Nethermind Research on Validator Ticket Pricing (Puffer Finance)

Research Summary

Introducing Validator Tickets

Puffer Finance enables node operators (NO) to borrow ETH for running validators by locking at least 1 ETH worth of pufETH, Puffer’s Liquid Restaking Token, as collateral. Becoming a Puffer validator requires purchasing a validator ticket (VT). One VT gives the right to run a validator for a single day. The funds from the sale of the VTs, excluding protocol fees, are distributed to pufETH holders.

Nethermind Research has investigated the methods for efficiently pricing VTs using a fixed price mechanism. We did not research auction mechanisms, as there were concerns from Puffer that an auction-based approach could lead to protocol centralization and validators being priced out of the system.

Nethermind Research conducted an extensive study to determine the best way to price VTs. This article outlines the key findings of our research and is an excerpt from our comprehensive report.

A new mechanism for liquid staking and restaking

Here are the key properties of VT for permissionless liquid staking and restaking:

• VTs lower barriers to entry by allowing NOs to start validating with just 1 ETH of collateral and a minimum of 28 VTs. Each NO needs a minimum of 28 VTs when they register, with one VT being used daily. NO can top up their number of VTs as they go.
• Minting VTs provides immediate rewards to stakers holding pufETH tokens, fueling growth for the liquid staking protocol (LSP). NOs can purchase VTs in the secondary market to become active even when the validator entry queue on the Beacon Chain is long.
• NOs are incentivized to perform well by purchasing VTs as they cannot recoup their upfront VT payment through underperformance. This addresses the “lazy NO” issue.
• NO keeps 100% of rewards, removing the need for protocols to police “rug-pooling” behavior, which involves rerouting the execution layer rewards.
• VTs create trading opportunities on the secondary market and allow participation in the MEV “lottery.”

VT Pricing Considerations

To ensure competitive yields, the rewards distributed to pufETH holders should reflect the total staking rewards minus a commission rate (currently 10% to 14% across platforms like Lido and Rocket Pool). Consequently, the price of the VT token should closely align with anticipated validator rewards for the next day.

Accurate pricing of VT tickets is crucial for the protocol’s success. If VT prices are too low, NOs profit at the expense of pufETH holders, and vice versa.

A NO’s return depends on the consensus rewards, the execution rewards received when they propose a block, and the yield on their pufETH bond. Costs include the price paid for the VT tickets on top of the validator infrastructure costs. Due to the uncertainty of execution rewards, buying a VT is often compared to a lottery ticket, as the MEV reward for block proposers can be significantly high.

Estimating Next Day Validator Rewards

Validators rewards come from two sources:

• Consensus Rewards:

The total consensus rewards distributed to validators on a given day are determined by the square root of the total ETH staked. This means the rewards are dependent on the number of validators.

For each block, a maximum defined number of ETH, known as the base reward, is issued for distribution to validators. This reward is determined by the following formula:

$\frac{7}{8}$ of the base reward is shared among all validators with the exception of the block proposer. Consensus rewards are quite stable and predictable since they are dependent on the number of validators, which is controlled by the activation and deactivation queue.

• Execution Rewards

Execution rewards, which depend on MEV opportunities, are challenging to predict accurately.

To price VT tickets, we need to forecast the expected validator reward. Daily MEV rewards can vary, as shown in the provided graph. As a result, the VT price must be dynamic.

Source Flashbots

To model the MEV reward, we analyzed daily mev-boost data collected by Flashbots from the Merge (September 2022 to March 2024). Our objective was to develop a model that accurately predicts the next day’s MEV, based on past MEV.

To mitigate the risk of overfitting, we implemented a robust methodology called Walk-Forward Validation. This approach involves incrementally updating models as new data becomes available, preventing overfitting and look-ahead bias.

To measure the accuracy of our modeling, we have used Root Mean Squared Error (RMSE). RMSE is a measure of the square root of the average of the squared differences between predicted and actual values, offering a comprehensive assessment of the model’s prediction errors and their magnitude. RMSE is a popular evaluation metric used in various fields, such as machine learning and data analysis, to compare different regression models or assess the quality of predictions, with lower RMSE values indicating better predictive accuracy.

Winsorizing to remove MEV outliers

Significant MEV spikes, often caused by liquidations, are unlikely to occur the next day. To address this, we implemented winsorization, which involves adjusting any value beyond twice the 10-day Simple Moving Average (SMA) to match the 10-day SMA within the training dataset.

By applying winsorization, we effectively remove noise and enhance the accuracy of our forecasting. The improvement was noticeable across all methodologies tested: simple moving average, exponential moving average, autoregressive integrated moving average, and machine learning models like XGBoost.

Simple Moving Average (SMA)

We tested several windows for moving averages and compared various lookback periods. Our findings showed that 1) winsorization improved predictions and 2) an 8-day window was the most optimal

Exponential Moving Average

The EMA method can be described as a SMA method with exponential weight decay. This approach allows the algorithm to respond more quickly to recent changes in the data by giving greater importance to newer data points compared to older ones.

$\hat{y}{i} = \mathrm{EMA}{i} = \alpha \cdot y_{i} + \mathrm{EMA}_{i-1},$

where $\alpha$ is a smoothing factor, ranging between 0 and 1.

We experimented with 30 evenly spaced values of $\alpha$ over a 0–1 interval. However, the minimum RMSE we could achieve was 307.5 ETH vs 303.9 ETH for SMA.

Other Methodologies Explored

We also tested popular time series prediction methods such as:

• Autoregressive Integrated Moving Average (ARIMA) models are widely used in time series forecasting to capture and predict patterns in data. They are particularly effective when dealing with data that exhibits trend and seasonality. They provide a flexible and powerful approach for time series forecasting by considering the autoregressive, differencing, and moving average components to capture and predict patterns in data.
• XGBoost, a gradient boosting algorithm, is well-suited for regression problems and can be effectively applied to time-series prediction by incorporating a feature set that captures temporal dependencies, as detailed in the Feature Engineering section. We used gas prices and ETH volatility as features.

Complex methods like ARIMA and XGBoost introduces additional parameters to calibrate, increasing the risk of overfitting. However, compared to SMA, these models only provided marginal improvements in terms of root mean square error (RMSE), which did not justify the added complexity.

Therefore, we decided to utilize a simple moving average to predict the next day’s expected MEV reward for each validator.

Discount Determination

The discount applied to expected validator returns should provide competitive returns for pufETH holders compared to other liquid staking protocols. It should also ensure that NOs are well compensated for their services. To achieve this, Puffer must charge fees lower than 10%. We conducted experiments with discount levels ranging from 6% to 8% to assess their impact on validator expected returns. These levels already represent an improvement for pufETH holders compared to rates charged by other protocols.

The distribution of validator profits is highly skewed, with most NOs occasionally receiving substantial rewards once they become block proposers.

To improve their risk-adjusted returns, NOs are incentivized to:

1. Run as many validators as possible, and
2. Be active on Puffer for extended periods, as this increases their chances of becoming a block proposer and earning the MEV reward.

To promote decentralization, NOs running a small number of validators need to generate attractive returns. In determining the optimal discount factor, we considered the following factors:

• Median annualized return for a validator: This represents the minimum return on capital achieved 50% of the time.
• Var 95% (Value at Risk): It measures the potential loss a validator may experience during 5% of the worst cases.
• Probability of earning a positive return

To better understand node operator profitability, we simulated validator returns using Monte Carlo simulations. Assuming an 8% discount, we examined various profitability metrics based on the protocol’s duration and the number of validators managed. With 20+ validators, node operators have a 90% probability of achieving a positive return over one year. For operators that run only one validator, this probability decreases to 56%.

Based on our simulations, NOs in Puffer Finance, after a minimum 6-month period, have a 50% chance of earning at least an 8% APR with 5 validators. Managing 20 validators increases the APR to 12%.

For solo validators, the risk measured by the Value at Risk (VaR 95%) of the APR remains high, even if they stay in the protocol for one year. This is because there is more than a 5% probability of not receiving any MEV reward during that period. However, the risk significantly reduces once a node operator manages over 10 validators and becomes negligible when managing 20 validators.

Overall, the risk-reward profile of running a Node Operator long-term is highly attractive starting from 10 validators, offering double-digit return expectations with limited capital losses. Unlike other liquid staking protocols, Puffer does not require posting a bond in its native token. This reduces the risk of bond depreciation if the native token’s value declines.

The Impact of Restaking on Profitability

The return expectations mentioned earlier are conservative and only account for rewards from Ethereum validating. By purchasing VT, Puffer validators will also earn restaking rewards from EigenLayer as well as potential emissions of Puffer’s native token.

Since AVS restaking is a new concept, we lack precise information about its potential yield, so it has been excluded from our analysis; however, these additional rewards would further increase their risk-adjusted returns.

Legal Disclaimer

This article has been prepared for the general information and understanding of the readers. The views and strategies described may not be suitable for all readers. Both past performance and yield may not be a reliable guide to future performance. All case studies are shown for illustrative purposes only and should not be relied upon as advice or interpreted as a recommendation.

The authors of this research paper have made reasonable efforts to ensure the accuracy of the information presented herein. However, they do not guarantee the accuracy, completeness, or reliability of any information or analysis provided. Nethermind shall not be liable for any errors, omissions, or inaccuracies in the information, nor for any actions taken in reliance thereon.

This article is based on the scope of materials and documentation made available to Nethermind by Puffer. It does not indicate Nethermind’s endorsement of any particular project or team, nor guarantee its security. No third party should rely on this article in any way, including for the purpose of making any decisions to buy or sell a product, service or any other asset.

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About Nethermind Research

Nethermind Research is the research arm of Nethermind, creating synergies between the fields of cryptography, decentralized finance, and protocol research. Our research solutions serve as the nexus where our theoretical knowledge meets real-world applications. Catering to a wide range of clients, from institutional players to Web3 organizations and DAOs, we specialize in solving industry problems via innovative applications of our research.