Considered to be the most advanced form of AMM to date, Uniswap V3 allows users to choose any price range for their positions and increase their capital efficiency even further. One of our goals for launching Optimism and integrating with Uniswap V3 is for users to take advantage of the cheaper and faster transactions on L2 while enjoying the full capital efficiency unlocked by Uniswap V3.
However, in exchange for capital efficiency, this additional feature introduces greater complexity for users in setting an agricultural price range from an infinite number of possible combinations.
To make things easier for our users, one of the key new features for this launch is the 3 recommended price ranges (Wide, Medium and Narrow) that users can choose from when opening a position in Uniswap V3 pools. The recommended price ranges resulted from the optimal determination provided price ratios based on historical analysis by our research team. Later in this article, we will discuss the rationale and thought process behind the selected parameters.
terminology
Before we dive into the analysis, here are some of the key terms used.
π‘
Provisioned Price Ratio (PPR) is a factor that is multiplied/divided by the current price to form lower and upper price ranges for liquidity provision. For example, if the current ETH price is $1500, a PPR of 2 would mean the price range is between $750 ($1500/2) and $3000 (1500 x $2). . Thus, the lower the PPR, the tighter the position’s price range will be.
π‘
leverage used to increase trading fees earned by adding additional assets. The higher a user’s leverage, the higher the risk of liquidation and potential temporary loss they may incur if prices change.
π‘
leverage ratio is the ratio between each loaned asset. For example, if a user borrows 100 USD ETH + 0 USDC to open an ETH-USDC pool position, the ETH:USDC lending ratio will be 1:0 (100% ETH) since all lending is in ETH. If the user borrows 50 USD ETH + 50 USDC instead, the credit ratio is 0.5:0.5 (50% ETH). And if the user borrows only 100 USDC, the credit ratio is 0:1 (0% ETH).
The analysis
Before determining the optimal price ratios (PPRs), we simulated Homora V2 farming strategies given the historical data using different PPR values, farming durations, leverages and credit ratios. The results of strategies with different PPRs are compared using the following evaluation metrics:
- Average PnL
- PnL volatility
- debt ratio
- Sharpe ratio
Evaluation metrics used
1. Average PnL
PnL is the percent change in dollar values ββfrom farming via Homora V2 relative to simply holding the assets. The higher the PnLs, the better.
However, depending on market conditions (e.g. bull/bear), farming at different times can produce very different PnL outcomes. Therefore, the average PnL over several agricultural periods is used to better represent the expected return.
2. PnL volatility
The PnL volatility is the standard deviation of the cultured PnLs over different time periods. The higher the volatility, the more uncertain the farming period will be of producing the desired results. So when comparing strategies with the same or a similar PnL, the strategy with lower volatility would better capture safety and predictability.
3. Debt Ratio
The debt ratio, which ranges from 0% to 100%, indicates how close farming positions are to liquidation. To assess whether a position is risky when farming on Homora V2, the maximum leverage ratio of a position is measured over the farming duration. The closer the maximum debt ratio is to 100%, the riskier a position is during the farming period.
4. Sharpe ratio
The Sharpe Ratio, or risk-adjusted return on a position, is used to compare PnLs for risk. The calculation is made using the average agricultural PnL divided by the PnL volatility. A higher Sharpe ratio represents an expected outcome with a potentially higher return at lower risk and is therefore a better indicator in our case.
Running the backtest simulation
We ran the backtest simulation with Uniswap V3 historical data for one year from June 2021 to June 2022. We performed all of the following parameter combinations:
- Breeding time (weeks): [1, 2, 4, 8, 12]
- Leverage : [1, 1.5, 2, 2.5, 3]
- Leverage Ratio: [0%, 50%, 100%]
For each combination of parameters (e.g. duration = 4 weeks, leverage = 2x and credit ratio = 50%), we compared the result based on our evaluation metrics for different PPR values βββ 1.1, 1.2, 1.3, 1, 5, 2, 3, and 4.
Results
For the results below, we have compiled the most relevant information to highlight the key outcomes of the process. For each parameter configuration, we compare the results of different PPRs to determine the optimal PPRs based on our evaluation metrics.
In Long-term storage (up to 12 weeks)our data show that a PPR of 2 outperforms other PPR scores and has the highest average PnL and Sharpe ratios while the maximum debt ratio remains within the safe threshold as shown in Table 1 and Table 2.
Table 1. Aggregated results of 8-week farming strategies given leverage = 2x and credit ratio = 50%.
Table 2. Aggregated results of 12-week farming strategies given Leverage = 2x and Loan Ratio = 50%.
Meanwhile, the optimal PPRs for medium breeding period (2 or 4 weeks) result in 1.5 and 2 see Table 3 and Table 4.
Table 3. Aggregated results of 2-week farming strategies given leverage = 2x and credit ratio = 50%.
Table 4. Aggregated results of 4-week farming strategies given leverage = 2x and credit ratio = 50%.
Last, short breeding period (1 week) are better suited for lower PPR values. As shown in Table 5, which illustrates the results using a leverage of 2x and a credit ratio of 50%, the optimal PPR indicates this 1.3.
Table 5. Aggregated results of 1-week farming strategies given Leverage = 2x and Loan Ratio = 50%.
Additional data points supporting the same results are shown in the appendix, using different leverage and leverage ratio values.
Diploma
We ran a backtest experiment on the profitability of positions from Uniswap V3 to Homora V2 based on our valuation metrics: Average PnLs, PnL Volatility, Debt Ratios and Sharpe Ratios. We select three optimal PPR values ββfor yield farming leverage 1.3, 1.5And 2 to accommodate the farming behavior of our users, whether they wish to open short-term or long-term positions.
in summary,
Narrow range (PPR=1.3) is best suited for short Breeding period: 1-2 weeks
Medium range (PPR=1.5) is best suited for Middle Growing time: 2-8 weeks
Large area (PPR=2) is best suited for long Growing time: 8-12 weeks
Attachment
Since the entire simulation generated a large amount of data and scenarios, we decided to select just a few to illustrate our process.
Here are some additional examples of farming strategies from other configuration settings that also closely match our results above for the optimal PPR values ββof 2, 1.5, and 1.3 for each range of farming duration.
Below are other examples of a different configuration with Leverage = 1.5x and Loan Ratio = 0% at different run times (1, 4 and 12 weeks).
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