Impermanent Loss vs. Staking Rewards: A Quantitative Framework for LP Decision-Making

For many DeFi participants, the decision between providing liquidity to an automated market maker (AMM) and simply staking a single asset can be a difficult one. Both strategies offer the potential for attractive returns, but they also come with their own unique risks and trade-offs. To make an informed decision, it is essential to move beyond a purely qualitative assessment and develop a quantitative framework for comparing the expected value of these two strategies.

The Core Components of the Framework

A robust quantitative framework for LP decision-making should incorporate the three key variables that determine the profitability of these strategies: staking rewards, trading fees, and impermanent loss.

• Staking Rewards: This is the most straightforward component of the framework. It represents the return that can be earned by staking a single asset. This is typically expressed as an annual percentage rate (APR) and can be easily obtained from the staking provider.
• Trading Fees: This is the primary source of income for LPs. It is a percentage of the trading volume in the pool and is distributed to LPs in proportion to their share of the pool. To estimate the potential trading fees, it is necessary to research the historical trading volume of the pool and the fee tier.
• Impermanent Loss: This is the most complex and often misunderstood component of the framework. It is the loss that an LP incurs when the price of the assets in the pool diverges. As we have discussed in previous articles, impermanent loss can be calculated using a specific formula and is a function of the price ratio of the two assets.

Building the Decision-Making Model

With these three components in hand, it is possible to build a model that compares the expected value of LPing versus single-asset staking. The model can be built in a spreadsheet and should be designed to be flexible enough to accommodate a wide range of different scenarios.

The first step is to define the inputs to the model. These should include:

• The initial investment amount.
• The expected staking APR.
• The expected daily trading volume of the pool.
• The fee tier of the pool.
• The expected volatility of the assets in the pool.

With these inputs, the model can then calculate the expected daily return from both staking and LPing. The daily return from staking is simply the initial investment multiplied by the daily staking rate. The daily return from LPing is the sum of the expected daily trading fees minus the expected daily impermanent loss.

To calculate the expected daily impermanent loss, it is necessary to make an assumption about the expected daily price movement of the assets. This can be based on historical volatility data or on a more subjective assessment of the market. Once an assumption has been made, the impermanent loss formula can be used to calculate the expected loss for that day.

Backtesting and Scenario Analysis

Once the model has been built, it can be used to backtest different strategies and perform scenario analysis. By inputting historical data for trading volume and price volatility, it is possible to see how the two strategies would have performed in the past. This can provide valuable insights into the relative risks and rewards of each strategy.

Scenario analysis can also be used to explore how the two strategies would perform under different market conditions. For example, the model can be used to see how the two strategies would perform in a bull market, a bear market, or a sideways market. This can help to identify the market conditions under which each strategy is likely to be most profitable.

Case Studies: When to LP and When to Stake

The decision of whether to LP or to stake will ultimately depend on the specific circumstances of the individual investor. However, there are some general principles that can be applied.

• LPing is generally more profitable in stable or sideways markets. In these markets, impermanent loss is likely to be low, and the income from trading fees can be substantial.
• Staking is generally more profitable in volatile or trending markets. In these markets, impermanent loss is likely to be high, and the income from trading fees may not be enough to offset the losses.

By using a quantitative framework to analyze the expected value of these two strategies, investors can make more informed decisions and increase their chances of success in the competitive world of DeFi. It is a evidence to the power of data-driven decision-making in a field that is often characterized by hype and speculation.