single DeFi short = DeFi, long = Decentralized Finance, PoW short = PoW, long
= Proof-of-Work, PoS short = PoS, long = Proof-of-Stake, LTVV short = LTV,
long = Loan-to-Value, HF short = HF, long = Health Factor, LT short = LT, long
= Liquidation Threshold, APR short = APR, long = Annual Percentage Rate, ROI
short = ROI, long = Return On Investment, JIT short = JIT, long = Just-in-
Time, NO short = NO, long = Node Operator, LSD short = LSD, long = Liquid
Staking Derivative, LST short = LST, long = Liquid Staking Tokens, DEX short =
DEX, long = Decentralized Exchange, CEX short = CEX, long = Centralized
Exchange, EOA short = EOA, long = Externally-Owned Account, NFT short = NFT,
long = Non-fungible Token, LP short = LP, long = Liquidity Provider, P2P short
= P2P, long = peer-to-peer, TVL short = TVL, long = Total Value Locked, CFMM
short = CFMM, long = Constant Function Market Maker, CPMM short = CPMM, long =
Constant Product Market Maker, DApp short = DApp, long = Decentralized
Application, DAO short = DAO, long = Decentralized Autonomous Organization,
CeFi short = CeFi, long = Centralized Finance, MEV short = MEV, long = Miner
Extractable Value, EV short = EV, long = Extractable Value, BEV short = BEV,
long = Blockchain Extractable Value, AMM short = AMM, long = Automated Market
Maker, FaaS short = FaaS, long = Front-running as a Service, SaaS short =
SaaS, long = Staking as a Service, HFT short = HFT, long = High-frequency
Trading, PGA short = PGA, long = Priority Gas Auction, BRF short = BRF, long =
Back-run Flooding, PRG short = PRG, long = Priority Gas Auction, AE short =
AE, long = Atomic Execution, BEET short = BEET, long = Break-even Extraction
Threshold, BAD short = BAD, long = Breaking Atomicity and Determinism, aamm
short = A2MM, long = Automated Arbitrage Market Maker, dfmm short = DFMM, long
= Dynamic Fee Market Maker, dfaamm short = A${}^{2}_{F}$MM, long = Automated
Arbitrage and Fee Market Maker, MVI short = MVI, long = Minimum Victim Input,
BSC short = BSC, long = Binance Smart Chain, KS short = KS, long = Kolmogorov-
Smirnov, 11institutetext:  Imperial College London
22institutetext: University of Sussex

# Leverage Staking with Liquid Staking Derivatives (LSDs): Opportunities and
Risks

Xihan Xiong 11 Zhipeng Wang 11 Xi Chen 22 William Knottenbelt 11
Michael Huth 11

###### Abstract

Lido, the leading LSD provider on Ethereum, allows users to stake an arbitrary
amount of ETH to receive stETH, which can be integrated with DeFi protocols
such as Aave. The composability between Lido and Aave enables a novel strategy
called “leverage staking”, where users stake ETH on Lido to acquire stETH,
utilize stETH as collateral on Aave to borrow ETH, and then restake the
borrowed ETH on Lido. Users can iteratively execute this process to optimize
potential returns based on their risk profile.

This paper systematically studies the opportunities and risks associated with
leverage staking. We are the first to formalize the leverage staking strategy
within the Lido–Aave ecosystem. Our empirical study identifies $262$ leverage
staking positions on Ethereum, with an aggregated staking amount of
$295{,}243$ ETH ($482$M USD). We discover that $90.13\%$ of leverage staking
positions have achieved higher returns than conventional staking. Furthermore,
we perform stress tests to evaluate the risk introduced by leverage staking
under extreme conditions. We find that leverage staking significantly
amplifies the risk of cascading liquidations. We hope this paper can inform
and encourage the development of robust risk management approaches to protect
the Lido–Aave LSD ecosystem.

##  1 Introduction

The Ethereum blockchain recently underwent the transition from PoW [25] to PoS
[12, 20, 4, 21] to achieve a more sustainable consensus mechanism. In the PoS-
based Ethereum, a validator stakes ETH to secure the system [6, 18] and
receives staking rewards. Nonetheless, solo staking poses significant entry
barriers, demanding capital commitment of $32$ ETH and technical expertise for
maintaining a validator node. Additionally, staked ETH becomes illiquid during
the staking period, restricting its availability for trading.

To address these challenges, Liquid Staking Derivatives (LSDs) emerged. Retail
users can stake an arbitrary amount of ETH on liquid staking platforms,
receiving LSD in return [19, 22]. LSD are fungible and tradable
representations of the staked ETH and the associated rewards. At present, Lido
stands as the leading LSD provider in terms of TVL ($13.8$B
USD)111https://defillama.com/, accessed on August $23$rd, $2023$..

Users can stake ETH on Lido to receive stETH, earning a staking APR of
$3.8\%$222https://lido.fi/ethereum, accessed on August $23$rd, $2023$.. stETH
can be integrated with DeFi lending platforms such as Aave, or DEX such as
Curve. The Aave–Lido LSD ecosystem allows users to earn rewards on their
staked ETH while still being utilized as collateral on
Aave333https://github.com/lidofinance/aave-asteth-deployment. The
composability between Lido and Aave enables a novel strategy known as
“leverage staking”, where users stake ETH on Lido to receive stETH, which is
then used as collateral on Aave to borrow ETH, subsequently restaked on Lido.
A financially rational user can iteratively execute this process to optimize
potential returns based on their risk profile.

While yielding higher returns, leverage staking also introduces potential
risks. Under adverse market conditions that result in a significant stETH
price decline, the Aave–Lido LSD ecosystem becomes vulnerable to “cascading
liquidations”, a phenomenon where multiple liquidations occur successively,
causing a downward spiral in the stETH price. Yet the opportunities and risks
associated with leverage staking remain relatively unexplored in academic
research. To close this gap, this paper provides a systematic study of the
leverage staking strategy with LSD, shedding light on its mechanics, potential
benefits for users, and inherent risks for stakeholders, while investigating
its implications for the broader DeFi ecosystem. We summarize the main
contributions of this paper as follows.

$\bullet$ Strategy Formalization. We establish a formal framework for leverage
staking with stETH, deriving the leverage multiplier and leverage staking APR.
To our knowledge, we are the first to model leverage staking strategy with
LSD.

$\bullet$ Empirical Measurement. We perform an empirical analysis of leverage
staking spanning $963$ days, from December $17$th, $2020$ to August $7$th,
$2023$. We detect $262$ leverage staking positions, with an aggregated staking
amount of $295{,}243$ ETH ($482$M USD). Our results show that $90.13\%$ of
leverage staking positions have achieved an APR higher than that of
conventional staking.

$\bullet$ User Behavior Analysis. We explore the stETH price deviation in
relation to the Terra crash incident. We analyze how users with leverage
staking positions behave when faced with potential liquidations. We discover
that users actively deleveraged their positions and collectively repaid a
substantial debt amounting to $74{,}983.6$ ETH, further intensifying the
selling pressure on stETH.

$\bullet$ Stress Testing. We perform stress tests on the Lido–Aave LSD
ecosystem to evaluate the risk of cascading liquidations under extreme
conditions. We first simulate the liquidation cascades among leverage staking
positions. We find that $93.13\%$ of these positions are liquidated.
Subsequently, we extend our simulations to include both leverage staking and
ordinary positions, showing that leverage staking significantly amplifies the
liquidation risk. We find that the stETH selling pressure from both
liquidations and the deleverage action create a ripple effect within the
system, exacerbating price decline and triggering more liquidations.

##  2 Background

###  2.1 Blockchain and DeFi

Permissionless blockchains are decentralized distributed ledgers that allow
any participant to join and engage without requiring authorization. Within
this landscape, Ethereum [25] emerges as a pioneering platform. It facilitates
the execution of smart contracts, enabling developers to build decentralized
applications.

DeFi [24] has recently emerged as a groundbreaking financial segment. DeFi
refers to a set of blockchain-based financial services and products that
operate without traditional intermediaries, using smart contracts to build an
open financial environment. DeFi innovations ranging from lending to DEX are
reshaping the financial system. The TVL in DeFi reached an all-time high of
$178$B USD in November, $2021$, with Ethereum dominating DeFi activities
($109$B USD, $61\%$).

###  2.2 Ethereum PoS

PoS, originally proposed in online forums [1] and later explored by the
academic community [8, 6, 11, 14, 5], has emerged as an energy-efficient
alternative to PoW.

Beacon Chain. On December $1$st, $2020$, Ethereum introduced its PoS-based
Beacon Chain that runs in parallel with Ethereum’s PoW Mainnet. In the Beacon
Chain, “staking” is introduced through a deposit mechanism, where participants
lock up $32$ ETH into the designated contract to become validators.

The Merge. On September $15$th, $2022$, the Merge enables Beacon Chain to
evolve as the consensus mechanism for the entire network [3]. Ethereum now
runs on the execution layer and the consensus layer. The _execution layer_ is
responsible for executing transactions, defining how the state of the Ethereum
network changes over time. The role of the _consensus layer_ entails
establishing agreement among validators regarding the state of the execution
layer. The Ethereum staking system offers various incentives to validators.
Rewards from the consensus layer include block proposal, attestation, and sync
committee rewards [12]. The execution layer introduces additional rewards,
including priority tips and MEV tips [9, 17]. Penalties also apply for
dishonest behavior.

The Shapella Upgrade. On April $12$th, 2023, Ethereum underwent the “Shapella
upgrade”. The Shapella upgrade combines the “Shanghai upgrade” and the
“Capella upgrade”, which took place on the Ethereum consensus layer and
execution layer simultaneously [10]. The Shapella upgrade primarily introduces
the capability to unstake ETH secured within the Ethereum network.

###  2.3 Staking Options

Ethereum participants are presented with four distinct staking options as
follows.

\- Solo Staking.

In solo staking, individual participants operate their validator nodes by
committing a threshold of $32$ ETH, thereby maintaining full control over
their staking rewards. However, solo staking necessitates technical expertise
to run and maintain a validator node. Furthermore, it demands a significant
capital commitment, which might be financially unfeasible for retail users.

\- SaaS.

For users with 32 ETH but limited technical expertise, SaaS offers a solution
to manage the validator’s hardware and software for the users, utilizing their
signing keys to undertake on-chain
tasks444https://ethereum.org/en/staking/saas/.

\- Pooled Staking.

For retail users with holdings below the $32$ ETH threshold, pooled staking
emerges as a feasible alternative, enabling them to collectively participate
in the network’s validation process, earn rewards, and capitalize on the
broader Ethereum ecosystem without the need for individual, full-node
commitments. Typically, staking pools charge fees, which are further split
between NO and the protocol DAO. NO run and maintain validator nodes on behalf
of the staking pool. The DAO selects NO and configures crucial parameters for
the protocol.

\- CEX Staking.

CEX, such as Coinbase and Binance, provide centralized and custodial staking
services to users. However, this exposes users to potential risks due to the
centralized nature of CEX staking.

###  2.4 LSD

Figure 1: Overview of the LSD Ecosystem.

Staking offers several advantages, from earning rewards to enhancing network
security. However, once ETH is locked for staking, it becomes illiquid for a
duration, making it inaccessible for trading. Given this challenge, the
concept of LSD emerged, representing staked assets and rewards in a tradable
form. Figure 1 provides an overview of the LSD ecosystem. When users stake ETH
within an LSD provider (e.g., liquid staking pools), they receive LSD in
return.

Liquid Staking Providers. At the time of writing, liquid staking protocols
accumulate a TVL of more than $18.94$B USD, securing the top position in TVL
across various DeFi sectors. Users can obtain LSD through two primary staking
methods: pooled staking and CEX staking (cf. Table 1). Pooled staking
protocols such as Lido, Rocket Pool, Frax, Stakewise, and Swell Network issue
LSD to users. CEX such as Coinbase and Binance also support LSD.

Lido is currently the leading LSD provider and ranks as the largest DeFi
protocol in terms of TVL ($13.8$B USD). Users stake ETH on Lido to receive
stETH in return. With over $285$M stakers, the total amount of ETH staked on
Lido reached $8.34$M in August $2023$, accounting for $74.6\%$ of the total
ETH staked on Ethereum. stETH implements the _rebasing mechanism_ , where
stETH holders’ account balances get adjusted daily to reflect the accumulated
rewards [2]. The rebase can be positive or negative, depending on the
validators’ performance.

###  2.5 DeFi Lending Protocols

DeFi lending protocols are decentralized platforms operating on blockchains
that facilitate P2P lending and borrowing of cryptocurrency assets through the
automated execution of smart contracts. At the time of writing, Aave stands as
the leading DeFi lending protocol, with a total TVL of $4.5$B USD
555https://defillama.com/protocol/aave, accessed on August $23$rd, $2023$..
Notably, Aave follows an over-collateralization model, meaning that users are
required to supply more collateral value than the borrowed amount. As an
illustration, when the collateral value amounts to $S$ ETH, the user’s
borrowing capacity is restricted to no more than $S\cdot l$ ETH, where
$l\in[0,1]$ denotes the LTVV ratio. In the event that the collateral value
falls below a specified threshold, users may need to add more collateral or
risk the liquidation of their asset to repay the borrowed amount and accrued
interest. To monitor the collateralization status of each position, Aave
utilizes LT to establish the threshold percentage that designates a position
as under-collateralized, and HF as a key metric to quantify the liquidation
status of a position. For example, user $\mathsf{U_{i}}$’s position can be
liquidated if $HF_{(\mathsf{U_{i}})}<1$ (cf. Equation 1).

${\small\begin{split}HF_{(\mathsf{U_{i}})}=\frac{\sum_{j}\text{collateralized
}\text{value of }\text{asset}_{j}\text{ in
}\texttt{ETH}\cdot\text{LT}_{j}}{\sum_{j}\text{borrowed }\text{value of
}\text{asset}_{j}\text{ in }\texttt{ETH}}\end{split}}$ (1)

##  3 System Model

Figure 2: Overview of Leverage Staking Strategy.

###  3.1 System Participants

We consider an LSD ecosystem with the following participants.

\- Users:

A user ($\mathsf{U_{i}}$) is a rational participant capable of engaging with
diverse DeFi platforms, employing various strategies to optimize its financial
gains.

\- Liquid Staking Providers:

$\mathsf{U_{i}}$ can stake native tokens (e.g., ETH) on liquid staking
platforms (e.g., Lido) to receive LSD (e.g., stETH) that can be used for
trading, collateralized borrowing, providing liquidity to DEX pools, etc.

\- Lending and Borrowing Providers:

$\mathsf{U_{i}}$ can supply one asset on DeFi lending platforms, such as Aave,
as collateral to borrow another asset.

###  3.2 Leverage Staking with LSDs

\- Leverage Staking Strategy:

LSD can be integrated into DeFi in various ways. For instance, DEX such as
Curve allow stETH holders to provide liquidity to the pool, at the risk of
potential impermanent loss. Alternatively, users can implement a so-called
“leverage staking strategy” which brings higher yield and higher risks.
Specifically, $\mathsf{U_{i}}$ first stakes a principal amount of $S$ ETH on
Lido at time $t_{0}$, acquiring $S$ amount of stETH. Next, $\mathsf{U_{i}}$
utilizes the stETH as collateral within Aave to borrow
$S$$\cdot$$l$$\cdot$$P_{t_{0}}^{\texttt{st}}$ amount of ETH, where $l$ denotes
the LTVV ratio and $P_{t_{0}}^{\texttt{st}}$ denotes the stETH to ETH price at
time $t_{0}$. $\mathsf{U_{i}}$ performs this _loop_ for $n$ times (cf. Figure
2) and ends in a leverage staking position of stETH.

\- Leverage Multiplier.

Assume $\mathsf{U_{i}}$ acquires a total asset (staked ETH on Lido) of
$A_{(S,n)}$ ETH through leverage staking with an initial principal amount of
$S$ ETH, the leverage multiplier $LevM_{(S,n)}$ is defined as the ratio
between $A_{(S,n)}$ and $S$.

##  4 Analytical Study

This section conducts an analytical study of the leverage staking strategy. We
begin by examining the standardized case and subsequently offer a generalized
formalization encompassing other potential scenarios.

We assume that $\mathsf{U_{i}}$ is capable of completing $n$ loops within a
short time interval such that the stETH price remains unchanged. As a rational
and risk-averse participant, $\mathsf{U_{i}}$ determines the value of $n$
according to its risk profile. By applying the leverage staking strategy,
$\mathsf{U_{i}}$ acquires a total investment of $A_{(S,n)}$ ETH, collateral of
$C_{(S,n)}$ stETH, and debt of $B_{(S,n)}$ ETH (cf. Equation 2).

${\small\begin{split}&A_{(S,n)}=S\times[1+l\cdot
P_{t_{0}}^{\texttt{st}}+...+(l\cdot
P_{t_{0}}^{\texttt{st}})^{n}]=S\times\frac{1-(l\cdot
P_{t_{0}}^{\texttt{st}})^{n+1}}{1-l\cdot P_{t_{0}}^{\texttt{st}}}\\\
&C_{(S,n)}=S\times[1+l\cdot P_{t_{0}}^{\texttt{st}}+...+(l\cdot
P_{t_{0}}^{\texttt{st}})^{n-1}]=S\times\frac{1-(l\cdot
P_{t_{0}}^{\texttt{st}})^{n}}{1-l\cdot P_{t_{0}}^{\texttt{st}}}\\\
&B_{(S,n)}=S\times[l\cdot P_{t_{0}}^{\texttt{st}}+...+(l\cdot
P_{t_{0}}^{\texttt{st}})^{n}]=S\times\frac{l\cdot
P_{t_{0}}^{\texttt{st}}-(l\cdot P_{t_{0}}^{\texttt{st}})^{n+1}}{1-l\cdot
P_{t_{0}}^{\texttt{st}}}\end{split}}$ (2)

Leverage Multiplier. Equation 3 derives the leverage multiplier
($LevM_{(S,n)}$). Figures 4 and 4 show how $LevM_{(S,n)}$ changes in response
to variations in $P_{t_{0}}^{\texttt{st}}$ and LTVV ratio respectively. It is
evident that $LevM_{(S,n)}$ increases with the increase of either stETH price
or LTVV. In addition, we can observe that $LevM_{(S,n)}$ gradually converges
to $\frac{1}{1-l\cdot P_{t_{0}}^{\texttt{st}}}$ when the number of leverage
staking loops ($n$) increases.

${\small\begin{split}&LevM_{(S,n)}=\frac{A_{(S,n)}}{S}=\frac{1-(l\cdot
P_{t_{0}}^{\texttt{st}})^{n+1}}{1-l\cdot
P_{t_{0}}^{\texttt{st}}};&\lim\limits_{n\to\infty}LevM_{(S,n)}=\frac{1}{1-l\cdot
P_{t_{0}}^{\texttt{st}}}\\\ \end{split}}$ (3)

Figure 3: $LevM_{(S,n)}$with varying $P_{t_{0}}^{\texttt{st}}$.

Figure 4: $LevM_{(S,n)}$with varying LTV.

Health Factor. The leverage staking strategy, although capable of generating
substantial returns, concurrently magnifies the risk of liquidation.
$\mathsf{U_{i}}$’s position may be susceptible to liquidation should the value
of collateralized stETH decrease due to the decline of the stETH price (i.e.,
$P_{t_{c}}^{\texttt{st}}$<$P_{t_{0}}^{\texttt{st}}$). As discussed in Section
2.5, Aave uses HF to track the status of each position. $\mathsf{U_{i}}$’s can
be liquidated if HF is less than $1$ (cf. Equation 4). In our leverage staking
example, the LTVV and LT are $69\%$ and $81\%$ respectively (see Table 2 for
the historical changes of Aave parameter configurations). Equation 5 suggests
that, to uphold a secure position, the largest acceptable percentage decrease
in stETH price is $\frac{l}{\text{LT}}-1=\frac{12}{81}\approx-14.8\%$. In the
event of liquidation, the user’s entire collateralized stETH amount of
$C_{(S,n)}$ will be liquidated, and this effect becomes more pronounced as the
number of loops ($n$) increases, as indicated by $LevM_{(S,n)}$.

${\small\begin{split}HF_{\mathsf{U_{i}}}(P_{t_{c}}^{\texttt{st}}|P_{t_{0}}^{\texttt{st}})&=\frac{\sum_{k}^{n}k^{\text{th}}\text{
collateralized }\texttt{stETH}\text{ value in
}\texttt{ETH}\cdot\text{LT}}{\sum_{k}^{n}k^{\text{th}}\text{ borrowed
}\texttt{ETH}\text{ value}}\\\ &=\frac{C(S,n)\cdot
P_{t_{c}}^{\texttt{st}}\cdot\text{LT}}{B(S,n)}=\frac{P_{t_{c}}^{\texttt{st}}\cdot\text{LT}}{P_{t_{0}}^{\texttt{st}}\cdot
l}\end{split}}$ (4)

${\small\begin{split}HF_{\mathsf{U_{i}}}(P_{t_{c}}^{\texttt{st}}|P_{t_{0}}^{\texttt{st}})\geq
1\implies\frac{P_{t_{c}}^{\texttt{st}}}{P_{t_{0}}^{\texttt{st}}}>\frac{l}{LT}\implies\Delta\%P^{\texttt{st}}_{\Delta
t}\geq\frac{l}{\text{LT}}-1\end{split}}$ (5)

APR. Equation 6 calculates leverage staking profitability. Let $r_{s}$,
$r_{c}$, $r_{b}$ represent the staking APR offered by Lido and the supply and
borrow interest rates provided by Aave, respectively. It is worth noting that
$r_{s}$ changes in accordance with the validator performance, while $r_{c}$
and $r_{b}$ vary based on Aave’s interest rate
model666https://docs.aave.com/risk/liquidity-risk/borrow-interest-rate.
$\mathsf{U_{i}}$ earns a staking APR of $R_{s}(n)$ from Lido, a supply APR of
$R_{c}(n)$ while pays a borrow APR of $R_{b}(n)$ to Aave. As such,
$\mathsf{U_{i}}$ obtains a net APR of $R_{Net}(n)=R_{s}(n)+R_{c}(n)-R_{b}(n)$.
The necessary condition for a rational $\mathsf{U_{i}}$ to apply leverage
staking rather than conventional staking is $R_{Net}(n)>r_{s}$.

${\small\begin{split}R_{Net}(n)&=R_{s}(n)+R_{c}(n)-R_{b}(n)=r_{s}\cdot\frac{A_{(S,n)}}{S}+r_{c}\cdot\frac{C_{(S,n)}}{S}-r_{b}\cdot\frac{B_{(S,n)}}{S}\\\
&=r_{s}\cdot LevM_{(S,n)}+r_{c}\cdot(LevM_{(S,n)}-(l\cdot
P_{t_{0}}^{\texttt{st}})^{n})-r_{b}\cdot(LevM_{(S,n)}-1)\end{split}}$ (6)

In addition to the standardized case discussed above, real-world leverage
lending situations can exhibit variation among users. For example, some users
may not supply all the received stETH as collateral on Aave. We refer
interested readers to Appendix 0.B for a generalized formalization of leverage
staking.

Figure 5: Leverage staking statistics.

Figure 6: Leverage staking distribution.

##  5 Empirical Study

We outline the empirical evaluation of leverage staking across Aave and Lido.

Data Colletction. We crawl the historical submitted events related to  Lido
stETH Token when users stake ETH on Lido. We crawl the on-chain events
involving users’ historical actions for adjusting positions on Aave V$2$
lending pool, including deposit, borrow, withdraw, and repay events. We use an
Ethereum Geth node on a Linux machine running Ubuntu 22.04 LTS, which is
equipped with AMD $48$-core CPU, $256$ GB of RAM, and $12\times 2$ TB SSD. We
capture all the targeted events from block $11{,}473{,}216$ (December $17$th,
$2020$) to block $17{,}866{,}191$ (August $7$th, $2023$), $963$ days in total.
We identify $290{,}984$ submitted events on Lido, $449{,}528$ deposit,
$238{,}388$ borrow, $336{,}746$ withdraw and $173{,}596$ repay events on Aave
V$2$ lending pool.

Leverage Staking Detection. We proceed to analyze the users who adopt leverage
staking across Lido and Aave. From the $449{,}528$ deposit and $238{,}388$
borrow events on Aave V$2$, we find that $743$ addresses are used to deposit
stETH as collateral and then borrow ETH. We then propose an algorithm (cf.
Algorithm 1) to identify the addresses involving leverage staking. Basically,
we extract the event sequence $(\texttt{submitted}$, deposit, borrow,
$\texttt{submitted})$ in chronological order, which follows the leverage
staking process shown in Figure 2.

Our investigations reveal the existence of $262$ addresses that have been
engaging in leverage staking activities across Lido and Aave V$2$ lending
pools, spanning the timeframe from December $17$th, $2020$ to August $7$th,
$2023$. Cumulatively, these addresses have amassed a total staking amount of
$295{,}243$ ETH. The distribution of leverage borrowing and staking amounts is
depicted in Figure 6. Interestingly, we observe that the volume of leverage
staking was substantially impacted by the Terra crash in May $2022$, leading
to a drastic decline from the peak monthly staking amount of $93{,}661$ ETH in
May $2022$ to just $11$ ETH in August $2022$. Moreover, the Ethereum Merge
brought about a resurgence in leverage staking, with a staking amount of
$9{,}814$ ETH in October 2022.

Leverage Staking Loops and Multipliers. Among the $262$ addresses that have
adopted leverage staking, we conduct an analysis focusing on two key elements:
the number of loops (denoted as $n$) and the leverage multiplier (denoted as
$LevM_{(S,n)}$), derived from their extracted action sequence
$\mathcal{E}_{s}$ (cf. Algorithm 1). To calculate the number of leverage
staking loops, we identify consecutive sub-sequences in $\mathcal{E}_{s}$
consisting of $(\texttt{submitted}$, deposit, $\texttt{borrow})$. The results,
as depicted in Figure 6, reveal that $145$ addresses ($55.35\%$) performed
leverage staking with a single loop ($n=1$). Notably, a smaller subset of $12$
addresses have engaged in leverage staking with more than eight loops, and
their cumulative staking activity amounts to an impressive amount of
$102{,}998$ ETH.

Furthermore, we compute $LevM_{(S,n)}$ for each address, taking into account
their initial stake amount and the cumulative sum of stake amounts (cf.
Equation 3). Figure 8 illustrates the distribution of $LevM_{(S,n)}$ across
various $n$. The trend indicates that an increasing loop count $n$ is
associated with a higher leverage multiplier in practical scenarios.
Additionally, it is noteworthy that the majority ($87.57\%$) of addresses
exhibit a $LevM_{(S,n)}$ smaller than $3.5$.

Figure 7: Leverage multiplier distribution.

Figure 8: Staking APR distribution.

Leverage Staking APR. We proceed to analyze the practical implications of
leverage staking APR. Our analysis centers on a subset of $152$ addresses that
have successfully repaid their debts and withdrawn their collateral from Aave
stETH–ETH positions. To calculate their _actual_ APR, as outlined in Equation
8, we consider the net earnings from deposit and withdraw actions, balanced
against the ETH accrued through borrow and repay actions. Additionally, we
account for the conversion of accrued ETH to stETH, factoring in the stETH
price at the time of the last withdraw action. The distribution of APR for
these $152$ addresses is visually depicted in Figure 8. Notably, our findings
reveal that a significant majority, precisely $137$ leverage staking addresses
$(90.13\%)$, have realized APR higher than the APR of conventional staking on
Lido.

##  6 Cascading Liquidation

Figure 9: stETH price on the primary and secondary market.

In this section, we offer an overview of the stETH price deviation in relation
to the Terra crash incident. We illustrate how the stETH price can potentially
lead to liquidation cascades within the Lido–Aave LSD ecosystem, especially in
the context of leverage staking. Furthermore, we conduct stress tests to
evaluate the risk of cascading liquidations under extreme conditions.

###  6.1 stETH Price Deviation and Terra Crash

As a rebasing LSD, stETH changes its token supply to distribute rewards to
stakers (cf. Section 2.4). As such, the stETH to ETH price in the primary
market (i.e., Lido) is $1$. While stETH is not required to trade on par with
ETH in the secondary market (e.g., Curve), the price is anticipated to
converge to $1$. Our empirical data show that stETH did maintain a loose peg
to ETH for most of its history. However, the stETH price began to drop from
May $12$th, $2022$, reaching its lowest point of $0.931$ on May $18$th, $2022$
(cf. Figure 9).

In fact, the stETH price decline can date back to the UST/LUNA depeg. The
Terra collapse undoubtedly instilled fear and triggered selling pressure
throughout the market [16, 15]. Specifically, following the UST/LUNA depeg
incident between May $7$th and $16$th, $2022$, investors grew concerned about
the security and stability of the Terra network. Amidst prevailing bearish
sentiment, investors swiftly moved to bridge back bETH (a wrapped version of
stETH on Terra) from Terra to Ethereum via the Wormhole contract. Our data
show that $614$K bETH was bridged to Ethereum, with a remarkable $98\%$ of
these bETH converted back to stETH. This mass conversion reflects the
widespread desire to exit Terra-based staking assets. Subsequently, the
secondary market experienced significant selling pressure, primarily from
institutions such as Celsius. This imbalance in the Curve stETH–ETH pool
contributed to the price decline of stETH.

###  6.2 Cascading Liquidation and User Behaviors

Figure 10: Illustration of the cascading liquidation risk.

Figure 11: Example of leveraging.

Figure 12: Example of deleveraging.

The decline in stETH price may trigger liquidation cascades within the
Lido–Aave LSD ecosystem, especially in the context of leverage staking (cf.
Figure 10). Specifically, the decline in stETH price reduces the HF of stETH
collateralized borrowing positions on Aave, potentially leading to
liquidations. In response to liquidations, users with leverage staking
positions can either take no action and undergo liquidation or choose to
deleverage their positions.

On the one hand, users with leverage staking positions may take no action when
their HF approach the critical threshold of $1$. In this case, their
collateralized stETH might be liquidated. The liquidators repay ETH to acquire
stETH, with the liquidation amount being amplified by $LevM_{(S,n)}$.
Subsequently, a significant amount of stETH is sold in the Curve pool,
contributing to additional selling pressure on stETH. This extensive selling
further imbalances the Curve stETH–ETH pool, resulting in a further decline in
stETH price. Consequently, an increasing number of positions, including both
leverage staking and ordinary positions, are vulnerable to liquidation as a
result of declining HF.

On the other hand, users can choose to deleverage their positions on Aave to
restore HF. Assuming $\mathsf{U_{i}}$ has executed a leverage staking strategy
with $n$ loops, $\mathsf{U_{i}}$ can initiate the deleveraging process with
the following steps. _(i)_ $\mathsf{U_{i}}$ executes a swap to convert stETH
into ETH within the Curve stETH–ETH pool. _(ii)_ The received ETH is then used
to repay the ETH borrowed in the $n^{th}$ loop. _(iii)_ $\mathsf{U_{i}}$ then
withdraws the stETH that was supplied in the $n^{th}$ loop from Aave and
continues converting it into ETH using the Curve pool. This “swap-repay-
withdraw” process is repeated as necessary to deleverage the position until HF
remains above $1$. Taking address 0xD27...701 as an example, the overall
trends of HF and leverage multiplier during the deleveraging process (cf.
Figure 12) exhibit a remarkable degree of symmetry when compared to those
observed in the leveraging process (cf. Figure 12). With each repay action,
the HF of the address increases, as indicated by the red line, while the
leverage multiplier decreases, as shown by the blue line. During the period
from May 8th, 2022 to May 18th, 2022, i.e., the first ten days after the Terra
crash (cf. Figure 9), we observed $13$ users actively deleveraging their
leverage staking positions, resulting in a total debt repayment of
$74{,}983.6$ ETH. However, even if a user manages to avoid liquidation by
deleveraging, the additional selling pressure generated by the swap
transactions on Curve can still intensify the decline in stETH price and make
other leverage staking and ordinary positions susceptible to liquidation.

To summarize, users with leverage staking positions can take different actions
in response to potential liquidations. However, regardless of their choice,
these actions may contribute to additional selling pressure on stETH, further
exacerbating the price decline and potentially triggering liquidation
cascades.

###  6.3 Stress Testing

Motivation. By crawling the liquidationcall events on Aave V$2$ lending pool
from December 17th, 2020 to August 7th, 2023, we identify $18$ liquidations
for the positions where users supplied stETH to borrow ETH and $7$
liquidations for leverage lending positions. However, drawing from the
LUNA–UST incident, we recognize that a token may become entirely devalued. In
the event that stETH faces a fate similar to LUNA’s devaluation, it could lead
to a surge in liquidations. Considering that stETH has historically only
experienced a relatively modest price decline (reaching a low of $0.931$), it
is imperative to conduct stress tests to assess the risk of cascading
liquidations under a worst-case scenario.

Therefore, we perform stress tests on the Lido–Aave LSD ecosystem under
extreme conditions, simulating potential selling pressure and subsequent
liquidation cascades if the stETH experiences a dramatic decline.
Specifically, we divide the Aave collateralized stETH borrowing positions into
the leverage staking group ($G_{L}$) and ordinary group ($G_{O}$). We simulate
the following cases:

Case 1:

We simulate liquidation cascades within $G_{L}$, with selling pressure
originating from the liquidation of leverage staking positions. We analyze the
changes in HF and how leverage staking amplifies the risk of cascading
liquidations.

Case 2:

We simulate liquidation cascades across both $G_{L}$ and $G_{O}$ to explore
their mutual impact. The selling pressure is generated by liquidations.

Case 3:

We simulate liquidation cascades across $G_{L}$ and $G_{O}$, assuming that
users in $G_{L}$ choose to deleverage their positions when HF approach a
threshold of $1.1$. The selling pressure arises from deleveraging and
potential liquidations.

Simulation Setup. We initialize the Curve stETH–ETH pool by forking its state
at block $17{,}500{,}000$ (June $17$th, $2023$), with reserve of $265{,}972$
ETH and $266{,}966$ stETH. Subsequently, we mimic the institutional selling
pressure (e.g., Celsius, see Figure 10) after Terra crash by simulating a sale
of $200{,}000$ stETH on Curve. This sizable transaction leads to the decline
in the stETH price, resulting in a new exchange rate of
$100~{}\texttt{stETH}=83.76~{}\texttt{ETH}$, denoted as $p_{0}=0.8376$.

Figure 13: Simualted HF distribution.

Figure 14: Simualted HF results.

Figure 15: stETH price and liquidation amount during the liquidation cascades.

$\bullet$ Simulation of Case 1. We initialize $262$ leverage staking
positions, each with an address that we have detected in Section 5. For each
position, the values of totalDebtETH, totalCollateralETH, and HF are set to
the corresponding values recorded in the transaction logs of that position’s
most recent borrowing transaction. Furthermore, the stETHPrice for all
positions is initialized as $p_{0}$.

_Simulation Process._ The simulation unfolds through a series of sequential
rounds. In each round, the stETHPrice for all positions is updated as the
current stETH price in the Curve stETH–ETH pool. Subsequently, the HF for each
position is recalculated, using the updated stETHPrice. If, at any point, a
position’s HF drops below the critical threshold of $1$, a simulated
liquidation event is triggered. In this scenario, a designated liquidator
steps in to settle the debt by repaying it in ETH. In return, the liquidator
receives the collateral in stETH. All received stETH is converted to ETH in
the Curve stETH–ETH pool, as shown in Figure 10. This process continues until
no more liquidatable positions remain.

_Simulation Results._ We analyze the liquidation amount, HF, and stETH price
during the simulation process. As shown in Figure 14, the simulation
terminates after $11$ rounds, and $244\thinspace(93.13\%)$ positions are
liquidated. A noteworthy observation is that HF of all positions exhibit a
gradual decrease, as depicted in Figure 14. This is directly attributed to the
successive price drops of stETH, as visualized in Figure 15. The cascading
liquidations result in a total liquidation amount of $128{,}998$ ETH,
ultimately driving the stETH price down to $0.15$.

As a comparison, we simulate the scenario where the above-mentioned $262$
positions do not utilize the leverage staking strategy. This involves setting
the initial values for totalCollateralETHs, totalDebtETHs, and HFs as the
values recorded in the transaction logs when the _first_ borrowing action for
the position occurred. As illustrated in Figure 15, the red bars and lines
represent the outcome of these simulations. Notably, the cascading liquidation
triggered by positions without leverage staking ceases after only three
rounds. Merely $13{,}329$ ETH ($\frac{1}{9.68}\times$ of the case with
leverage staking) will be liquidated, and the stETH price remains more than
$0.79$ ETH. Our simulation findings indicate that leverage staking
significantly amplifies the risk of cascading liquidation.

Figure 16: Case 2 simulation results.

Figure 17: Case 3 simulation results.

$\bullet$ Simulation of Case 2. We simulate the scenario where $G_{L}$ and
$G_{O}$ co-exist on Aave. We initialize a total of $524$ positions, equally
divided into two groups. We then execute an identical simulation process as in
Case 1, recording the number of liquidated addresses and the stETH price
throughout the simulation.

_Simulation Results._ As depicted in Figure 17, the simulation terminates
after just $7$ rounds, resulting in an aggregate liquidation amount of
$146{,}330$ ETH and a significant drop in the stETH price to $0.11$. Clearly,
the situation in Case 2 is more severe than in Case 1. This is due to the
liquidation of both leverage staking and ordinary positions, further
intensifying the decline in the stETH price.

$\bullet$ Simulation of Case 3. We proceed to simulate the scenario where
$G_{L}$ and $G_{O}$ co-exist on Aave, with users in $G_{L}$ opting to
deleverage their positions. We initiate $256$ leverage staking addresses and
$256$ ordinary positions. At the beginning of each round, users in $G_{L}$
monitor their positions’ HF and initiate the deleveraging if $\ac{HF}<$ $1.1$.
The deleveraged stETH is then swapped for ETH in the Curve stETH–ETH pool,
causing a subsequent drop in the stETH price. Subsequently, the HF for each
position is recalculated based on the updated stETH price. The remainder of
the simulation process mirrors that of Case 1.

_Simulation Results._ In this case, the stETH price declines due to
deleveraging and liquidation, as depicted in Figure 17. Notably, the price
swiftly declines to $0.03$ within just three rounds. In this case, although
users in $G_{L}$ avoid liquidation by closing positions before reaching
$HF<1$, their deleveraging actions exacerbate the stETH price drop,
heightening liquidation risks for users in $G_{O}$.

Limitation. A notable limitation of our simulation is the omission of
arbitrage activities. Should sizable arbitrage transactions be executed, they
could act as stabilizing forces to restore the price equilibrium and prevent
continuous declines.

###  6.4 Discussion

Our simulation results reveal important insights. If stETH faces extreme
conditions and undergoes a significant price decline, the Aave–Lido LSD
ecosystem is at risk of cascading liquidation, especially with the presence of
leverage staking. The stETH selling pressure, arising from both liquidations
and deleveraging, can initiate a ripple effect within the system, resulting in
a further decline in the stETH price and more liquidations. As such, it is
imperative for Lido and Aave to develop robust approaches to mitigate the risk
of cascading liquidations, particularly during periods of significant market
volatility. Proactive risk management is essential for building a stable
staking and lending environment.

##  7 Related Work

There is currently limited academic literature on liquid staking. Scharnowski
_et al._ [19] analyze the liquid staking basis (e.g., the discrepancy) between
the prices of LSD in the primary and secondary market. They observe that the
liquid staking basis widens during times of increased cryptocurrency
volatility and decreased liquidity in the secondary market. Cintra  _et al._
[7] utilize the Bayesian Online Changepoint Detection (BOCD) algorithm to
identify potential depeg incidents using price data from the curve stETH–ETH
pool. This research shows that the proposed approach can assist users in
managing potential risks.

There are also several studies on DeFi lending platforms. For example,
Heimbach  _et al._ [13] conduct a study on the impact of the Ethereum merge on
two DeFi lending platforms, Compound and Aave. They investigate the actions
taken by Aave to mitigate the liquidation risk of collateralized stETH
positions. Wang  _et al._ [23] present a formal model for evaluating under-
collateralized DeFi lending platforms and conduct a risk assessment for
leverage lending positions.

##  8 Conclusion

This paper systematically studies leverage staking with LSD. We propose a
formal model to capture the leverage staking strategy within the Lido–Aave
ecosystem. We empirically detect and analyze leverage staking positions,
assessing the leverage staking amount, leverage multiplier, and APR. We
analyze the volatility of stETH price and its impact on liquidations. We
analyze the deleveraging actions undertaken by users and the selling pressure
arising from the liquidation, recognizing their potential to exacerbate
declines in the stETH price, thereby possibly triggering cascading
liquidations. We conduct stress tests to evaluate the risk introduced by
leverage staking under extreme conditions. Our simulation results indicate
that leverage staking can amplify the risks of cascading liquidations. We hope
that our work will inform and encourage DeFi lending and staking protocols to
develop robust risk assessment approaches for effectively monitoring and
mitigating the risks associated with leverage staking, as well as enhancing
the protection of stakeholders within the LSD ecosystem.

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##  Appendix 0.A Supplementary Figures and Tables

Protocol | Type | Mechanism | LSD |  TVL(USD) |  Staked ETH | Fee | APR
---|---|---|---|---|---|---|---
Lido | Pooled | Rebasing | stETH | 13.8B | 8.34M | 10% | 3.8%
Coinbase | CEX | Reward-bearing | cbETH | 2.09B | 1.21M | 25% | 3.74%
Rocket | Pooled | Reward-bearing | rETH | 1.47B | 892K | 14% | 4.32%
Binance | CEX | Reward-bearing | wBETH | 730M | 709K | 10% | 3.85%
Frax | Pooled | Dual-token |  frxETH-sfrxETH | 417M | 253K | 10% | 4.78%
Stakewise | Pooled | Dual-token |  sETH2-rETH2 | 157M | 96K | 10% | 3.83%
Swell | Pooled | Reward-bearing | swETH | 76M | 46K | 10% | 3.37%

Table 1: Statistics of top LSD providers on Ethereum, as of August $23$rd,
$2023$.

Block Number | Transaction Hash | LTV | LT
---|---|---|---
14289297 | 0x94780dc1914af5aec3b6d303e2d974669074bbceb6d1baac7d93ad0400593db0 | 0.70 | 0.75
14693506 | 0x993926559f17a579c3b0c0b5fc83fd3c9d5772e9b314f7f0e78e704c6b984726 | 0.73 | 0.75
14804760 | 0xbc40546b65ada9f5d4f8346f405a5f9c0da6d8f66bb27b7c64c0efa70eeae080 | 0.69 | 0.81
14837221 | 0x5206c144845ac63f982125f51c31b0fc474655281e2d433f8270505d87f8bbf4 | 0.70 | 0.75
14999895 | 0x25e33e04d2e5d92acd91f542a2677045e59b2d6b385e4fa0315a404396bc5c99 | 0.69 | 0.81
15759644 | 0x48653014a79433bf5f21781424b306a697f4476077a8b92e17b2ae6eda58706e | 0.72 | 0.83
16392718 | 0xdcaa33ddef0700a2a625e0b7a0c2da14499901e42c073064390f11dd83cefd19 | 0.69 | 0.81

Table 2: Historical changes of Aave V$2$ parameter configurations.

###  0.A.1 Liquid Staking Providers

Table 1 provides the statistics of top LSD providers on Ethereum.

###  0.A.2 Aave Parameter Configuration

Table 2 depicts the historical changes of Aave parameter configurations. We
crawl the collateralConfigurationChanged events for Aave V$2$ lending pool.

##  Appendix 0.B Generalized Formalization For Leverage Staking

In addition to the standardized cases discussed in Section 4, real-world
leverage lending situations can exhibit substantial variation among users.
Specifically, we consider the following variations. _(i)_ Within each leverage
staking loop, $\mathsf{U_{i}}$ may choose not to supply all the stETH acquired
from Lido as collateral on Aave. Instead, in the $k^{\text{th}}$ loop,
$\mathsf{U_{i}}$ may opt to supply only $c_{k}$ ($c_{k}\in[0,1]$) percent of
the stETH. _(ii)_ In the $k^{\text{th}}$ loop, $\mathsf{U_{i}}$ has the option
to borrow an amount of ETH that is less than the maximum borrowing capacity.
In this scenario, $\mathsf{U_{i}}$’s effective borrowing capacity becomes
$b_{k}\cdot l$, where $b_{k}\in[0,1]$. _(iii)_ In the $k^{\text{th}}$ loop,
$\mathsf{U_{i}}$ has the flexibility to restake part of the borrowed ETH on
Lido. In this scenario, $\mathsf{U_{i}}$ may choose to restake only $s_{k}$
($s_{k}\in[0,1]$) percent of the borrowed ETH.

Let $LevM_{(S,n)}$, $ColM_{(S,n)}$, and $BorM_{(S,n)}$be the leverage
multiplier, collateral multiplier, and borrowing multiplier respectively. We
know that $LevM_{(S,n)}=\frac{A_{(S,n)}}{S}$,
$ColM_{(S,n)}=\frac{C_{(S,n)}}{S}$ and $BorM_{(S,n)}=\frac{B_{(S,n)}}{S}$.
Equation 7 introduces a more generalized formalization to accommodate these
variations.

${\small\begin{split}&LevM_{(S,n)}=\sum_{k=1}^{n+1}[\prod_{i=1}^{k}s_{i}\cdot\prod_{j=1}^{k-1}c_{j}\cdot\prod_{m=1}^{k-1}b_{m}\cdot(l\cdot
P_{t_{0}}^{\texttt{st}})^{k-1}]\\\
&ColM_{(S,n)}=\sum_{k=1}^{n}[\prod_{i=1}^{k}s_{i}\cdot\prod_{j=1}^{k}c_{j}\cdot\prod_{m=1}^{k-1}b_{m}\cdot(l\cdot
P_{t_{0}}^{\texttt{st}})^{k-1}]\\\
&BorM_{(S,n)}=\sum_{k=1}^{n}[\prod_{i=1}^{k}s_{i}\cdot\prod_{j=1}^{k}c_{j}\cdot\prod_{m=1}^{k}b_{m}\cdot(l\cdot
P_{t_{0}}^{\texttt{st}})^{k}]\\\
&HF_{\mathsf{U_{i}}}(P_{t_{c}}^{\texttt{st}}|P_{t_{0}}^{\texttt{st}})=\frac{ColM_{(S,n)}\cdot
P_{t_{c}}^{\texttt{st}}\cdot\text{LT}}{BorM_{(S,n)}}\end{split}}$ (7)

##  Appendix 0.C Leverage Staking Detection Algorithm

Algorithm 1 depicts our approach to detect leverage staking addresses.

Input: An address $\mathsf{addr}$

Output: $\mathsf{addr}$’s leverage staking actions.

1

2Extract $\mathsf{addr}$’s deposit events $\\{w_{i}\\}_{i}$ and borrow events
$\\{b_{j}\\}_{j}$ on Aave, and submitted events $\\{s_{k}\\}_{k}$ on Lido;

3Let
$\mathcal{E}=\\{w_{i}\\}_{i}\bigcup\\{b_{j}\\}_{j}\bigcup\\{s_{k}\\}_{k}$;

4Convert $\mathcal{E}$ to a sequence $\mathcal{E}_{s}$ by sorting
$\mathcal{E}$ in chronological order;

5if  _$\mathcal{E}_{s}$ contains a sub-sequence with a order of
$(\texttt{submitted}$, deposit, borrow, $\texttt{submitted})$_ then

6 if  _For the sub-sequence $(\texttt{submitted}_{0}$, deposit, borrow,
$\texttt{submitted}_{1})$: _(i)_ The stETH amount received in
$\texttt{submitted}_{0}$ event $\approx$ the stETH amount in deposit event;
_(ii)_ The stETH amount in deposit event $>$ the ETH amount in borrow event;
_(iii)_ The ETH amount in borrow event $\approx$ the ETH amount in
$\texttt{submitted}_{1}$ event _ then

7 return $\mathcal{E}_{s}$;

8 return $\emptyset$;

9 else

10 return $\emptyset$;

Algorithm 1 Leverage Staking Detection.

##  Appendix 0.D Additional Leverage Staking Measurement Results

###  0.D.1 Actual APR Computation

Equation 8 represents our proposed method for calculating the _actual_ APR in
the context of leverage staking. This approach involves the net earnings
yielded from deposit and withdraw actions, which are then offset against the
ETH consumed during borrow and repay actions. Furthermore, our calculation
takes into consideration the conversion of consumed ETH to stETH, factoring in
the stETH price at the moment of the last recorded deposit action.

$\displaystyle\mathsf{actualAPR}=\frac{\left(\mathsf{earnedstETH}-\frac{\mathsf{accuredETH}}{p_{\texttt{stETH}}}\right)\cdot\frac{3600\cdot
24\cdot
365}{12}}{\mathsf{totalDepositstETH}\cdot\left(\mathsf{lastWithdrawBlock}-\mathsf{firstDepositBlock}\right)}$
(8)
$\displaystyle\mathsf{accruedstETH}=\mathsf{totalWithdrawstETH}-\mathsf{totalDepositstETH}$
$\displaystyle\mathsf{accruedETH}=\mathsf{totalRepayETH}-\mathsf{totalBorrowETH}$