# Do You Care About Your Positions? Users Under Liquidation Risk in Decentralized Lending Protocol

Boyang Mu, Natkamon Tovanich, Julien Prat

► To cite this version:

Boyang Mu, Natkamon Tovanich, Julien Prat. Do You Care About Your Positions? Users Under Liquidation Risk in Decentralized Lending Protocol. IEEE International Conference on Blockchain and Cryptocurrency, IEEE ComSoc, Jun 2025, Pisa, Italy. 10.1109/ICBC64466.2025.11114495. hal-05041569

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Submitted on 21 Apr 2025

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# Do You Care About Your Positions? Users Under Liquidation Risk in Decentralized Lending Protocol

Boyang Mu

CREST, CNRS, ENSAE Paris

Institut Polytechnique de Paris

Palaiseau, France

boyang.mu@ensae.fr

Natkamon Tovanich

CREST, CNRS, École Polytechnique

Institut Polytechnique de Paris

Palaiseau, France

natkamon.tovanich@ensae.fr

Julien Prat

CREST, CNRS, École Polytechnique

Institut Polytechnique de Paris

Palaiseau, France

julien.prat@ensae.fr

**Abstract**—Lending protocols have transformed the Decentralized Finance (DeFi) ecosystem, driving innovation while also introducing new risks. This study develops a machine learning framework to predict user behavior and assess factors influencing changes in health ratios within the Compound V2 protocol. By analyzing user historical data, position metrics, and market conditions, we propose machine learning-based models to predict whether users will adjust their positions or face liquidation. We find that Random Forest and XGBoost models excel in predicting these outcomes, with features like collateral values, historical risk exposure, and asset composition playing significant roles. Additionally, panel regression models reveal insights into health ratio dynamics over time and across asset types, as well as user sophistication. These findings offer a better understanding of user behavior, highlighting opportunities for improved risk modeling and adaptive strategies in DeFi lending.

**Index Terms**—decentralized finance, lending protocols, user modeling, decision-making, liquidation, financial risks

## I. INTRODUCTION

Since their inception in 2018, lending protocols have become a cornerstone of the Decentralized Finance (DeFi) ecosystem. They enable users to borrow and lend without relying on financial intermediaries. The innovative design of lending protocols introduces new sources of risk that are still poorly understood. This article focuses on the primary risk for borrowers, namely liquidation risk. To mitigate the impact of defaults, lending protocols try to ensure that all their loans remain over-collateralized. They continuously monitor borrowers' positions, activating a liquidation mechanism that triggers the sale of collateral when its value falls below a certain threshold. Although such a mechanism is crucial to maintain the solvency of the protocols, it can lead to liquidation spirals and systemic failures if not properly managed [1]–[3].

During liquidation events, outstanding debts are settled by a liquidator who receives a share of the collateralized assets in return. As documented in [4], prevailing mechanisms tend to favor liquidators, often resulting in the sale of excessive collateral at the borrowers' expense. To avoid such losses, borrowers facing potential liquidation have several options. The most common strategy is to adjust their positions by adding

more collateral. Alternatively, borrowers short on cash may use flash loans to pay off their debt and close their positions [5]. However, this option is not always feasible, especially for large positions or when liquidity in decentralized exchanges is insufficient. Inappropriate strategies can exacerbate systemic risks and undermine the stability of lending protocols [6].

Given these risks, it is crucial to develop an accurate and efficient method for predicting borrowers' behavior. This paper aims to create a framework using machine learning models to predict the likelihood of a borrower rebalancing their position to avoid liquidation. Moreover, we also use our framework to identify the key factors influencing changes in users' health ratios. This paper makes the following contributions to the existing literature:

1. **Predictability of borrowers' behavior:** We propose a machine learning-based method to predict a borrower's decision when her position is deemed “risky.” Specifically, we leverage the availability of historical information and the observability of each borrower's exposure at the time of decision-making.

2. **Explainability of health ratio:** The “riskiness” of an account is determined by its health ratio. We provide a robust estimation method to assess the marginal effect of relevant features on changes in the health ratio.

## II. RELATED LITERATURE

A growing body of literature examines the risks associated with lending protocols, emphasizing market dynamics, platform-specific risks, and systemic vulnerabilities. However, the study of user behavior and their decision-making process remains comparatively underexplored.

Chaudhary and Pinna (2022) [1] rely on a multi-asset agent-based model to evaluate DeFi market risk, finding that the ecosystem is relatively robust against price volatility. Conversely, Perez et al. (2021) [3] show that while the efficiency of liquidations on protocols like Compound have improved over time, even small price changes (e.g., 3%) can lead to significant liquidation events involving assets worth over $10 million. They also highlight the role of misconceptions surrounding stablecoins in amplifying liquidation risks. Heimbach and Huang (2023) [7] investigate leverage dynamics using wallet-level data from major platforms, finding that factors

<footnote>This work was supported by the *Blockchain@X Academic Chair* and the CHIST-ERA grant *FairOnChain*, by Agence Nationale de la Recherche (ANR-23-CHRO-0002).</footnote>
such as loan-to-value (LTV) requirements, borrowing rates, and market conditions significantly influence leverage, with higher leverage ratios undermining lending resilience.

Two studies closely related to our work contribute to understanding liquidation costs and credit risk modeling in DeFi. Moallemi and Patange (2024) [5] analyze optimal collateral holdings that balance capital and liquidation costs using user data from Aave V2. They observed a slightly higher median health factor than the model’s optimal predictions. Palaiokrassas et al. (2024) [8] explore machine learning techniques to assess users’ credit risk, utilizing a multi-chain dataset to highlight the predictive power of transaction-based features.

Our study differs from prior work by offering a more granular analysis of users’ health factors. Instead of focusing solely on median health factors as in [5], we examine their entire distribution and find that the majority of user health ratios on Compound V2 are just around the risky threshold, suggesting relatively sophisticated user behavior. This contrasts with the patterns observed on Aave V2, which may reflect differences in users’ strategies aligned with the cost-benefit framework [5].

Additionally, our work expands upon prior credit risk assessment approaches [8] by incorporating a broader set of predictive features. These include risk measures such as health ratios, market price volatility, and user position details. We also emphasize the interpretability of user decisions by analyzing historical public and private data to identify factors that contribute to changes in health ratios. This dual focus on predictive modeling and behavioral analysis offers fresh insights into the reasoning behind users’ decisions in DeFi lending markets.

### III. DESCRIPTION OF THE COMPOUND V2 PROTOCOL

We focus on the Compound V2 protocol, one of the earliest and leading decentralized lending platforms [9]. Compound facilitates borrowing and lending through a collection of liquidity pools. Each liquidity pool corresponds to a specific asset, where $K = \{1, 2, ..., k\}$ represents the set of all assets supported by the protocol.

For a user $u$ at a given snapshot $t$, their financial state within the Compound protocol is characterized by:

1) **Lending Vector** $l_{u,t} = (l_{u,t}^1, l_{u,t}^2, ..., l_{u,t}^k)$. The amounts $l_{u,t}^i$ represent the units of the asset $i$ that user $u$ has supplied to the protocol but has not used as collateral.

2) **Collateral Vector** $c_{u,t} = (c_{u,t}^1, c_{u,t}^2, ..., c_{u,t}^k)$. The amounts $c_{u,t}^i$ represent the units of the asset $i$ that user $u$ has used as collateral in the protocol. Unlike the lending vector, the collateral vector flags which assets have been allocated for collateral purposes.

3) **Borrowing Vector** $b_{u,t} = (b_{u,t}^1, b_{u,t}^2, ..., b_{u,t}^k)$. The amounts $b_{u,t}^j$ represent the units of the asset $j$ that user $u$ has borrowed from the protocol.

The Compound protocol assesses the risk associated with each user by calculating their health factor $H_{u,t}$ at time $t$ for a user $u$. This metric compares the value of their collateralized assets to their borrowed assets, defined as:

<figure><img src="image_2.png" /><figcaption>Fig. 1. Daily total deposits, total borrows, and loan-to-deposit ratio (LDR) in the Compound V2 protocol</figcaption></figure>

$$H_{u,t} = \frac{\sum_{i \in K} (l_{u,t}^i \cdot p_t^i \cdot c f^i)}{\sum_{j \in K} (b_{u,t}^j \cdot p_t^j)}, \quad (1)$$

where $p_t^i$ and $p_t^j$ represent the market prices of assets $i$ and $j$ at time $t$, respectively. The collateral factor, $c f^i$, is the maximal proportion of the collateral value of asset $i$ that can be utilized for borrowing.

A health factor $H \ge 1$ indicates that the user’s position is over-collateralized and, therefore, secure. Conversely, a health factor $H < 1$ indicates that the position is under-collateralized and at risk of liquidation. In such cases, a liquidator can repay a portion of the user’s debt on their behalf. The liquidator is compensated by seizing a corresponding amount of the user’s collateral at a discounted rate. Liquidation helps maintain the protocol’s solvency by enforcing over-collateralization, thereby minimizing the risk of accumulating irrecoverable debt during periods of price volatility.

The evolution of total deposits (the sum of lending and collateral vectors), total borrowings, and the loan-to-deposit ratio in Compound V2 is depicted in Fig. 1. The protocol experienced rapid growth from 2021 to 2022, driven by heightened user engagement and liquidity mining incentives. However, this momentum waned as competition intensified and liquidity mining incentives diminished.

### IV. DATA

The dataset used in this study consists of panel data that captures the behaviors and account characteristics of Compound’s users. Our primary objective is to analyze users’ decisions when their positions become risky, specifically whether they replenish their positions or risk liquidation.

#### A. Data Collection

We collected daily snapshots of all user positions from the official Compound V2 subgraph [10] hosted on The Graph [11], a decentralized protocol for indexing blockchain data. The dataset spans from the protocol’s inception on May 7, 2019, to June 15, 2024. Our dataset captures the protocol’s growth, peak, and decline while spanning critical periods, including ETH price surges and declines, the DeFi summer (2020-2021), and the subsequent crypto winter (2021-2022).

For each snapshot $t$, users in a “risky” position with respect to liquidation were identified as having a health ratio below 1.1
<figure><img src="image_3.png" /><figcaption>Fig. 2. Time-series statistics of the Compound V2 protocol and users at risk: (a) Number of users at risk and the percentage of the total borrowed amount at risk, (b) Distribution of borrowed amounts for users at risk, and (c) Number of *adjustPosition* and *isLiquidated* users over time.</figcaption></figure>

on a given day, consistent with the criteria established by [7]. A lower health ratio indicates a higher risk of liquidation due to a decline in the market value of the collateral. For each user identified as “risky”, their activities and positions were tracked at snapshot $t+1$ (the following day).

In our dataset, we identified 2,237,579 risky positions across 9,123 user accounts. Fig. 2 (a) illustrates the number of users at risk and the percentage of the borrowed amount at risk. Over time, the number of users at risk has increased, likely driven by granular users leaving small “dust” positions unpaid, where the transaction fees exceed the repayment value, as depicted in Fig. 2 (b). Between mid-2020 and 2022, the high percentage of borrowed amounts at risk suggests that users employed strategic behavior to optimize their health ratios, potentially influenced by liquidity mining incentives. This trend subsided after 2022, as these users appear to have exited the protocol.

User positions are divided into two groups based on their status at snapshot $t+1$. These groups represent the dependent variables in the analysis.

1. **adjustPosition**: True if the user adjusts their position to improve their health ratio by repaying loans or increasing collateral; False otherwise.

2. **isLiquidated**: True if the user's position is liquidated due to inaction or insufficient adjustments; False otherwise.

Among these risky positions, 22,136 positions (5,626 users) involved users adjusting their positions, while 10,984 positions (3,509 users) were liquidated at the snapshot $t+1$. This distribution indicates a notable class imbalance in the classification task. Fig. 2 (c) illustrates the temporal trends of *adjustPosition* and *isLiquidated* accounts. Notably, both categories exhibited a sharp increase during periods of sudden ETH price drops.

## B. Feature Extraction

For each risky position, we extract a set of independent variables that capture users' positions, characteristics, and market conditions at snapshot $t$.

**User Historical Metrics:** measure the user's historical activities and behavior in the protocol.

* **days**: Total days the user has been active in the protocol.

* **accumRisky**: Number of days the user has been in a risky position.

* **accumAdjustPosition**: Number of days the user adjusted their position to improve their health ratio.

* **accumLiquidate**: Number of days the user's positions were liquidated.

* **periodRisky**: Number of consecutive days the account has remained in a risky position.

* **periodNoAdjust**: Number of consecutive days the account has not taken any actions to adjust its position.

* **periodRiskyNoAdjust**: Number of consecutive days the account stays in a risky position without making adjustments.

**User Position Metrics:** describe the aggregated user's current financial state.

* **supplyUSD**, **borrowUSD**, **collateralUSD**: Total values (in USD) of supplied, borrowed, and collateralized assets. Since the latter two variables exhibit a highly skewed distribution, we transform these amounts into their natural logarithms, creating $log(borrowUSD)$ and $log(collateralUSD)$, respectively.

* **maxCollateralUSD**: The maximum amount of collateral value that can be used to support borrowing, calculated as: $\sum_{i \in \mathcal{K}} (l_{u,t}^i \cdot p_t^i \cdot c f^i)$

* **health**: The health ratio of the user's position at the snapshot $t$.

* **countBorrow** and **countCollateral**: The number of distinct assets borrowed and used as collateral.

**Asset Composition Metrics:** represent the composition and concentration of assets in user positions.

* **pctBorrowStable** and **pctCollateralStable**: Percentage of stablecoins in borrow and collateral assets.

* **hhiBorrow** and **hhiCollateral**: Herfindahl-Hirschman indices measuring the concentration of borrowing and collateral assets. A value close to 0 indicates a highly diversified portfolio, while a value close to 1 indicates a highly concentrated portfolio dominated by a single asset.

* **pctSelfBorrow**: The percentage of self-borrowed assets, where a user borrows against the same supplied collateral [12]. This behavior is driven by lending protocol incentives, which reward users with protocol tokens for engaging in both lending and borrowing activities [13].
* *countBorrow* and *countCollateral*: The number of tokens borrowed or collateralized. They capture the quantitative aspect of the Herfindahl-Hirschman indices, and provide a granular measure of the diversity of the user's portfolio.

**Market Condition Metrics** capture market conditions and volatility, including:

* *borrowPctChange* and *collateralPctChange*: Percentage daily price changes for borrow and collateral assets between snapshots *t* and *t* + 1

* *borrowVolatility7D* and *collateralVolatility7D*: Price volatility of borrow and collateral assets, calculated as the standard deviation of *borrowPctChange* or *collateralPctChange* over the past 7 days.

For users with more than one lending or borrowing asset, we calculate a weighted average for each metric, using the value of the user's borrow or collateral in USD as weights.

We also collected a 1-minute market price for each asset from the Kaggle dataset [14] and further updated the price dataset using the Syve's market data API [15], provided by the same publisher. Using this dataset, we compute 1-minute volatility for each asset at days *t* and *t* + 1 to capture day market dynamics that may influence users' decision-making.

## V. METHOD

In this study, we analyze the decision-making behavior of users in the Compound V2 protocol when their positions become risky. Our objective is to understand how users respond to risk and what factors influence their actions. We design two experiments to explore user behavior and decision-making:

1. **Experiment 1: Predict User Behaviors** examines users' decision-making behavior when their positions become risky. Using user positions at snapshot *t*, we aim to predict the following outcomes at snapshot *t* + 1: (i) whether the user adjusts their position and (ii) whether the user is liquidated. This is formulated as a binary classification problem, employing machine learning techniques to improve predictive performance.

2. **Experiment 2: Explaining Variations in Health Ratio** examines the factors influencing changes in the health ratio of risky users at snapshot *t* + 1. These factors are incorporated into a panel ordinary least-squares (OLS) regression model for evaluating the impact of the explanatory variables on changes in the health ratio.

By integrating the predictive insights from Experiment 1 with the explanatory analysis in Experiment 2, we aim to better understand user behavior and the factors driving risky positions in Compound V2.

### A. Classification Models

To classify user behavior in Compound, we utilized two groups of machine learning algorithms: (i) standalone models, including Logistic Regression and Decision Tree, and (ii) ensemble models, including Random Forest, XGBoost, and LightGBM. All classification models were trained and evaluated using the Python *scikit-learn* library [16].

1. **Logistic Regression** served as the baseline model due to its simplicity and interpretability. It models the probability of outcomes as a linear combination of the input features. We applied regularization techniques, specifically L1 and L2 penalties to prevent overfitting and improve generalization.

2. **Decision Tree** model allows for non-linear relationships in the data. This model partitions the feature space into distinct regions by recursively splitting the data based on feature thresholds.

3. **Random Forest** model creates an ensemble of decision trees and aggregates their prediction. The trees are trained on bootstrapped subsets of the data using random feature selection for each split [17].

4. **XGBoost** improves the efficiency in model training time through parallelized tree-building and regularization. By employing L1 and L2 penalties, XGBoost reduces overfitting and improves the model's ability to handle complex relationships in the data [18].

5. **LightGBM** uses a leaf-wise growth strategy, which enables faster training and better handling of large-scale datasets. This makes it an effective alternative to XG-Boost in scenarios where training speed and dataset size are critical [19].

To address the class imbalance, we train the model using *class_weight=balanced* parameter. This approach assigns greater weight to the minority class, ensuring that the model's predictions are not biased toward the majority class.

**Model Training.** The dataset is divided into an 80% training set and a 20% test set, maintaining consistent proportions of class 0 and class 1 across both sets. The hyperparameters for each model are fine-tuned with a 3-fold cross-validation on the training set to maintain computational feasibility and prevent excessive training time.

We designed three feature groups for model training: (i) The first group includes original features from user positions, such as health ratio, asset balances, and collateral values, forming the baseline for prediction. (ii) The second group augments these features with the 1-minute price volatility of day *t*, capturing the influence of the previous day's price fluctuations on user decisions. (iii) The third group also incorporates the 1-minute price volatility of the current day *t* + 1 to assess the impact of intraday market movements on user behavior.

**Evaluation** We evaluated the models' performance on the 20% test set. Given the class imbalance in the dataset—where fewer users adjust their positions or are liquidated—we employed a range of robust evaluation metrics, including precision, recall, F1-score, and AUROC (Area Under the Receiver Operating Characteristic Curve).

We report two types of score to assess model performance:

1. **Macro-averaged metrics** compute the unweighted average of precision, recall, and F1-score across both classes, treating each class equally regardless of its size. This ensures that the majority class does not overshadow the performance of the minority class.
<figure><img src="image_4.png" /><figcaption>Fig. 3. Comparison of model performances on adjustPosition isLiquidated classifications</figcaption></figure>

2) **Class 1 metrics** evaluate how well the model predicts the target outcomes of the minority class (adjustPosition or isLiquidated) since this is the primary focus of our study.

## B. Panel Regression Models

To explain variations in the health ratio, we employ a base-line panel ordinary least-squares (OLS) regression model. This model is particularly suited for analyzing longitudinal data, as it accounts for repeated observations of the same entities over time. The model implementation from the *linearmodels* library was utilized for our analysis [20].

The panel OLS model to explain changes in the health ratio $\Delta H_u = H_{u,t+1} - H_{u,t}$ of user u after entering a risky position is defined as:

$$ \Delta H_u = \alpha + \mathbf{X}_{u,t}\beta + \mu_u + \lambda_t + \epsilon_{u,t}, \quad (2) $$

where $\mathbf{X}_{u,t}$ is a vector of selected explanatory variables at the snapshot t, and $\beta$ contains the coefficients that capture the impact of explanatory variables on $\Delta H_u$.

To mitigate the impact of outliers, we filter out observations with borrowing positions below $10 and instances where the absolute change in the health ratio exceeded 30 ($|H_{u,t+1} - H_{u,t}| > 30$). These positions typically belong to passive users attempting to close their accounts but are deterred by gas fees exceeding the value of their positions, which falls outside the scope of our analysis.

We incorporate two types of fixed effects into the model to address unobserved heterogeneity:

1) **Entity Effect ($\mu_u$)** captures user-specific characteristics that are constant overtime (e.g., risk preferences and investment strategies) but vary across users.

2) **Time Effect ($\lambda_t$)** captures factors that vary over time (e.g., macroeconomic conditions and market-wide trends) but are consistent across users.

Beyond the baseline model, we examine how the health ratio evolves over time and across different asset types.

1) **Time Periods:** Compound has experienced significant capital inflows and outflows, with a peak of $12 billion in total value locked in 2021 [21]. We split the dataset into annual subsamples and estimated the coefficients for

each period to investigate whether the observed patterns remained stable over time.

2) **Borrowed Asset Types:** Previous studies, such as To-vanich et al. (2023), have shown that users frequently use ETH as collateral to borrow USDC stablecoins [12]. To explore portfolio-specific effects, we conduct separate analyses based on asset composition. Specifically, we compare users who borrow only stablecoins with those who have cryptocurrency assets. This segmentation ensures robustness in our findings by accounting for differences in portfolio strategies and risk profiles.

The results from the panel OLS models reveal the potential factors driving changes in the health ratio and how these relationships evolve across different time periods and portfolio compositions.

# VI. RESULTS

This section presents the performance of our classification models for predicting *adjustPosition* and *isLiquidated*, along with a panel regression analysis to identify factors influencing changes in users' health ratios.

## A. Evaluating the performance of classification models

Using a 20% test set, we evaluate the performance of classification models after cross-validation and hyperparameter tuning on the training set. The models predict two key outcomes at snapshot $t+1$: (i) *adjustPosition* which forecasts whether users will provide additional liquidity; and (ii) *isLiquidated* which predicts whether an account will be liquidated.

**Classification of adjustPosition:** Fig. 3 (a) reveals that non-linear models, in particular, Random Forest and XGBoost, outperform linear models, highlighting the complexity of this classification task. Among these, Random Forest emerges as the best performer, achieving the highest macro F1-score and AUROC when utilizing the $t$ volatility feature set. This result suggests that inter-day price volatility at day $t$ plays a crucial role in predicting users' decisions to adjust their liquidity pool positions. Nonetheless, incorporating inter-day volatility at $t+1$ did not significantly improve classification performance. RandomForest also demonstrates an improvement in evaluation metrics for the positive class (class 1) compared to other ensemble tree models, such as XGBoost and LightGBM.
<figure><img src="image_5.png" /><figcaption>Fig. 4. Model performance over time using sliding-window training</figcaption></figure>

**Classification of isLiquidated:** Fig. 3 (b) also demonstrate that non-linear models perform effectively at predicting *isLiquidated*. Random Forest achieves the best precision and F1-score for both macro and class 1 using the original feature set. In contrast, XGBoost provides the best results in terms of recall and AUROC when incorporating the *t* and *t* + 1 volatility features, demonstrating a slight improvement over Random Forest. XGBoost's result highlights inter-day price volatility as a critical signal in predicting liquidation events. In both models, the positive class (class 1) metrics are closely aligned with the macro metrics, suggesting that the models effectively capture patterns in the minority class rather than being biased toward the majority class.

To evaluate the impact of temporal changes in classification performance, we trained models using data from year *y* and tested them on year *y*+1, comparing their performance against a global model trained on the entire dataset. As shown in Figure 4, models trained on individual years generally underperformed relative to the global model, suggesting that incorporating data across multiple years improves model robustness. However, we observed notable performance deviations in 2021 and 2023 for the *adjustPosition* model, indicating potential shifts in user behavior during these periods.

## B. Feature importance on classification models

We extract feature importance scores for each classification task from the best-performing classification models with the highest AUROC values, reflecting their ability to distinguish between the two target classes: Random Forest with *t* volatility features is used for predicting *adjustPosition*, while XGBoost with both *t* and *t* + 1 features is used for predicting *isLiquidated*. Fig. 5 presents the feature importance scores for the top 20 variables in each model.

**Factors influencing adjustPosition predictions.** The Random Forest model identifies user position and historical features as key predictors of *adjustPosition*. Among them, *periodNoAdjust* (0.0625) stands out as a key feature, reflecting the number of consecutive days a user has not taken any actions to adjust their position. User positions also largely influence the decision, including *maxCollateralUSD* (0.0589), *collateralUSD* (0.0567), *borrowUSD* (0.0558), and *health* (0.0522). The first three variables indicate the user's position size, while *health* reflects their current risk level.

<figure><img src="image_6.png" /><figcaption>Fig. 5. Feature importance scores of the top 20 variables: (a) Random Forest model for predicting *adjustPosition* and (b) XGBoost model for predicting *isLiquidated*.</figcaption></figure>

Market conditions also influence users' *adjustPosition* decisions, with features such as *collateralPctChange* (0.0392), *collateralVolatility7D* (0.0321), and *borrowPctChange* (0.0239) Among intraday volatility metrics, *LINK(t)* (0.02811), *WETH(t+1)* (0.0246), and *WBTC(t)* (0.0236) stand out. These findings suggest that asset-level volatility metrics, while modest in impact, have a noticeable effect on position adjustments.

Overall, the feature importance scores in the *adjustPosition* model suggest that users' decision-making primarily hinges on their historical activity and current financial status, rather than short-term price fluctuations.

**Factors influencing isLiquidated predictions.** The XG-Boost model identifies *maxCollateralUSD* (0.1440) as the most influential feature, highlighting the dominant role of users' maximum collateral value in predicting liquidation events. It is followed by *pctSelfBorrow* (0.0904), which represents the percentage of borrowed assets that match the supplied collateral, typically driven by the incentive to earn protocol tokens. Historical behavior factors, such as *isLiquidated(t)* (0.0567), *periodRiskyNoAdjust* (0.0477), and *periodRisky* (0.0338), indicate that users' past risk exposure and liquidation events at *t* significantly impact the model's predictions. Additionally, daily volatility metrics for *WETH(t+1)* (0.0635), *LINK(t+1)* (0.0202) and *WBTC(t+1)* (0.0153) contribute to predicting liquidation events. Features beyond the top 5 have secondary importance, with relatively mild impact.

The feature importance scores in the *isLiquidated* model indicate that user position metrics and historical risk behaviors are the key factors driving liquidation outcomes, while market conditions and volatility metrics offer additional context.

## C. Discussion on panel regression models

To better understand user behavior, we analyze the health ratio changes for users who adjusted their positions or faced liquidation versus those who did not. The histograms in Fig. 6 reveal that risky users tend to maintain or slightly improve
<figure><img src="image_7.png" /><figcaption>Fig. 6. Histograms on changes in the health ratio</figcaption></figure>

their health ratios, likely as a strategy to avoid liquidation. While price fluctuations can cause health ratios to fluctuate, these users consistently keep their ratios near the borderline threshold, reflecting a deliberate and strategic approach to optimizing their positions in response to market volatility.

We apply panel regression to assess the impact of various variables on changes in the health ratio. Table I reports the regression estimates, standard deviations, and significance levels for our baseline model. In addition, we ran separate regression models by year and borrowed asset types to validate whether the effects remain consistent over time and across borrowing asset categories. For each regression, we focus on significant variables categorized by the feature metrics and the size of their influence on the change in health ratio.

**Baseline Regression Model.** We run a panel regression model for the entire dataset as the baseline. Our results show that the variables related to users’ historical information are significant. Still, their impact on changes in the health ratio is relatively weak (e.g., *periodRisky*, *periodNoAdjust*, and *periodRiskyNoAdjust*). For instance, if a user’s position remains risky for an extended period without adjustment at time *t*, the health ratio tends to increase due to price effects or liquidations. This effect holds across regressions by year and asset type.

The baseline model also reveals that a user’s health ratio tends to increase with the number of assets in their position, likely mitigating idiosyncratic risks. Specifically, everything else being equal, each additional borrowed asset (*countBorrow*) increases the health ratio by 0.0013, while each additional collateral asset (*countCollateral*) raises it by 0.6.

Asset-wise, the regression shows that using more stablecoins as borrowed or collateral (*pctBorrowStable* or *pctCollateralStable*) assets can decrease the health ratio, with a larger decline observed in borrowed assets. Furthermore, when a portfolio’s borrowed assets are more concentrated (higher *hhiBorrow*), the health ratio tends to increase, whereas the concentration in collateral assets (*hhiCollateral*) tend to lead to a decline in health ratio. The underlying mechanism behind these contrasting effects becomes clearer when the types of borrowed assets are analyzed separately. Additionally, self-borrowing (*pctSelfBorrow*) generally leads to a decrease in the health ratio. This ambiguous effect is explored below when we discuss regressions by borrowing asset types.

Market conditions also impact changes in the health ratio.

All else being equal, a one-percentage-point increase in the price volatility of a collateral asset (*collateralVolatility7D*) increases the health ratio by 0.0354. However, this aggregate effect varies for users with different types of assets and levels of sophistication over time, which will be analyzed separately in the following extensions.

**Regression by Years.** We fit the panel regression model separately for each year from 2019 to 2024, capturing the significant variation in user inflows and outflows within the Compound V2 protocol over time (Fig. 2 (a)).

A general trend is that factors of all metrics have a stronger effect in 2020, and this decreases steadily over time. This is because there is a huge user inflow between 2020 and 2021 when the Compound protocol is particularly active (Fig. 2 (b)). The following user outflows have weakened many market mechanisms, leading to a decline in the effects of all features.

For the users who adjust their positions in 2020, the health ratio would still, on average, decline, while for those who adjust in 2022, the health ratio would improve, indicating a growing proportion of sophisticated users. Liquidations significantly enhanced the health ratio in 2020 and 2021, while the impacts in 2022, 2023, and 2024 are no longer significant, matching our previous observations that liquidation events occur less frequently as time goes by.

The user historical metrics also provide rich information after sub-sampling. For users with a longer period of risky positions, the impact was positive and significant in 2021, 2022, 2023, and 2024, while insignificant in 2020. This reflects the inflow of users with mixed types but the outflow of more unsophisticated users relative to sophisticated ones, who are more adept at managing risky positions.

**Regression by Borrowing Asset Types.** By separating users who borrow only stablecoins from those who borrow both stablecoins and risky assets, we observe that everything else being equal, users who adjust their positions tend to expect an increase in their health ratio, which is different from what the baseline regression indicates. This is because the subsampling approach fixes variations on the borrowing side and captures the effects of over-collateralization.

Another key difference between the two groups is seen in the price effect. For users who borrow only stablecoins, the price volatility of collateral assets has more influence on the health ratio than those who borrow both stable and risky assets. This is likely attributable to the price stability of stablecoins.

Asset-wise, we observe that increasing the number of stablecoins borrowed is less effective in improving the health ratio than increasing risky assets. If managed appropriately, risky assets contribute to a more efficient portfolio, leading to a better health ratio.

Regarding self-borrowing, users who borrow cryptocurrencies experience a slightly stronger negative effect on their health ratio (coefficient ≈ -0.001, *p* < 0.001) compared to those who borrow only stablecoins, who exhibit a similar coefficient but with weaker statistical significance (*p* < 0.01). This can be explained by the fact that self-borrowing can act
<table><caption>TABLE I
PANELS REGRESSION MODEL ESTIMATION RESULTS</caption><thead><tr><th rowspan="2">Variable</th><th rowspan="2">Baseline</th><th colspan="4">Year</th><th colspan="2">Borrowing Assets</th></tr><tr><th>2020</th><th>2021</th><th>2022</th><th>2023</th><th>2024</th><th>Stablecoins</th><th>Cryptocurrencies</th></tr></thead><tbody><tr><td>adjustPosition(t)</td><td>-0.0053***<br>(-0.0009)</td><td>-0.015***<br>(0.003)</td><td>-0.002<br>(0.002)</td><td>0.005***<br>(0.002)</td><td>0.000<br>(0.001)</td><td>0.003<br>(0.003)</td><td>0.010***<br>(0.001)</td><td>0.010***<br>(0.002)</td></tr><tr><td>isLiquidated(t)</td><td>0.0106***<br>(0.0012)</td><td>0.027***<br>(0.010)</td><td>0.011***<br>(0.004)</td><td>-0.002<br>(0.002)</td><td>-0.002<br>(0.002)</td><td>0.000<br>(0.004)</td><td>0.003*<br>(0.001)</td><td>-0.001<br>(0.003)</td></tr><tr><td>borrowPctChange</td><td>0.0421***<br>(0.0026)</td><td>0.098***<br>(0.029)</td><td>0.034***<br>(0.005)</td><td>0.033***<br>(0.003)</td><td>0.041***<br>(0.002)</td><td>0.037***<br>(0.002)</td><td>-0.000<br>(0.012)</td><td>0.058***<br>(0.003)</td></tr><tr><td>collateralPctChange</td><td>-0.0434***<br>(0.0023)</td><td>-0.189***<br>(0.034)</td><td>-0.046***<br>(0.007)</td><td>-0.028***<br>(0.002)</td><td>-0.024***<br>(0.001)</td><td>-0.024***<br>(0.002)</td><td>-0.073***<br>(0.002)</td><td>-0.055***<br>(0.004)</td></tr><tr><td>borrowVolatility7D</td><td>-0.0071<br>(0.0049)</td><td>0.063<br>(0.073)</td><td>-0.002<br>(0.011)</td><td>-0.007<br>(0.007)</td><td>0.009**<br>(0.004)</td><td>-0.022***<br>(0.004)</td><td>0.002<br>(0.013)</td><td>0.002<br>(0.005)</td></tr><tr><td>collateralVolatility7D</td><td>0.0354***<br>(0.0044)</td><td>0.139*<br>(0.080)</td><td>0.075***<br>(0.014)</td><td>0.046***<br>(0.004)</td><td>0.015***<br>(0.002)</td><td>0.028***<br>(0.003)</td><td>0.072***<br>(0.004)</td><td>0.027***<br>(0.006)</td></tr><tr><td>log(borrowUSD)</td><td>0.0001<br>(0.0001)</td><td>0.000<br>(0.000)</td><td>0.000<br>(0.000)</td><td>0.000***<br>(0.000)</td><td>0.000***<br>(0.000)</td><td>0.000***<br>(0.000)</td><td>0.000*<br>(0.000)</td><td>0.000**<br>(0.000)</td></tr><tr><td>log(collateralUSD)</td><td>-0.0002***<br>(4.183e-05)</td><td>-0.000<br>(0.000)</td><td>-0.000<br>(0.000)</td><td>-0.000***<br>(0.000)</td><td>-0.000***<br>(0.000)</td><td>-0.000***<br>(0.000)</td><td>-0.000*<br>(0.000)</td><td>-0.000*<br>(0.000)</td></tr><tr><td>countBorrow</td><td>0.0013<br>(0.0007)</td><td>0.021***<br>(0.005)</td><td>-0.009***<br>(0.002)</td><td>-0.001<br>(0.001)</td><td>0.002**<br>(0.001)</td><td>-0.008***<br>(0.002)</td><td>0.004**<br>(0.000)</td><td>0.001***<br>(0.000)</td></tr><tr><td>countCollateral</td><td>0.0026***<br>(0.0004)</td><td>0.001<br>(0.003)</td><td>0.011***<br>(0.001)</td><td>-0.001<br>(0.001)</td><td>0.000<br>(0.001)</td><td>0.009***<br>(0.002)</td><td>0.000***<br>(0.000)</td><td>0.000**<br>(0.000)</td></tr><tr><td>pctBorrowStable</td><td>-0.0058***<br>(0.0012)</td><td>-0.007<br>(0.011)</td><td>-0.029***<br>(0.005)</td><td>-0.003<br>(0.002)</td><td>-0.009***<br>(0.002)</td><td>-0.007<br>(0.005)</td><td>/<br>/</td><td>/<br>/</td></tr><tr><td>pctCollateralStable</td><td>-0.0028**<br>(0.0010)</td><td>-0.001<br>(0.009)</td><td>-0.005<br>(0.005)</td><td>0.001<br>(0.004)</td><td>0.004***<br>(0.002)</td><td>-0.001<br>(0.002)</td><td>0.001<br>(0.000)</td><td>0.000<br>(0.000)</td></tr><tr><td>hhiBorrow</td><td>0.0187***<br>(0.0019)</td><td>0.061***<br>(0.017)</td><td>0.040***<br>(0.008)</td><td>0.004<br>(0.003)</td><td>0.005*<br>(0.003)</td><td>0.024***<br>(0.006)</td><td>0.011***<br>(0.001)</td><td>0.003***<br>(0.001)</td></tr><tr><td>hhiCollateral</td><td>-0.0034***<br>(0.0019)</td><td>-0.014<br>(0.009)</td><td>-0.023***<br>(0.004)</td><td>-0.002**<br>(0.001)</td><td>-0.004***<br>(0.001)</td><td>-0.007***<br>(0.002)</td><td>-0.003***<br>(0.000)</td><td>-0.000<br>(0.001)</td></tr><tr><td>pctSelfBorrow</td><td>-0.0063***<br>(0.0013)</td><td>-0.007<br>(0.007)</td><td>-0.004<br>(0.005)</td><td>-0.002<br>(0.002)</td><td>0.011***<br>(0.004)</td><td>0.005<br>(0.005)</td><td>-0.001**<br>(0.000)</td><td>-0.001***<br>(0.000)</td></tr><tr><td>days</td><td>-3.518e-05<br>(1.56e-05)</td><td>-0.000***<br>(0.000)</td><td>-0.000***<br>(0.000)</td><td>-0.000***<br>(0.000)</td><td>-0.000***<br>(0.000)</td><td>-0.000***<br>(0.000)</td><td>-0.000***<br>(0.000)</td><td>-0.000***<br>(0.000)</td></tr><tr><td>periodRisky</td><td>5.134e-06***<br>(5.225e-07)</td><td>0.000<br>(0.000)</td><td>0.000***<br>(0.000)</td><td>0.000***<br>(0.000)</td><td>0.000***<br>(0.000)</td><td>0.000***<br>(0.000)</td><td>-0.000<br>(0.000)</td><td>0.000<br>(0.000)</td></tr><tr><td>perioNoAdjust</td><td>-4.499e-07<br>(5.482e-07)</td><td>0.000<br>(0.000)</td><td>-0.000<br>(0.000)</td><td>-0.000***<br>(0.000)</td><td>-0.000***<br>(0.000)</td><td>-0.000***<br>(0.000)</td><td>0.000***<br>(0.000)</td><td>0.000<br>(0.000)</td></tr><tr><td>periodRiskyNoAdjust</td><td>3.732e-05***<br>(1.412e-06)</td><td>0.000**<br>(0.000)</td><td>0.000***<br>(0.000)</td><td>0.000***<br>(0.000)</td><td>0.000***<br>(0.000)</td><td>0.000<br>(0.000)</td><td>-0.000***<br>(0.000)</td><td>-0.000***<br>(0.000)</td></tr></tbody></table>

Note: * p < 0.05, ** p < 0.01, *** p < 0.001. Standard errors are in parentheses.

as a hedging strategy. Considering over-collateralization, self-borrowing of both stablecoins and cryptocurrencies generally results in a net additional cost for users.

## VII. DISCUSSION AND CONCLUSION

This study examines the dynamics of user behavior in DeFi lending protocols in Compound V2 protocol. By leveraging machine learning models, especially Random Forest and XG-Boost, we accurately predict user decisions, including position adjustments and liquidations. These findings reveal the pivotal role of key metrics, such as collateral values, market volatility, and historical risk exposure, in influencing these outcomes.

Panel regression analysis further reveals the evolving interplay between health ratios and market conditions, highlighting how user sophistication and asset composition shape risk management strategies. By sub-sampling, we also uncover variations in these effects over time and across different asset-holding groups. Importantly, the study demonstrates that users with a borderline health ratio become more sophisticated, as they are less subject to liquidation events over time and could better manage their positions amidst market volatility.

Our findings provide actionable insights for designing and optimizing decentralized lending platforms. By incorporating predictive analytics, DeFi protocols can better anticipate user

behavior and integrate these insights into simulations like [12], [22] to assess and prevent systemic risks. While our study effectively predicts user behavior, it does not fully account for psychological and behavioral factors—such as panic selling or overconfidence—that may influence decision-making under stress. Another limitation of our work is that relying on historical snapshot data may not fully reflect real-time strategies employed by users during periods of extreme market volatility. These aspects could be better analyzed through behavioral modeling and simulation-based approaches.

Future work could focus on enhancing predictive models to better capture user decision-making in response to evolving market conditions. In particular, dynamic modeling techniques, such as long short-term memory (LSTM), offer promising avenues for learning temporal dependencies to enhance predictive accuracy. To mitigate the effects of model drift over time, online learning and retraining strategies could be applied to enhance model robustness and adaptability in response to evolving user behavior. Furthermore, improving the computational efficiency of the models is essential for real-time deployment and integration into protocol-level dashboards. As DeFi grows in scale and complexity, this work lays a foundation toward user-centric risk modeling to enhance protocol resilience and financial stability in decentralized markets.
## ACKNOWLEDGMENT

We extend our profound gratitude to Myriam Kassoul for her early contributions and insightful input on the models presented in this work. We also sincerely thank Nicolas Soulié and Maximilian Schäfer for their constructive feedback and engaging discussions.

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## APPENDIX

We provide detailed model performance results for the adjustPosition and isLiquidated classification tasks in Table II and Table III, respectively. These tables report precision, recall, F1-score, and AUROC for both the macro average and class 1 (the positive class). We also report the total training time required for each model configuration. Our experiments were conducted on a server equipped with 503 GB of RAM and an Intel Xeon Gold 5317 CPU with 12 cores (24 threads) running at 3.00 GHz.
<table><caption>TABLE II
COMPARISON OF MODEL PERFORMANCES ON *adjustPosition* CLASSIFICATION</caption><thead><tr><th>Model</th><th>Feature Sets</th><th>Precision</th><th>Macro Recall</th><th>F1-score</th><th>Precision</th><th>Class 1 Recall</th><th>F1-score</th><th>AUROC</th><th>Time (s)</th></tr></thead><tbody><tr><td rowspan="3">Logistic Regression</td><td>Original features</td><td>0.564376</td><td>0.606193</td><td>0.579750</td><td>0.135447</td><td>0.224701</td><td>0.169014</td><td>0.606193</td><td>263.56</td></tr><tr><td>+ 1-min volatility day <i>t</i></td><td>0.565390</td><td>0.606674</td><td>0.580691</td><td>0.137468</td><td>0.225498</td><td>0.170808</td><td>0.606674</td><td>367.96</td></tr><tr><td>+ 1-min volatility day <i>t</i> + 1</td><td>0.525954</td><td>0.817202</td><td>0.520626</td><td>0.054359</td><td>0.745817</td><td>0.101332</td><td>0.817202</td><td>581.84</td></tr><tr><td rowspan="3">Decision Tree</td><td>Original features</td><td>0.963865</td><td>0.773002</td><td>0.843325</td><td>0.931612</td><td>0.546348</td><td>0.688766</td><td>0.773002</td><td>189.68</td></tr><tr><td>+ 1-min volatility day <i>t</i></td><td>0.964646</td><td>0.774200</td><td>0.844491</td><td>0.933153</td><td>0.548738</td><td>0.691085</td><td>0.774200</td><td>297.53</td></tr><tr><td>+ 1-min volatility day <i>t</i> + 1</td><td>0.958781</td><td>0.778282</td><td>0.846077</td><td>0.921353</td><td>0.556972</td><td>0.694256</td><td>0.778282</td><td>391.16</td></tr><tr><td rowspan="3">Random Forest</td><td>Original features</td><td>0.994566</td><td>0.948036</td><td>0.970133</td><td>0.990023</td><td>0.896149</td><td>0.940750</td><td>0.948036</td><td>3,744.89</td></tr><tr><td>+ 1-min volatility day <i>t</i></td><td>0.996503</td><td><b>0.950706</b></td><td><b>0.972479</b></td><td>0.993851</td><td><b>0.901461</b></td><td><b>0.945404</b></td><td><b>0.950706</b></td><td>3,634.51</td></tr><tr><td>+ 1-min volatility day <i>t</i> + 1</td><td><b>0.996735</b></td><td>0.946725</td><td>0.970382</td><td><b>0.994384</b></td><td>0.893493</td><td>0.941242</td><td>0.946725</td><td>3,621.28</td></tr><tr><td rowspan="3">XGBoost</td><td>Original features</td><td>0.970075</td><td>0.783388</td><td>0.853239</td><td>0.943855</td><td>0.567065</td><td>0.708479</td><td>0.783388</td><td>181.14</td></tr><tr><td>+ 1-min volatility day <i>t</i></td><td>0.978319</td><td>0.816752</td><td>0.880857</td><td>0.959775</td><td>0.633732</td><td>0.763398</td><td>0.816752</td><td>248.41</td></tr><tr><td>+ 1-min volatility day <i>t</i> + 1</td><td>0.979064</td><td>0.822066</td><td>0.884935</td><td>0.961173</td><td>0.644356</td><td>0.771506</td><td>0.822066</td><td>321.57</td></tr><tr><td rowspan="3">LightGBM</td><td>Original features</td><td>0.981708</td><td>0.757429</td><td>0.835031</td><td>0.967565</td><td>0.515007</td><td>0.672214</td><td>0.757429</td><td>31,046.80</td></tr><tr><td>+ 1-min volatility day <i>t</i></td><td>0.982653</td><td>0.760753</td><td>0.838087</td><td>0.969398</td><td>0.521647</td><td>0.678294</td><td>0.760753</td><td>31,404.64</td></tr><tr><td>+ 1-min volatility day <i>t</i> + 1</td><td>0.981924</td><td>0.764068</td><td>0.840704</td><td>0.967883</td><td>0.528287</td><td>0.683505</td><td>0.764068</td><td>31,801.26</td></tr></tbody></table>

<table><caption>TABLE III
COMPARISON OF MODEL PERFORMANCES ON *isLiquidated* CLASSIFICATION</caption><thead><tr><th>Model</th><th>Feature Sets</th><th>Precision</th><th>Macro Recall</th><th>F1-score</th><th>Precision</th><th>Class 1 Recall</th><th>F1-score</th><th>AUROC</th><th>Time (s)</th></tr></thead><tbody><tr><td rowspan="3">Logistic Regression</td><td>Original features</td><td>0.517970</td><td>0.501253</td><td>0.501512</td><td>0.040000</td><td>0.002778</td><td>0.005195</td><td>0.501253</td><td>311.14</td></tr><tr><td>+ 1-min volatility day <i>t</i></td><td>0.497965</td><td>0.500000</td><td>0.498980</td><td>0.000000</td><td>0.000000</td><td>0.000000</td><td>0.500000</td><td>413.05</td></tr><tr><td>+ 1-min volatility day <i>t</i> + 1</td><td>0.558700</td><td>0.636896</td><td>0.581522</td><td>0.120351</td><td>0.282222</td><td>0.168743</td><td>0.636896</td><td>535.57</td></tr><tr><td rowspan="3">Decision Tree</td><td>Original features</td><td>0.940876</td><td>0.956972</td><td>0.948778</td><td>0.882101</td><td>0.914444</td><td>0.897981</td><td>0.956972</td><td>61.56</td></tr><tr><td>+ 1-min volatility day <i>t</i></td><td>0.949598</td><td>0.955070</td><td>0.952317</td><td>0.899561</td><td>0.910556</td><td>0.905025</td><td>0.955070</td><td>96.52</td></tr><tr><td>+ 1-min volatility day <i>t</i> + 1</td><td>0.949615</td><td>0.964788</td><td>0.957074</td><td>0.899516</td><td>0.930000</td><td>0.914504</td><td>0.964788</td><td>120.26</td></tr><tr><td rowspan="3">Random Forest</td><td>Original features</td><td><b>0.989065</b></td><td>0.986900</td><td><b>0.987980</b></td><td><b>0.978237</b></td><td>0.973889</td><td><b>0.976058</b></td><td>0.986900</td><td>1,748.38</td></tr><tr><td>+ 1-min volatility day <i>t</i></td><td>0.989051</td><td>0.986345</td><td>0.987694</td><td>0.978212</td><td>0.972778</td><td>0.975487</td><td>0.986345</td><td>2,144.70</td></tr><tr><td>+ 1-min volatility day <i>t</i> + 1</td><td>0.987720</td><td>0.987450</td><td>0.987585</td><td>0.975542</td><td>0.975000</td><td>0.975271</td><td>0.987450</td><td>2,493.79</td></tr><tr><td rowspan="3">XGBoost</td><td>Original features</td><td>0.948916</td><td>0.955622</td><td>0.952244</td><td>0.898194</td><td>0.911667</td><td>0.904880</td><td>0.955622</td><td>161.80</td></tr><tr><td>+ 1-min volatility day <i>t</i></td><td>0.985856</td><td>0.988275</td><td>0.987063</td><td>0.971808</td><td>0.976667</td><td>0.974231</td><td>0.988275</td><td>232.56</td></tr><tr><td>+ 1-min volatility day <i>t</i> + 1</td><td>0.985375</td><td><b>0.989940</b></td><td>0.987646</td><td>0.970831</td><td><b>0.980000</b></td><td>0.975394</td><td><b>0.989940</b></td><td>309.82</td></tr><tr><td rowspan="3">LightGBM</td><td>Original features</td><td>0.956607</td><td>0.968985</td><td>0.962713</td><td>0.913467</td><td>0.938333</td><td>0.925733</td><td>0.968985</td><td>25,234.81</td></tr><tr><td>+ 1-min volatility day <i>t</i></td><td>0.959282</td><td>0.974273</td><td>0.966656</td><td>0.918774</td><td>0.948889</td><td>0.933588</td><td>0.974273</td><td>23,920.38</td></tr><tr><td>+ 1-min volatility day <i>t</i> + 1</td><td>0.963375</td><td>0.975680</td><td>0.969446</td><td>0.926948</td><td>0.951667</td><td>0.939145</td><td>0.975680</td><td>24,734.28</td></tr></tbody></table>