analysis helps understand the risk and return characteristics of yield farming. Since

this is a complex investment strategy that is easily accessible to retail investors and sub-

ject to signiﬁcant downside risks, we believe that our ﬁndings are helpful to regulators in

determining the need for better risk disclosure and investor protection.

In an untabulated study, we regress the one-week ahead yield farming return on past one-week return

with farm ﬁxed eﬀects and ﬁnd a regression coeﬃcient of 0.0084 that is statistically insigniﬁcant, which

implies that yield farming performance is not persistent.

Electronic copy available at: https://ssrn.com/abstract=4063228

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Electronic copy available at: https://ssrn.com/abstract=4063228

Figure 1: Growing Popularity of Decentralized Finance

In this ﬁgure, we plot the total value locked (TVL) of all decentralized ﬁnance platforms

in billions of dollars, as reported by DeFiLlama. The ﬁgure starts on January 1, 2020 and

ends on September 5, 2021.

Electronic copy available at: https://ssrn.com/abstract=4063228

Figure 2: Oﬀered Farm Yields

In this ﬁgure, we plot the annualized farm yields oﬀered to yield farmers. In Panel (a), we

provide the historical annualized oﬀered farm yields during the period between September

23, 2020 and September 5, 2021. In Panel (b), we restrict our sample period to extend from

October 20, 2020 to September 5, 2021. The solid blue line indicates the median annualized

oﬀered farm yield. Dark and light shaded areas represent the interquartile range, as well as

the 10th and 90th percentiles of the yield farm distribution, respectively.

(a)

(b)

Electronic copy available at: https://ssrn.com/abstract=4063228

Figure 3: Model-Implied Price Impact due to Yield Farming

In this ﬁgure, we illustrate how the size of investment in yield farming creates price impact,

which aﬀects returns from yield farming. The parameter f deﬁnes the relative ratio of the

size of the investment to the size of the liquidity pool, i.e. investment/size of liquidity pool

). Consider two cryptocurrencies A and B in a liquidity pool with token B being

the numeraire token such as BNB or BUSD. Panel (a) shows the relation between f and

the price impact on token A when purchasing token A for providing liquidity (together

with token B) to a pool. The y-axis plots the multiple to the current price of token A in

U.S. dollars. A value of 2 implies that a yield farmer would have to pay twice the current

market price of token A to acquire it for liquidity provision. Panel (b) plots the relation

between f and the price impact on token A when selling it after liquidity withdrawal from

the pool. Panel (c) plots the impact of investment size on gross returns from capital gain

and impermanent loss. For example, λ(f) = 0.5 implies that the gross return of capital

gain and impermanent loss is halved by the price impact.

(a) (b)

(c)

Electronic copy available at: https://ssrn.com/abstract=4063228

Figure 4: Liquidity and Oﬀered Farm Yield

In this ﬁgure, we show the relation between a yield farm’s oﬀered yield and its aggregate

liquidity. The x-axis corresponds to the logarithm of size of liquidity in the yield farm in

units of $1 million. The y-axis corresponds to the logarithm of one plus the annualized

oﬀered farm yield measured in decimal units. (For example, 50% of the annualized farm

yield is 0.5 in decimal units.) The blue dots are observations measured at a daily frequency.

The red dashed line plots the best linear ﬁt obtained by regressing the logarithm of (1 +

annualized oﬀered farm yield) on the logarithm of the size of liquidity in the yield farm.

Electronic copy available at: https://ssrn.com/abstract=4063228

Figure 5: Number of Active Yield Farms and Total Value Locked in PancakeSwap

In this ﬁgure, we plot the number of active farms and Total Value Locked (TVL) in the

sample period between September 23, 2020 (beginning of yield farming at PancakeSwap)

and September 5, 2021, at a weekly frequency. In Panel (a), we provide the time series of

active farms during our sample period. We deﬁne active farms as farms whose multipliers

are larger than 0, implying that investors who stake LP tokens in these farms receive non-

negative yields. In Panel (b), we plot TVL of active farms, or the amount of liquidity

deposited for yield farming. The vertical axis is in millions of USD.

(a)

(b)

Electronic copy available at: https://ssrn.com/abstract=4063228

Figure 6: Duration of Yield Farms

In this ﬁgure, we plot a histogram of yield farm durations (in terms of days) during our

sample period starting on October 20, 2021 and ending on September 5, 2021. The duration

of a yield farm is deﬁned as the number of days during which a farm’s yield multiplier is

positive. Thus, we consider a yield farm to be active/alive as long as staked LP tokens

generate non-zero passive income for yield farmers.

Electronic copy available at: https://ssrn.com/abstract=4063228

Figure 7: Remaining liquidity in PancakeSwap v1 after the launch of PancakeSwap v2

In this ﬁgure, we plot total value locked in liquidity pools of yield farms at PancakeSwap

v1 whose new counterpart yield farms are available in PancakeSwap v2. On April 24,

2021, farms corresponding to liquidity pools in PancakeSwap v1 stopped providing farm

yields. Instead, PancakeSwap encouraged farmers to move to corresponding counterpart

farms available in PancakeSwap v2 so that the existing yield farmers could continue to earn

farm yields. The blue lines in Panels (a) and (b) are total value locked in the liquidity

pools whose new counterpart yield farms are available in PancakeSwap v2. The red dashed

lines in Panels (a) and (b) indicate the date on which PancakeSwap v2 was launched. The

sample period in Panel (a) is from October 20, 2020 to September 5, 2021, whereas Panel

(b) focuses on the period since PancakeSwap v2 was launched.

(a)

(b)

Electronic copy available at: https://ssrn.com/abstract=4063228

Figure 8: Staking Ratio of LP Tokens

In this ﬁgure, we plot the ratio of LP tokens staked in active yield farms listed in Pan-

cakeSwap, relative to the total number of LP tokens distributed as rewards for liquidity

provision in the liquidity pools. Thus, the LP staking ratio is deﬁned as the number of LP

tokens of a liquidity pool staked in its corresponding farm, divided by the total number of

outstanding LP tokens for the liquidity pool. The solid blue line indicates the median an-

nualized oﬀered farm yield. Dark and light shaded areas represent the interquartile range,

as well as the 10th and 90th percentiles of the yield farm distribution, respectively.

Electronic copy available at: https://ssrn.com/abstract=4063228

Figure 9: Average Gas Fee to Enter and Exit a Yield Farming Position

In this ﬁgure, we compute the average gas fee paid by users on PancakeSwap (Panel (a))

and SushiSwap (Panel (b)) to enter (exit) a yield farming position on each day since the

inception of the respective platform. For one round of yield farming, the total gas fee paid is

the entry fee on the portfolio formation day, plus the exit fee on the last day of the holding

period. For PancakeSwap, the average cost to enter (exit) over all days is $1.39 ($1.89).

For SushiSwap, the average cost to enter (exit) over all days is $109.12 ($164.34).

Oct 2020 Jan 2021 Apr 2021 Jul 2021

Cost in USD

(a) PancakeSwap USD Gas Costs

Average Cost to Enter a Yield Farming Position

Average Cost to Exit a Yield Farming Position

Oct 2020 Jan 2021 Apr 2021 Jul 2021

200

400

600

800

Cost in USD

(b) SushiSwap USD Gas Costs

Average Cost to Enter a Yield Farming Position

Average Cost to Exit a Yield Farming Position

Electronic copy available at: https://ssrn.com/abstract=4063228

Figure 10: Investment Size and Investment Performance

In this ﬁgure, we plot the hypothetical performance of two diversiﬁed yield-farming in-

vestment strategies in PancakeSwap and SushiSwap as a function of investment size. In

Panel (a) and Panel (b), we present the results regarding PancakeSwap and SushiSwap,

respectively. The Value-Weighted (Equal-Weighted) investment strategy consists of a value-

weighted (equal-weighted) portfolio of all yield farm returns, beginning on October 20, 2020

and re-balancing every seven days thereafter until September 5, 2021. In all ﬁgures, the

x-axis is the investment size on a logarithmic scale. The y-axis in the ﬁrst panel is the annu-

alized average return. The y-axis in the second panel is the annualized standard deviation

of returns. The y-axis in the third panel is the annualized Sharpe ratio of returns. More

details for speciﬁc investment sizes can be found in Table 9.

(a)

Size of investment (USD)

-4

-2

Annualized Log Return

Value-Weighted Yield Farming

Equal-Weighted Yield Farming

Size of investment (USD)

1.2

1.4

1.6

Annualized Return S.D.

Value-Weighted Yield Farming

Equal-Weighted Yield Farming

Size of investment (USD)

-1

Annualized Sharpe Ratio

Value-Weighted Yield Farming

Equal-Weighted Yield Farming

(a.1) Investment Size vs. Average Log Return

(a.2) Investment Size vs. Standard Deviation of Return

(a.3) Investment Size vs. Sharpe Ratio

Electronic copy available at: https://ssrn.com/abstract=4063228

(b)

Size of investment (USD)

-2

-1

Value-Weighted Yield Farming

Equal-Weighted Yield Farming

Size of investment (USD)

0.8

0.9

1.1

1.2

1.3

1.4

Annualized Return S.D.

Value-Weighted Yield Farming

Equal-Weighted Yield Farming

Size of investment (USD)

-2

-1

Annualized Sharpe Ratio

Value-Weighted Yield Farming

Equal-Weighted Yield Farming

(b.1) Investment Size vs. Average Log Return

(b.2) Investment Size vs. Standard Deviation of Return

(b.3) Investment Size vs. Sharpe Ratio

Electronic copy available at: https://ssrn.com/abstract=4063228

Figure 11: Relationship between Return on Yield Farming and Flow to Yield Farms

In this ﬁgure, we plot the correlation between log returns on yield farming and ﬂows to a

farm. Return on yield farming and ﬂow to a farm are deﬁned in Section 4. The x-axis is the

week diﬀerence (w) between the timing of returns and ﬂows. If w is positive, the timing of

the ﬂow is w weeks after that of the return. If w is negative, the timing of return is w weeks

after that of the ﬂow. The blue bar plots the correlation coeﬃcients for the two variables

and the red error bar plots the 95% conﬁdence interval for the estimated correlation.

Electronic copy available at: https://ssrn.com/abstract=4063228

Table 1: Literature on Decentralized Finance and Decentralized Exchanges

This table summarizes a selection of key academic studies that focus on decentralized exchanges (DEXs) within the emerging

ecosystem of decentralized ﬁnance. We indicate whether the study is primarily of empirical or theoretical nature, and list the

decentralized platforms studied in each paper: Uniswap, SushiSwap, PancakeSwap. We also emphasize whether the study

focuses on liquidity mining/provision and market making, strategic trading and hedging or yield farming.

Theory vs. Empirical DEX Activity

Liquidity Provision/ Strategic Trading/ Yield

Study Theory Empirical Uniswap SushiSwap PancakeSwap Market Making Hedging Farming

Angeris, Kao, Chiang, Noyes, and Chitra (2019) X X X

Aoyagi (2021) X X X

Aoyagi and Ito (2021) X X X X

Neuder, Rao, Moroz, and Parkes (2021) X X X X

Park (2021) X X X X

Lehar and Parlour (2021) X X X X X

Han, Huang, and Zhong (2021) X X X

Capponi and Jia (2021) X X X X X

This study X X X X

Electronic copy available at: https://ssrn.com/abstract=4063228

Table 2: Top 10 Cryptocurrency Decentralized Exchanges

In this table, we report information regarding the 10 largest cryptocurrency decentralized

exchanges in terms of daily trading volume as of October 9, 2021. For each exchange, we

provide information on the daily trading volume (in $ million), the market share (in %),

the number of markets at the exchange, the exchange type (swap, aggregator, order book,

...), whether spots or derivatives are traded on a DEX, and the month/year in which the

exchange was launched. Source: https://coinmarketcap.com/rankings/exchanges/dex/.

Rank DEX Daily Volume Mkt Share # Markets Type Spot Launch

($ million) (%) /Derivatives Date

1 dYdX $1,756.41 25.05% 13 Orderbook Derivatives Apr 2019

2 PancakeSwap (V2) $1,185.34 16.90% 1667 Swap Spot Apr 2021

3 Uniswap (V3) $789.82 11.26% 627 Swap Spot May 2021

4 1inch Liquidity $515.69 7.35% 26 Swap Spot Dec 2020

Protocol

5 Uniswap (V2) $287.57 4.10% 1556 Swap Spot Nov 2018

6 Sushiswap $278.78 3.98% 387 Swap Spot Sep 2020

7 Honeyswap $220.18 3.14% 66 Swap Spot Jul 2020

8 MDEX $206.81 2.95% 140 Swap Spot Jan 2021

9 QuickSwap $96.52 1.38% 330 Swap Spot Oct 2020

10 Raydium $93.89 1.34% 112 Swap Spot Feb 2021

Electronic copy available at: https://ssrn.com/abstract=4063228

Table 3: Top 10 Yield Farms in PancakeSwap

In this table, we report information regarding top 10 farms in terms of total value locked

(TVL) as of the end of our sample period, September 5, 2021. For each farm deﬁned by a

unique cryptocurrency pair, we provide information on the start date of a farm, annualized

oﬀered farm yield (in %), and total value locked (TVL, in $ million).

Farm Cryptocurrency Start Date TVL Oﬀered Farm Yield

Rank Pairs ($ million) (%)

1 CAKE-BNB 23-Sep-2020 931.72 34.90%

2 BUSD-BNB 23-Sep-2020 506.74 18.06%

3 USDT-BUSD 1-Oct-2020 285.28 7.15%

4 USDT-BNB 13-Oct-2020 278.04 17.51%

5 ETH-BNB 6-Oct-2020 250.73 8.14%

6 BTCB-BNB 6-Oct-2020 169.60 12.07%

7 USDC-BUSD 12-Jan-2021 140.96 5.82%

8 MBOX-BNB 8-Jun-2021 122.68 6.62%

9 BTCB-BUSD 29-Apr-2021 114.71 17.69%

10 USDC-USDT 28-Jun-2021 103.29 7.86%

Electronic copy available at: https://ssrn.com/abstract=4063228

Table 4: Summary Statistics

In this table, we report summary statistics on the return characteristics from yield farming and alternative investment

strategies. The sample period is October 20, 2020 to September 5, 2021. The sample includes 219 unique liquidity pools

associated with 219 unique yield farms. In Panel A, we report the cross-sectional average daily mean (Mean), median

(Median), 25th (p25) and 75th (p75) percentiles of the log return distribution and the corresponding standard deviation

(SD), skewness (Skew), kurtosis (Kurt), the ﬁrst order autocorrelation coeﬃcient (AC1), the number of time series (#T S)

and the average number of observations for each time series (OBS). In Panel B, we report the same information aggregated

at a weekly frequency starting from October 20, 2020. All return-based statistics are annualized.

Panel A: Daily

Variable Mean SD p25 Median p75 Skew Kurt AC1 #TS OBS

Yield Farming Related Strategy

Yield Farming 1.4770 1.2589 -10.7408 1.9316 13.8564 -0.3061 7.6484 -0.0999 219 129.4749

Liquidity Mining 0.1944 1.2869 -12.2038 0.5753 12.6476 -0.3148 7.7429 -0.0974 219 129.4749

Buy and Hold (Capital Gain) 0.4910 1.2770 -11.7385 0.5155 12.2615 -0.0900 7.8647 -0.0944 219 129.4749

Benchmark Strategy

Bitcoin 1.6872 0.8184 -6.6577 0.9842 10.2659 -0.0602 4.5463 -0.0723 1 321

Ethereum 2.6641 1.1056 -9.3253 3.3788 15.5856 -0.5416 7.4258 -0.0893 1 321

MVIS 10 index 2.2795 1.0574 -7.8283 2.9056 15.0479 -0.7909 7.4093 -0.1282 1 321

MVIS 100 index 1.9048 0.9186 -6.9797 1.6245 12.8309 -0.6778 6.5268 -0.1336 1 321

Crypto Market Return 1.8627 0.9469 -5.7472 3.7891 11.9020 -1.4206 10.9296 -0.1654 1 321

S&P 500 index 0.3170 0.1337 -0.7547 0.3198 1.6078 -0.5792 4.9087 -0.0679 1 221

Panel B: Weekly

Variable Mean SD p25 Median p75 Skew Kurt AC1 #TS OBS

Yield Farming Related Strategy

Yield Farming 1.6976 1.1884 -2.9113 1.9471 6.6150 -0.1660 3.7229 0.0407 219 20.3881

Liquidity Mining 0.0630 1.2472 -4.7842 0.5348 5.2841 -0.2664 3.7847 0.0317 219 20.3881

Buy and Hold (Capital Gain) 0.3759 1.2015 -4.1795 0.4920 5.0737 -0.1368 4.0227 0.0230 219 20.3881

Benchmark Strategy

Bitcoin 1.6072 0.8039 -1.5417 1.9565 5.0711 -0.1920 3.6945 0.0506 1 45

Ethereum 2.4798 0.9592 -1.2047 1.8896 7.6812 -0.0942 3.4519 0.1703 1 45

MVIS 10 index 2.1920 0.8930 -1.0153 2.1312 5.5719 -0.5030 3.9603 0.1024 1 45

MVIS 100 index 1.8275 0.7417 -0.4450 2.0685 4.1985 -0.7626 4.4258 0.1546 1 45

Crypto Market Return 1.7272 0.7913 -1.5302 2.5532 5.1645 -1.0549 5.0982 0.2006 1 45

S&P 500 index 0.3230 0.1351 -0.3794 0.3520 0.6915 0.7631 4.6875 -0.4165 1 45

Electronic copy available at: https://ssrn.com/abstract=4063228

Table 5: Return Decomposition

In this table, we decompose each return series into the contributions arising from (a) capital

gains, (b) impermanent losses, (c) trading fees, and (d) farm yields. The sample period is

October 20th, 2020 to September 5th, 2021. In Panel A, we report summary statistics

on the return characteristics for each component. We report the cross-sectional average

daily mean log return (Ret) median (Median), 25th (p25) and 75th (p75) percentiles of the

log return distribution and the corresponding standard deviation (SD), skewness (Skew),

kurtosis (Kurt), the ﬁrst order autocorrelation coeﬃcient (AC1), and the average number

of observations for each time series (OBS). We also report the same information sorted

by terciles in terms of average in-sample oﬀered yield. In Panel B, we report the same

information aggregated at a weekly frequency starting from October 20, 2020. All return-

based statistics are annualized.

Panel A: Daily

Component Mean SD p25 Median p75 Skew Kurt AC1 OBS

Full Sample

Capital Gains 0.3829 1.2473 -11.8466 0.5121 12.3606 -0.0750 7.7172 -0.1022 129.4749

Impermanent Loss -0.4108 0.0767 -11.8466 -0.0884 -0.0220 -5.5866 49.4831 0.0951 129.4749

Trading Fees 0.1136 0.0072 0.0475 0.0768 0.1348 2.9542 18.4164 0.4701 129.4749

Farm Yields 1.5392 0.0308 1.1351 1.4704 1.8573 0.9113 5.4694 0.7625 129.4749

Tercile 1

Capital Gains 1.5524 1.0403 -8.2413 1.3081 11.1555 0.0160 8.4568 -0.1375 176.9863

Impermanent Loss -0.2530 0.0473 -8.2413 -0.0493 -0.0107 -6.6853 71.5797 0.1203 176.9863

Trading Fees 0.1137 0.0093 0.0448 0.0722 0.1318 3.0882 21.4939 0.5547 176.9863

Farm Yields 0.5298 0.0162 0.3268 0.4561 0.6560 1.5669 8.4307 0.8110 176.9863

Tercile 2

Capital Gains 0.4381 1.2154 -11.0216 0.3898 11.6992 -0.0009 8.0638 -0.0888 113.2055

Impermanent Loss -0.4002 0.0654 -11.0216 -0.0807 -0.0187 -5.3846 42.6768 0.1089 113.2055

Trading Fees 0.1144 0.0066 0.0457 0.0753 0.1347 3.1567 19.7484 0.4815 113.2055

Farm Yields 1.3681 0.0354 0.9040 1.2894 1.7581 0.6009 3.8779 0.8166 113.2055

Tercile 3

Capital Gains -0.8418 1.4861 -16.2769 -0.1616 14.2270 -0.2401 6.6310 -0.0805 89.2329

Impermanent Loss -0.5792 0.1174 -16.2769 -0.1353 -0.0365 -4.6900 34.1930 0.0563 89.2329

Trading Fees 0.1127 0.0056 0.0519 0.0828 0.1378 2.6308 14.1237 0.3759 89.2329

Farm Yields 2.7196 0.0409 2.1746 2.6657 3.1579 0.5660 4.0995 0.6598 89.2329

Electronic copy available at: https://ssrn.com/abstract=4063228

Panel B: Weekly

Component Mean SD p25 Median p75 Skew Kurt AC1 OBS

Full Sample

Capital Gains 0.3461 1.2002 -4.1780 0.4610 5.0141 -0.1377 4.0485 0.0272 20.388

Impermanent Loss -0.5088 0.1371 -4.1780 -0.1405 -0.0348 -2.2584 8.7455 0.0195 20.388

Trading Fees 0.1096 0.0147 0.0478 0.0743 0.1335 1.7011 6.0237 0.3370 20.388

Farm Yields 1.3756 0.0821 0.9822 1.2894 1.6796 0.6626 3.9011 0.5046 20.388

Tercile 1

Capital Gains 1.5212 1.0023 -2.5983 1.4304 5.6450 0.0347 4.2930 0.0100 27.299

Impermanent Loss -0.3026 0.0900 -2.5983 -0.0843 -0.0199 -2.7355 12.4430 0.0083 27.299

Trading Fees 0.1143 0.0142 0.0497 0.0804 0.1403 1.5098 5.4746 0.4405 27.299

Farm Yields 0.5120 0.0414 0.3160 0.4306 0.6290 1.1461 4.7528 0.5899 27.299

Tercile 2

Capital Gains 0.1257 1.1676 -4.0669 0.4520 4.3535 -0.1662 4.2069 -0.0238 18.045

Impermanent Loss -0.5512 0.1567 -4.0669 -0.1402 -0.0351 -2.2074 8.0561 -0.0019 18.045

Trading Fees 0.1279 0.0165 0.0592 0.0857 0.1609 1.8292 6.4456 0.2905 18.045

Farm Yields 1.3377 0.0938 0.9119 1.2394 1.6932 0.4193 3.6178 0.5361 18.045

Tercile 3

Capital Gains -0.6087 1.4307 -5.8688 -0.4995 5.0439 -0.2816 3.6458 0.0953 15.821

Impermanent Loss -0.6726 0.1645 -5.8688 -0.1969 -0.0494 -1.8322 5.7375 0.0520 15.821

Trading Fees 0.0865 0.0132 0.0345 0.0569 0.0993 1.7691 6.1683 0.2789 15.821

Farm Yields 2.2773 0.111 1.7187 2.1982 2.7166 0.4224 3.3329 0.3878 15.821

Electronic copy available at: https://ssrn.com/abstract=4063228

Table 6: Variance Decomposition

In this table, we report the proportion of variation in the aggregate return series explained

by each of the four return components arising from (a) capital gains, (b) impermanent

losses, (c) trading fees, and (d) farm yields. For the variance decomposition, we split the

covariance terms equally for each component. We report the variance decomposition for

the overall population, and for each tercile of the population sorted by their average oﬀered

yield throughout the sample period. The sample period is October 20, 2020 to September

5, 2021.

Panel A: Daily

Component Full Sample Tercile 1 Tercile 2 Tercile 3

Capital Gains 0.9995 1.0077 1.0073 0.9836

Impermanent Loss -0.0059 -0.0132 -0.0137 0.0091

Trading Fees 0.0011 0.0019 0.0011 0.0003

Farm Yields 0.0053 0.0036 0.0053 0.0071

Panel B: Weekly

Component Full Sample Tercile 1 Tercile 2 Tercile 3

Capital Gains 1.0055 1.0073 1.0142 0.9949

Impermanent Loss -0.0141 -0.0304 -0.0159 0.0039

Trading Fees 0.0072 0.0191 0.0016 0.0010

Farm Yields 0.0014 0.0041 0.0001 0.0002

Electronic copy available at: https://ssrn.com/abstract=4063228

Table 7: Lack of Sophistication of Yield Farmers

In this table, we report the statistics that describe behaviors of yield farmers. The presented

statistics are all farmer-level variables. In Panel A, we present summary statistics of yield

farmers. No. Farms is the number of farms in which an yield farmer invests. Staked Balance

is the dollar value of LP tokens staked in farms. LP Balance is the dollar value of LP tokens.

Eﬃciency is average of eﬃciency of each farm. Eﬃciency is deﬁned as the length of time

for which the user has staked his/her LP tokens in a farm divided by the length of the time

for which the user has kept the liquidity in a corresponding liquidity pool. Oﬀered Farm

Yield is time-weighted average of the oﬀered yield at the beginning of the holding period.

In Panel B, we decompose the yield farmers into two groups depending on the Eﬃciency

using 0.98 as a threshold. In Panel C, we decompose the yield farmers into quintiles by LP

Balance.

Panel A: Yield Farmers

Variables Mean SD p25 Median p75 OBS

No. Farms 1.81 1.52 1.00 1.00 2.00 207,699

Staked Balance ($) 6,539.36 201,986.99 33.95 173.26 823.89 207,699

LP Balance ($) 6,959.62 203,816.10 61.88 222.05 954.66 207,699

Eﬃciency 0.82 0.35 0.95 1.00 1.00 207,699

Oﬀered Farm Yield 1.53 1.35 0.27 1.24 2.59 207,699

Panel B: Yield Farmers by Eﬃciency

No. Farms Staked LP Eﬃciency Oﬀered OBS

Balance ($) Balance ($) Farm Yield

Eﬃciency≤0.98

Mean 1.59 1,695.34 3,099.74 0.40 1.40 60,514

(SD) (1.36) (37,885.67) (62,729.03) (0.41) (1.48)

Eﬃciency>0.98

Mean 1.90 8,530.95 8,546.58 0.998 1.58 147.185

(SD) (1.57) (238,682.27) (238,734.04) (0.004) (1.29)

Panel C: Yield Farmers by LP Balance.

No. Farms Staked LP Eﬃciency Oﬀered OBS

Balance ($) Balance ($) Farm Yield

Quintile 1

Mean 1.446 17.938 25.553 0.672 1.530 41540

S.D. (0.990) (14.335) (10.581) (0.437) (1.500)

Quintile 2

Mean 1.592 68.277 84.421 0.797 1.610 41540

S.D. (1.181) (38.069) (24.726) (0.368) (1.374)

Quintile 3

Mean 1.829 204.396 236.434 0.855 1.614 41539

S.D. (1.493) (99.663) (71.232) (0.318) (1.313)

Quintile 4

Mean 1.999 660.956 742.677 0.883 1.581 41540

S.D. (1.676) (324.585) (260.844) (0.290) (1.298)

Quintile 5

Mean 2.198 31745.103 33708.856 0.917 1.310 41540

S.D. (1.941) (450779.453) (454767.188) (0.248) (1.235)

Electronic copy available at: https://ssrn.com/abstract=4063228

Table 8: Returns from Yield Farming Portfolios

This table reports the summary statistics for percentage excess returns from yield farming investment strategies. We take the

perspective of a U.S. investor and report all information from the perspective of an initial USD investment. Excess returns

are computed relative to the three-month U.S. Treasury bill secondary market rate source from the Federal Reserve Bank

of St.Louis. All returns are value-weighted using the pools’ aggregate liquidity as weighting factors. The column (OBS)

reports the number of observations. We report the mean return (Mean), the standard deviation, 25th percentile, median,

75th percentile, skewness, and kurtosis of the yield farming strategies, as well as the serial correlation, the Sharpe ratio, the

alpha from a three factor model based on the work of Liu, Tsyvinski, and Wu (2019), and the t-statistic for alpha from

the three-factor regressions. The sample period is October 20, 2020 to September 5, 2021. All return-based statistics are

annualized. Because we report excess returns and alphas as annualized log returns, the mean return and alpha can be lower

than −1, unlike arithmetic returns.

Panel A: Daily

Strategy Mean SD p25 Median p75 Skew Kurt AC1 SR α t-stat of α OBS

Yield Farming Related Strategy

Yield Farming 2.3712 0.8194 -4.7524 2.5652 10.8074 -0.2228 9.8805 -0.0969 2.8938 1.3778 1.8653 321

Liquidity Mining 1.8598 0.8164 -5.2658 1.8591 10.3550 -0.2635 9.8465 -0.1028 2.2782 0.4454 0.7994 321

Buy and Hold (Capital Gain) 1.9628 0.8235 -5.3285 1.9200 10.4074 -0.0110 9.9887 -0.0979 2.3835 0.6137 1.0024 321

Benchmark Strategy

Bitcoin 1.6872 0.8184 -6.6577 0.9842 10.2659 -0.0602 4.5463 -0.0723 2.0617 -0.2851 -0.6508 321

Ethereum 2.6641 1.1056 -9.3253 3.3788 15.5856 -0.5416 7.4258 -0.0893 2.4096 0.1948 0.2920 321

MVIS 10 index 2.2795 1.0574 -7.8283 2.9056 15.0479 -0.7909 7.4093 -0.1282 2.1557 321

MVIS 100 index 1.9048 0.9186 -6.9797 1.6245 12.8309 -0.6778 6.5268 -0.1336 2.0736 321

Crypto Market Return 1.8627 0.9469 -5.7472 3.7891 11.9020 -1.4206 10.9296 -0.1654 1.9672 321

S&P 500 index 0.3170 0.1337 -0.7547 0.3198 1.6078 -0.5792 4.9087 -0.0679 2.3707 221

Panel B: Weekly

Strategy Mean SD p25 Median p75 Skew Kurt AC1 SR α t-stat of α OBS

Yield Farming Related Strategy

Yield Farming 2.4294 0.8182 -0.7666 1.8066 4.4608 0.2980 3.6981 0.2875 2.9692 1.3125 1.6202 45

Liquidity Mining 1.9008 0.8048 -1.4499 1.4603 4.1851 0.2101 3.6353 0.2661 2.3620 0.3867 0.6565 45

Buy and Hold (Capital Gain) 2.0114 0.8322 -1.2989 1.5381 4.2499 0.3494 3.8112 0.2664 2.4170 0.4965 0.7489 45

Benchmark Strategy

Bitcoin 1.6072 0.8039 -1.5417 1.9565 5.0711 -0.1920 3.6945 0.0506 1.9993 0.0256 0.0405 45

Ethereum 2.4798 0.9592 -1.2047 1.8896 7.6812 -0.0942 3.4519 0.1703 2.5853 0.9998 0.9839 45

MVIS 10 index 2.1920 0.8930 -1.0153 2.1312 5.5719 -0.5030 3.9603 0.1024 2.4547 45

MVIS 100 index 1.8275 0.7417 -0.4450 2.0685 4.1985 -0.7626 4.4258 0.1546 2.4639 45

Crypto Market Return 1.7272 0.7913 -1.5302 2.5532 5.1645 -1.0549 5.0982 0.2006 2.1829 45

S&P 500 index 0.3230 0.1351 -0.3794 0.3520 0.6915 0.7631 4.6875 -0.4165 2.3919 45

Electronic copy available at: https://ssrn.com/abstract=4063228

Table 9: Impact of Trading Frictions on Returns from Yield Farming Portfolios

This table reports the summary statistics for percentage excess returns from yield farming investment strategies, accounting

for trading costs and price impact. We take the perspective of a U.S. investor and report all information from the perspective

of an initial USD investment. Excess returns are computed relative to the three-month U.S. Treasury bill secondary market

rate sourced from the Federal Reserve Bank of St.Louis. All returns are value-weighted using the pools’ aggregate liquidity as

weighting factors. The column (OBS) reports the number of observations. We report the mean return (M ean), the standard

deviation, skewness, and kurtosis of the yield farming strategies. We also report the Sharpe ratio (SR), information ratio

(IR), the alpha from a three factor model based on the work of Liu, Tsyvinski, and Wu (2019), and the t-statistic for alpha

from the three-factor regressions. The sample period is October 20, 2020 to September 5, 2021. All return-based statistics

are annualized. Because we report excess returns and alphas as annualized log returns, the mean return and alpha can be

lower than −1, unlike arithmetic returns.

Panel A: Daily

Strategy Mean SD SR IR α t-stat of α OBS

Frictionless benchmark

Yield Farming (Full Sample) 2.3712 0.8194 2.8938 2.0745 0.8624 1.8653 321

Yield Farming (Tercile 1) 2.0915 0.7198 2.9055 2.0981 0.7668 1.8865 321

Yield Farming (Tercile 2) 3.2008 1.1479 2.7885 1.8959 0.1006 1.7047 321

Yield Farming (Tercile 3) 3.0816 1.1921 2.5851 1.1550 0.7860 1.0385 321

Gas fee, Trading fee & Price impact ($5,000)

Yield Farming (Full Sample) -26.4169 1.3840 -19.0869 -25.0460 -27.9663 -22.5199 321

Yield Farming (Tercile 1) -7.7689 0.8175 -9.5034 -18.5515 -9.1026 -16.6804 321

Yield Farming (Tercile 2) -6.7097 1.2287 -5.4610 -12.8857 -8.8066 -11.5860 321

Yield Farming (Tercile 3) -6.8976 1.2708 -5.4276 -11.7501 -9.1889 -10.5650 321

Gas fee, Trading fee & Price impact ($10,000)

Yield Farming (Full Sample) -13.5242 1.0002 -13.5209 -23.0259 -15.0443 -20.7035 321

Yield Farming (Tercile 1) -3.7343 0.7526 -4.9621 -12.5993 -5.0622 -11.3286 321

Yield Farming (Tercile 2) -2.6828 1.1772 -2.2790 -7.7721 -4.7775 -6.9883 321

Yield Farming (Tercile 3) -2.9473 1.2199 -2.4161 -7.2670 -5.2353 -6.5341 321

Gas fee, Trading fee & Price impact ($100,000)

Yield Farming (Full Sample) -2.6171 0.8253 -3.1710 -9.7941 -4.1261 -8.8063 321

Yield Farming (Tercile 1) -0.3128 0.7212 -0.4337 -4.4779 -1.6416 -4.0262 321

Yield Farming (Tercile 2) 0.4327 1.1480 0.3769 -2.8528 -1.6692 -2.5651 321

Yield Farming (Tercile 3) -1.0320 1.1933 -0.8648 -4.8001 -3.3647 -4.3160 321

Gas fee, Trading fee & Price impact ($1,000,000)

Yield Farming (Full Sample) -2.6072 0.8204 -3.1778 -9.8129 -4.1454 -8.8232 321

Yield Farming (Tercile 1) -1.5290 0.7270 -2.1032 -7.6089 -2.9082 -6.8415 321

Yield Farming (Tercile 2) -3.8629 1.1715 -3.2975 -9.2186 -6.0497 -8.2888 321

Yield Farming (Tercile 3) -16.3170 1.6737 -9.7489 -13.7716 -19.1047 -12.3826 321

Electronic copy available at: https://ssrn.com/abstract=4063228

Panel B: Weekly

Strategy Mean SD SR IR α t-stat of α OBS

Frictionless benchmark

Yield Farming (Full Sample) 2.4294 0.8182 2.9692 1.9616 0.8345 1.6202 45

Yield Farming (Tercile 1) 2.2181 0.7227 3.0691 2.0365 0.7761 1.6821 45

Yield Farming (Tercile 2) 2.9351 1.1181 2.6250 1.5503 0.8426 1.2805 45

Yield Farming (Tercile 3) 3.4141 1.2372 2.7594 1.5633 1.1650 1.2912 45

Gas fee, Trading fee & Price impact ($5,000)

Yield Farming (Full Sample) -1.5554 0.9705 -1.6027 -6.2233 -3.4437 -5.1404 45

Yield Farming (Tercile 1) 0.8462 0.7563 1.1188 -1.7431 -0.6884 -1.4398 45

Yield Farming (Tercile 2) 1.5449 1.1528 1.3401 -1.1207 -0.6338 -0.9257 45

Yield Farming (Tercile 3) 1.9968 1.2713 1.5707 -0.4265 -0.3298 -0.3523 45

Gas fee, Trading fee & Price impact ($10,000)

Yield Farming (Full Sample) 0.2140 0.8754 0.2444 -3.3110 -1.5210 -2.7348 45

Yield Farming (Tercile 1) 1.4016 0.7371 1.9016 -0.2204 -0.0847 -0.1821 45

Yield Farming (Tercile 2) 2.0990 1.1339 1.8512 -0.0569 -0.0315 -0.0470 45

Yield Farming (Tercile 3) 2.5397 1.2526 2.0275 0.3447 0.2629 0.2848 45

Gas fee, Trading fee & Price impact ($100,000)

Yield Farming (Full Sample) 1.7146 0.8216 2.0867 0.2628 0.1123 0.2171 45

Yield Farming (Tercile 1) 1.8715 0.7231 2.5883 1.1305 0.4315 0.9338 45

Yield Farming (Tercile 2) 2.5264 1.1179 2.2599 0.8114 0.4457 0.6702 45

Yield Farming (Tercile 3) 2.7842 1.2345 2.2553 0.7709 0.5837 0.6368 45

Gas fee, Trading fee & Price impact ($1,000,000)

Yield Farming (Full Sample) 1.7076 0.8148 2.0956 0.3298 0.1414 0.2724 45

Yield Farming (Tercile 1) 1.6874 0.7169 2.3536 0.7577 0.2913 0.6258 45

Yield Farming (Tercile 2) 1.9163 1.1038 1.7360 -0.1502 -0.0838 -0.1241 45

Yield Farming (Tercile 3) 0.4974 1.2779 0.3892 -1.5780 -1.3805 -1.3034 45

Electronic copy available at: https://ssrn.com/abstract=4063228

Table 10: Flow Regressions

In this table, we report the results for the liquidity ﬂow regressions. We regress the farm

Flow over the next 7 days (a week) on Oﬀered Farm Yield, past Flow, past Log return

on yield farming, past Log crypto MKT return, and Log (Liquidity). Flow, Oﬀered Farm

Yield, past Log return, and Log (Liquidity) are deﬁned in Section 4. Log crypto MKT

return is logarithm of the cryptocurrency market return, the construction process for which

is explained in Section 5.4 in detail. The sample period is October 20, 2020 to September

5, 2021. Standard errors are clustered at the farm level.

∗

∗∗

, and

∗∗∗

indicate statistical

signiﬁcance at the 10%, 5%, and 1% levels, respectively.

(1) (2) (3) (4) (5) (6)

F low

t,t+7

Of fered F arm Y ield

0.0149

∗∗

0.0149

∗∗

0.0973

∗∗∗

0.114

∗∗∗

(0.0063) (0.0072) (0.0138) (0.0156)

F low

t−7,t

0.0528

∗

0.0449 0.0391 -0.0125

(0.0284) (0.0299) (0.0288) (0.0305)

F low

t−14,t−7

0.0118 0.00543 0.00808 -0.0227

(0.0248) (0.0257) (0.0259) (0.0269)

F low

t−21,t−14

-0.0136 -0.0182 -0.00856 -0.0222

(0.0220) (0.0228) (0.0223) (0.0226)

F low

t−28,t−21

-0.0259 -0.0295

∗

-0.0297

∗

-0.0440

∗∗

(0.0167) (0.0173) (0.0176) (0.0179)

Log return

t−7,t

0.122

∗∗∗

0.110

∗∗∗

0.164

∗∗∗

0.0969

∗∗∗

(0.0386) (0.0370) (0.0373) (0.0359)

Log return

t−14,t−7

0.00505 -0.00241 0.0581 0.0337

(0.0396) (0.0396) (0.0378) (0.0368)

Log return

t−21,t−14

0.0109 0.000981 0.0672

∗

0.0304

(0.0376) (0.0381) (0.0369) (0.0360)

Log return

t−28,t−21

0.0224 0.0154 0.0721

∗∗

0.0443

(0.0368) (0.0373) (0.0359) (0.0372)

Log crypto M KT return

t−7,t

-0.120

∗∗∗

-0.106

∗∗∗

-0.160

∗∗∗

-0.0965

∗∗∗

(0.0414) (0.0390) (0.0399) (0.0368)

Log crypto M KT return

t−14,t−7

-0.00342 0.00564 -0.0545 -0.0416

(0.0439) (0.0441) (0.0429) (0.0415)

Log crypto M KT return

t−21,t−14

-0.00578 0.00317 -0.0673

∗

-0.0603

(0.0386) (0.0393) (0.0389) (0.0374)

Log crypto M KT return

t−28,t−21

-0.0212 -0.0156 -0.0782

∗∗

-0.0859

∗∗

(0.0388) (0.0390) (0.0385) (0.0371)

Log(Liquidity

) 0.0005 0.0044 -0.0514

∗∗∗

-0.0527

∗∗∗

(0.0028) (0.0031) (0.0071) (0.0100)

Farm FE X X X

N 3016 3012 3012 3016 3012 3012

0.003 0.009 0.011 0.086 0.084 0.129

adj. R

0.002 0.005 0.006 0.026 0.019 0.067

Electronic copy available at: https://ssrn.com/abstract=4063228

Appendix

Figure A.1: UI of Yield Farms in PancakeSwap

In this ﬁgure, we provide a snapshot of user-interface environment of yield farms in Pan-

cakeSwap.

Electronic copy available at: https://ssrn.com/abstract=4063228

Figure A.2: Investment outcome from liquidity provision vs. Investment outcome from a

buy-and-hold strategy

In this ﬁgure, we compare investment outcome from liquidity provision with investment

outcome from a simple buy-and-hold strategy. A liquidity provider buys equal U.S. dollar

amount of token A and token B of a liquidity pool at time t. y-axis is the ratio of investment

outcome from a liquidity provision and investment outcome from a simple buy-and-hold

strategy at time t + h minus 1. x-axis is the growth of the ratio of prices of token A and

token B between time t and t + h, i.e.,

t+h

where ρ

Electronic copy available at: https://ssrn.com/abstract=4063228

Figure A.3: Relation between Model-implied and Listed Oﬀered Farm Yields

In this ﬁgure, we compare the oﬀered farm yields calculated using Equation (8)

on the y-axis to those listed on the PancakeSwap’s homepage on the x-axis

(https://pancakeswap.ﬁnance/farms). The listed farm yields are manually collected from

Pancakeswap’s web page at midnight Greenwich Meridian Time (GMT) on October 11,

2021. All values are reported in percentage points. The blue circles represent all observa-

tions and the red dashed line connects (0%,0%) and (300%,300%), i.e., a 45-degree line. A

linear regression where we regress the calculated on the listed farm yields obtains an R

1.00 and an estimated regression line given by by

= 1.002 × y

− 0.001.

Electronic copy available at: https://ssrn.com/abstract=4063228

Table A.1: Chain of Transactions for Yield Farming Strategies

In this table, we itemize the individual transactions in a yield farming strategy. We explain how each step of the yield farming

strategy can change the number of tokens in a liquidity pool and we describe three diﬀerent types of transaction costs: gas

fees, trading fees, and price impact. We refer to a hypothetical pair of cryptocurrency tokens A and B in a liquidity pool

(LP) A/B.

Step Timing Event # Tokens A # Tokens B Trading Frictions

in LP for A/B in LP for A/B Gas Fee Trading Fee Price Impact

1 t Yield farming starts. α

2 t

The yield farmer buys ∆

units of token A us-

ing a part of his/her fund, I

= fL

, using ∆

units of token B. This generates a temporary

price change from price impact. α

− ∆

+ ∆

X X X

3 t

The yield farmer buys token B in a liquid pool

for B using the rest of his/her fund. α

− ∆

+ ∆

X X

4 t

Arbitrageurs correct the price by supplying ∆

of token A and receiving ∆

of token B. α

5 t

The yield farmer provides liquidity to the pool

and receives LP tokens. Denote the fraction of

his/her tokens to the tokens in the current pool

by s(f ). (1 + s(f ))α

(1 + s(f ))α

6 t

The yield farmer stakes the LP tokens in a

farm. (1 + s(f ))α

(1 + s(f ))α

7 t + h h days elapse. (1 + s(f ))α

t+h

(1 + s(f ))α

t+h

8 t + h

The yield farmer receives (harvests) realized

farm yields in CAKE tokens. (1 + s(f ))α

t+h

(1 + s(f ))α

t+h

9 t + h The yield farmer withdraws his/her LP tokens. (1 + s(f))α

t+h

(1 + s(f ))α

t+h

10 t + h The yield farmer sells their CAKE tokens. (1 + s(f))α

t+h

(1 + s(f ))α

t+h

X X

11 t + h

The yield farmer redeems their LP tokens at

the liqudity pool and receives his/her shares of

token A and B. α

t+h

12 t + h

The yield farmer sells his/her ∆

t+h

s(f)α

t+h

of token A using the same pool. This

generates a temporary price change from price

impact. They receive ∆

t+h

of token B in ex-

change from the liquidity pool. α

t+h

+ ∆

t+h

− ∆

t+h

X X X

13 t + h

The yield farmer sell his/her (∆

t+h

+s(f )α

t+h

)

of token B in a liquid pool for B. α

t+h

+ ∆

t+h

− ∆

t+h

X X

14 t + h

Arbitrageurs correct the price by supplying

∆

t+h

of token B and receiving ∆

t+h

of token

A. A new round of yield farming starts again. α

t+h

Electronic copy available at: https://ssrn.com/abstract=4063228

Table A.2: Token Pairs used for Conversion of Token Prices into U.S. Dollars

In this table, we list tokens used as numeraires in the liquidity pools included in our data.

Frequency refers to the number of liquidity pools in which the corresponding token is used

as the numeraire. PancakeSwap Token Pairs Used lists the token pairs in PancakeSwap

liquidity pools used for the conversion of token prices into U.S. dollars. Data from Coin-

MarketCap lists the tokens whose prices we collect from CoinMarketCap.

Numeraire Token Numeraire Frequency PancakeSwap Data from

Token Symbol Token Pairs Used CoinMarketCap

Wrapped Binance Coin BNB 146 BNB-BUSD BUSD

Binance USD BUSD 50 None BUSD

TerraUSD UST 6 None UST

Binance-Peg Ethereum ETH 4 ETH-BNB, BNB-BUSD BUSD

PancakeSwap Token CAKE 4 Cake-BNB, BNB-BUSD BUSD

Binance-Peg Bitcoin BTCB 3 BTCB-BNB, BNB-BUSD BUSD

Binance-Peg Tether USDT 2 None USDT

Binance-Peg USD Coin USDC 2 None USDC

pTokens Bitcoin PBTC 1 PBTC-BNB, BNB-BUSD BUSD

QIAN Governance Token KUN 1 KUN-BUSD BUSD

Total 219

Electronic copy available at: https://ssrn.com/abstract=4063228

Table A.3: Summary Statistics of Coins used for Constructing Cryptocurrency Factors

In this table, we provide summary statistics of cryptocurrencies used for construction of

cryptocurrency factors. Our sample period for cryptocurrency factors starts on December

28, 2013 and ends on September 5, 2021. The unit for market capitalization and daily

trading volume in this table is $ million.

Year # Coins Market Capitalization Daily Trading Volume

Mean Median Mean Median

2013 26 409.8 7.3 2.01 0.05

2014 100 260.1 4.1 1.21 0.03

2015 79 136.9 2.8 1.13 0.10

2016 157 171.5 3.5 1.76 0.02

2017 675 427.9 9.9 17.89 0.13

2018 1,250 415.8 10.9 23.64 0.15

2019 1,175 227.8 6.0 68.67 0.18

2020 1,520 301.0 6.8 121.25 0.29

2021 2,291 724.8 13.9 146.86 0.53

Electronic copy available at: https://ssrn.com/abstract=4063228

Table A.4: Comparison of Cryptocurrency Three-Factor Regressions

This table compares the regression results for portfolios sorted on one-week momentum by

quintile. The sample period used in Liu, Tsyvinski, and Wu (2019) is from the beginning

of 2014 to the end of 2018, which we interpret to be from the ﬁrst week in 2014 to the 52nd

(last) week of 2018.

Panel A: Regressions from Quintile

Liu, Tsyvinski, and Wu (2019) 1 2 3 4 5

α -0.015 -0.010 -0.003 0.025 -0.012

t(α) -1.970 -1.525 -0.657 1.470 -1.080

CMKT

1.041 1.029 0.958 1.093 0.924

CSM B

0.124 0.014 0.204 0.072 0.297

CMOM

-0.164 -0.125 -0.071 0.072 0.424

0.531 0.606 0.687 0.198 0.435

Panel B: Replicated Regressions Quintile

1 2 3 4 5

α -0.019 -0.015 -0.004 0.031 -0.013

t(α) -2.640 -2.362 -0.718 1.562 -1.230

CMKT

0.994 0.957 0.873 1.119 0.996

CSM B

0.019 0.030 0.150 -0.034 0.081

CMOM

-0.148 -0.056 -0.045 -0.040 0.325

0.578 0.635 0.699 0.190 0.503

Electronic copy available at: https://ssrn.com/abstract=4063228

B.1 Appendix for Conceptual Framework

B.1 Capital gains and impermanent loss

In this section, we outline the procedure for deriving the main equations of Section 4 as-

suming that there are no trading frictions such as trading fees and gas fees. For expositional

purposes, we consider the following scenario:

• Suppose a liquidity provider provides 1 BNB and 100 BUSD, a stablecoin pegged to

U.S. dollar, to a liquidity pool.

• There is a total of 10 BNB and 1,000 BUSD in the pool after this liquidity provision.

Therefore, the liquidity provider’s share is 10%.

• After h days, the price of BNB becomes 200 BUSD.

• The liquidity provider withdraws his/her liquidity.

The constant product model imposes a condition that the product of two tokens should

be constant. In this case, k = α

= 10 × 1, 000 = 10, 000, where α

is the number

of cryptocurrency i in the liquidity pool. Let A and B be BNB and BUSD, repectively.

Consider t as today and t + h as h days after today. The value of A (BNB) in the pool

should be identical to the value of B (BUSD) at any t, i.e. P

= P

for all t. See

Lemma 1 for more details.

Lemma 1) P

= P

in a constant product model.

Proof) Under the constant product model, the product of the quantities of two cryptocur-

rencies should be constant, i.e. α

= k. This implies that

∂α

= −

. To purchase δ,

a trader needs to pay δ

., which means that P

δ = P

→ P

= P

Since we have two equations: P

= P

and k = α

, we can solve for both α

and





, α





Electronic copy available at: https://ssrn.com/abstract=4063228

Given that the rate of exchange for 1 BNB becomes 200 BUSD (which is equivalent to $200,

assuming that BUSD is perfectly pegged to the U.S. dollar) at time t + h:

t+h

10, 000 × ($1/$200) =

√

50 = 7.07,

t+h

10, 000 × ($200/$1) =

2, 000, 000 = 1414.21.

The liquidity provider’s share is 10%. If he/she withdraws their liquidity, he/she will get

0.707 BNB and 141.421 BUSD. This amounts to 0.707 × 200 + 141.421 × 1 = $282.82. In

the crypto community, the impermanent loss is often deﬁned as the percentage of the ratio

of investment outcomes at time t + h in two scenarios: (1) providing liquidity to the pool

at t or (2) directly holding the underlying assets. If the liquidity provider simply held the

assets (1 BNB and 100 BUSD), he/she would now have $300 = 1 × 200 + 100 × 1 worth of

assets. In this case, the impermanent loss is (282.82/300−1)×100 = -5.727%. To formalize

this, we compute the following measure which is the ratio of investment outcomes at time

t + h in two scenarios minus 1. In this example, the liquidity provider’s share is 10%. Let’s

assume that his/her share in general is ω.

ω(P

t+h

+ P

t+h

)

ω(P

t+h

+ P

t+h

)

− 1

Note that α

in the denominator is the same as the number of shares the liquidity provider

initially held, whereas α

in the numerator is the number of shares after trading activities

Electronic copy available at: https://ssrn.com/abstract=4063228

between t and t + h.

ω(P

t+h

+ P

t+h

)

ω(P

t+h

+ P

t+h

)

− 1



t+h



t+h

+ α

t+h



t+h



+ α

− 1



t+h





t+h





t+h





t+h











− 1



t+h



t+h



t+h



− 1

Denote the relative price of token A to token B at t by ρ

). Then, the above expression

is reduced to

t+h

√

t+h

√

− 1 =

√

t+h

√

− 1 =

t+h

+ 1

− 1.

The above ﬁgure shows the relation between change of the relative price (

t+h

) and the

impermanent loss, deﬁned as the ratio of investment outcomes at time t + h in the two

scenarios, minus 1. If ρ changes and

t+h

deviates from 1, the liquidity provider experiences a

loss compared to a simple position of holding underlying tokens from t. It is straightforward

to show that this loss, also called the impermanent loss, is non-positive:

t+h

− 1 =

−

(

t+h

−1)

t+h

However, the above approach is not directly applicable to our analysis because we analyze

returns from liquidity provision, rather than comparing an investment outcome at t + h

with an investment outcome in a hypothetical situation at t + h. Therefore, our goal is to

Electronic copy available at: https://ssrn.com/abstract=4063228

simplify the liquidity provider’s gross return, expressed as follows:

ω(P

t+h

+ P

t+h

)

ω(P

+ P

)

We can decompose the above expression into two parts.

t+h

+ P

t+h

+ P



+ P



t,t+h



+ P



t,t+h



t+h

+ P

t+h

+ P

−



+ P



t,t+h



+ P



t,t+h



We call the ﬁrst term capital gains, which is a return that an investor can earn if he/she

holds α

and α

shares of token A and B until time t+ h without providing liquidity to the

pool. We deﬁne the second term as impermanent loss in our context, which is the diﬀerence

between the return on liquidity provision and capital gains.

First, the capital gains are reduced to

t,t+h

thanks to Lemma 1. Second, in

order to simplify the impermanent loss, we use Lemma 1 again.

t+h

+ P

t+h

+ P

−



+ P



t,t+h



+ P



t,t+h



t+h

−



t,t+h



t+h



t+h







−



t,t+h



t,t+h

−



t,t+h



= −



t,t+h

−

t,t+h



The impermanent loss deﬁned in the context of return on liquidity provision is closely

related to the impermanent loss deﬁned as the ratio of investment outcomes at time t + h

Electronic copy available at: https://ssrn.com/abstract=4063228

in the two scenarios minus 1. It is straightforward to show that

−



t,t+h

−

t,t+h





t,t+h







t+h

+ 1

− 1





B.2 Trading frictions in yield farming

In this section, we explain trading frictions in yield farming and how they can aﬀect the

performance of a yield farming strategy. We investigate three diﬀerent trading frictions:

gas fees, trading fees, and price impact.

Gas fees

Table A.1 lists 14 steps for one round of the yield farming strategy. Out of the 14 steps,

10 require the farmer to pay gas fees. The gas fee is the transaction cost that BSC users

need to pay whenever they execute transactions that require computational resources of the

network. The gas fee is typically not proportional to the size of the transaction. We discuss

in Section 5.2 about how we collect gas fee data in yield farming. We subtract the gas fee

in each round of yield farming from invested capital to incorporate the eﬀect of gas fee on

the performance of yield farming.

Trading fees

Let c

∗

=0.0025 (0.25%) denote the fraction of trading volume that traders need to pay

in trading fees at PancakeSwap. In Step 2, when a yield farmer buys token A, he/she

pays a 0.25% trading fee. Because this trading fee does not apply to token B, the farmer

pays eﬀectively half of the trading fee

c∗

(=0.125%) of the additional liquidity that he/she

provides. Moreover, the farmer has to pay an additional fee of 0.25%: when he/she converts

the withdrawn token A to token B, he/she pays additional

c∗

fraction of trading fee. The

farmer also needs to pay also

c∗

of trading fee in Step 3 and Step 13. Given that the yield

farmer pays

c∗

our times, the yield farmer’s gross return on capital gain and impermanent

loss should be

(1 − 2c

∗

)



t+h

+ P

t+h



+ P

= (1 − 2c

∗

)



t,t+h



−



t,t+h

−

t,t+h





In Step 10, the yield farmer also needs to pay trading fees when he/she sells CAKE tokens

Electronic copy available at: https://ssrn.com/abstract=4063228

harvested from farming. For this, we multiply (1 − c

∗

) on the realized farm yield term in

equation (10).

Price impact

Executing a yield farming strategy involves buying and selling token A. In Step 2, a yield

farmer buys token A. As a result of price impact, the yield farmer will buy token A at a price

above the current market price. Symmetrically, the yield farmer will sell token A at a price

below the current market price. Such adverse price impacts will result in additional losses

for the yield farmer. The size of the loss is proportional to the relative size of investment

) to the size of the liquidity pool, i.e., I

= fL

. We go through each step in Table A.1

to investigate the price impacts involved in a yield farming strategy.

(1) Step 1: We start from a liquidity pool with two tokens A and B. It has α

of token A

and α

of token B and the prices of token A and B are denoted as P

and P

(2) Step 2: An yield farmer buys ∆

number of token A using a part of his/her fund,

= f L

. What is important here is that the yield farmer must obtain tokens A and B

proportionally to α

/α

. For this purpose, we divide his/her fund into xI

and (1 − x) I

to allocate towards token A and B, respectively. The yield farmer ﬁrst converts $xI

token B in a liquid market for B. Then, the farmer will have

of token B on hand, which

he/she will convert to token A by means of the liquidity pool. Due to the constant product

model assumption,



− ∆







= α

If we solve this for ∆

∆





+ xI

xfα

+ xf

(3) Step 3: The yield farmer uses the rest of their funds, $(1 − x) I

, to buy token B in a

liquid market for B. Then, he/she will get ∆

of token B where ∆

is expressed as follows.

∆

(1 − x) I

(1 − x) fL

Electronic copy available at: https://ssrn.com/abstract=4063228

Finally, we ﬁnd x that satisﬁes

∆

xfα

+xf

(1−x)fL

xfα

+xf

(1−x)f

(

)



1 − x

 

1 + 2xf



Therefore,



1 − x

 

1 + 2xf



= 1.

If we solve for x,

x =

f − 1 +

+ 1

There are two solutions, but only the above solution is positive.

(4) Step 4: Arbitrageurs correct the price by supplying ∆

of token A and receiving ∆

of token B in return, after which the liquidity pool becomes basically identical to the initial

pool.

(5) Step 5: The yield farmer provides their liquidity to the pool and receives LP tokens.

For simplicity of notation, let’s deﬁne s(f), the ratio of the yield farmer’s share to the

current share in the liquidity pool before the yield farmer provides the liquidity.

s(f) =

∆

+xI

xfL

+ xfL

f ×



f−1+

√



+ f ×

f−1+

√

f − 1 +

+ 1

f +

+ 1

After the liquidity provision by the yield farmer, the shares of token A and B become

(1 + s(f)) and α

(1 + s(f)) . Now, we measure the price impact when the yield farmer

buys ∆

of token A. The farmer uses $xI

to buy ∆

of token A. This means that the

eﬀective price paid by the farmer is:

∆

xfL

xfα

+xf





xfα

+xf

= 2P



+ xf



= P

(1 + 2fx)

= P



1 +



f − 1 +

+ 1



Given that f − 1 +

+ 1 > 0,

> P

(6) Step 6: The yield farmer stakes the P tokens to a farm.

Electronic copy available at: https://ssrn.com/abstract=4063228

(7) Step 7: The yield farmer waits for h days. After the trading activities the shares of

token A and B become α

t+h

(1 + s(f)) and α

t+h

(1 + s(f)) .

(8) Step 8: The yield farmer receives (harvest) realized farm yields in Cake tokens.

(9) Step 9: The yield farmer withdraws his/her LP tokens from the farm.

(10) Step 10: The yield farmer sells Cake tokens.

(11) Step 11: The yield farmer withdraws his/her liquidity from the liquidity pool by

sending the LP tokens to the pool. After the farmer’s withdrawing liquidity, the shares of

token A and B in the pool become α

t+h

and α

t+h

(12) Step 12: The yield farmer sells his ∆

t+h

= s(f)α

t+h

of token A and receives ∆

t+h

token B. Currently, there are α

t+h

and α

t+h

of token A and token B in the pool. After the

farmer’s sending ∆

t+h

= s(f)α

t+h

of token A, he/she receives ∆

t+h

token B. Due to the

constant product model,



t+h

+ s(f)α

t+h



t+h

− ∆

t+h



= α

t+h

→ ∆

t+h

s(f)

1 + s(f)

t+h

The farmer sends s(f )α

t+h

of token A and in return P

t+h

∆

t+h

worth of USD. This means

that the eﬀective price that the yield farmer receives when selling token A is

t+h

∆

t+h

s(f)α

t+h

s(f)

1+s(f)

t+h

s(f)α

t+h

s(f)

1+s(f)

t+h

s(f)α

t+h



1 + s(f)



t+h

So the yield farmer sells at a lower price than P

t+h

(13) Step 13: The yield farmer sells ∆

t+h

+ s(f)α

t+h

of token B in a liquid market for

token B.

(14) Step 14: An arbitrageur corrects the price by supplying ∆

t+h

of token B and receiving

∆

t+h

of token A. A new round of yield farming starts again.

Now we compute the return of this yield farming strategy considering the price impact.

First, the yield farmer uses his/her fund I

= fL



s(f)α



+ P

(s(f)α

) to buy

s(f)α

and s(f)α

shares of token A and B at

and P

. After h days, the yield farmer

Electronic copy available at: https://ssrn.com/abstract=4063228

withdraws s(f )α

t+h

and s(f )α

t+h

shares of token A and B and sell them at

t+h

and P

t+h

Then, its gross return is expressed as

t+h



s(f)α

t+h



+ P

t+h

(s(f)α

t+h

)



s(f)α



+ P

(s(f)α

)

t+h

+ P

t+h

+ P

We simplify this as follows.

t+h

+ P

t+h

+ P



1+s(f)



t+h

+ P

t+h



1 +



f − 1 +

+ 1



+ P



1+s(f)

+ 1



t+h



1 +



f − 1 +

+ 1



+ 1



1+s(f)

+ 1

f + 1 +

+ 1

t+h

=λ (f)

t+h

+ P

t+h

+ P

=λ (f)



t+h



−



t+h

−

t+h



where

λ (f) =

1+s(f)

+ 1

f + 1 +

+ 1

f−1+

√

+ 1

f + 1 +

+ 1

3f + 3

+ 1 − 1



2f + 2

+ 1 − 1



f + 1 +

+ 1



In sum, if we take into account of both price impact and trading fee, return will be

(1 − 2c

∗

)λ (f)



t+h



−



t+h

−

t+h



where (1 − 2c

∗

)λ (f) < 1.

Figure 3 illustrates the price impact in buying and selling token A and λ(f), which summa-

rizes the overall eﬀect of price impacts on the performance of yield farming. Panel A shows

the relation between f and

is greater than or equal to 1 and increasing in f, which

implies that the yield farmer pays higher prices than the current market price when they

purchase token A, which is attenuated as the size of his/her investment increases. Panel B

shows the relationship between f and

t+h

. This is less than or equal to 1 and decreasing

Electronic copy available at: https://ssrn.com/abstract=4063228

in f, which means that the yield farmer sells token A at a larger discount as the size of

investment increase. Finally, Panel C plots λ(f) with respect to f . λ(f ) is less than or

equal to 1, decreasing in f , and its eﬀect is substantial when f is large. For example, if the

yield farmer’s investment is very small such that f is close 0, λ(f) = 1 and therefore, there

is no eﬀect. However, if the yield farmer invests as much as the size of the pool (f = 1),

he/she will lose more than 50% of their gross return.

C.1 Accuracy of Constructed Cryptocurrency Factors

As a test of the accuracy of our methodology, we replicate the three-factor regressions from

Table 11 in Liu, Tsyvinski, and Wu (2019) for portfolios sorted on one-week momentum

by quintile, a set of implementable trading strategies not used in the construction of the

three factors. In table A.4, we compare our parameter estimates to those obtained in Liu,

Tsyvinski, and Wu (2019). The two are near-identical with only minor deviations, which

may be from small variations in the sample period used and/or changes in the markets for

which Coinmarketcap tracks price data.

In addition, it is worth noting that the estimates for alpha obtained in Liu, Tsyvinski,

and Wu (2019) are reported in weekly frequency, whereas our measures of alpha have been

annualized. For instance, a weekly alpha of 0.025, as is the case for the fourth quintile of

one-week momentum in table A.4, translates into a yearly alpha of 2.611 when annualized.

Therefore, the magnitudes of our estimates of alpha for yield-farming strategies are rea-

sonably comparable to strategies analyzed in table 11 of Liu, Tsyvinski, and Wu (2019),

in which three-factor weekly alphas exceed 0.02 (or an annualized alpha of 1.80) for many

price- and momentum-based strategies.

Electronic copy available at: https://ssrn.com/abstract=4063228