# Estimated APR for CLMM ## Overview In a CLMM pool, fees are distributed proportionally to in-range liquidity at each tick. Calculating an accurate APR across all ticks and LPs is extremely complex—traditional constant product APR formulas don't apply. **Projected returns for CLMMs should be considered estimates at best.** Raydium displays three APR estimation methods: 1. **Overall pool estimated APR** — pool-wide average 2. **Delta method** — based on your position's share of liquidity 3. **Multiplier method** — based on historical price range overlap *** ### Overall pool estimated APR Assumes trading fees and emissions are distributed across all liquidity in the pool, including out-of-range positions. $$ APR = \sum(d\_{365}, h\_{24}, s\_{3600}, b\_{0.5}) \times \frac{(perBlockReward \times rewardPrice) + totalTradingFee}{totalLiquidityValue} $$ *** ### Delta method Calculates estimated APR based on your position's implied change (delta) in pool liquidity, determined by your price range and size. **Condition** $$ i\_l \leq i\_c < i\_u $$ Where: | Variable | Description | | -------- | ------------- | | $$i\_l$$ | lowerTickId | | $$i\_c$$ | currentTickId | | $$i\_u$$ | upperTickId | **Token amounts in a position** $$ \Delta Y = \Delta L \times (\sqrt{P} - \sqrt{P\_l}) $$ $$ \Delta X = \Delta L \times \left(\frac{1}{\sqrt{P}} - \frac{1}{\sqrt{P\_u}}\right) $$ **Calculating ΔL** For estimation of tokenA ($$\Delta X$$) and tokenB ($$\Delta Y$$) we need to know $$\Delta L$$: $$ (\Delta Y \times pUSDY) + (\Delta X \times pUSDX) = targetAmount $$ So we take: $$ (\Delta L \times (\sqrt{P} - \sqrt{P\_l}) \times pUSDY) + (\Delta L \times \left(\frac{1}{\sqrt{P}} - \frac{1}{\sqrt{P\_u}}\right) \times pUSDX) = targetAmount $$ Then: $$ \Delta L = \frac{targetAmount}{(\sqrt{P} - \sqrt{P\_l}) \times pUSDY + \left(\frac{1}{\sqrt{P}} - \frac{1}{\sqrt{P\_u}}\right) \times pUSDX} $$ After calculating for $$\Delta L$$, we can calculate $$\Delta X$$ and $$\Delta Y$$ using: $$ \Delta Y = \Delta L \times (\sqrt{P} - \sqrt{P\_l}) $$ $$ \Delta X = \Delta L \times \left(\frac{1}{\sqrt{P}} - \frac{1}{\sqrt{P\_u}}\right) $$ **Estimated daily fee** $$ Fee = feeTier \times volume24H \times \frac{\Delta L}{L + \Delta L} $$ Where: | Variable | Description | | ------------- | -------------------------------------------------------------------------------- | | $$volume24H$$ | Average of 24h volume | | $$L$$ | Total liquidity (cumulative of liquidityNet from all ticks that $$i \leq i\_c$$) | | $$\Delta L$$ | Delta liquidity | **Liquidity amounts** And can be calculated from: $$ liquidityAmount0 = amount0 \times \frac{\sqrt{P\_u} \times \sqrt{P\_l}}{\sqrt{P\_u} - \sqrt{P\_l}} $$ $$ liquidityAmount1 = \frac{amount1}{\sqrt{P\_u} - \sqrt{P\_l}} $$ | Condition | $$\Delta L$$ | | ------------------------------------------- | ------------------------------------------------------- | | If $$i\_c < i\_l$$ | $$\Delta L = liquidityAmount0$$ | | If $$i\_c > i\_u$$ | $$\Delta L = liquidityAmount1$$ | | If $$i\_c \geq i\_l$$ && $$i\_c \leq i\_u$$ | $$\Delta L = \min(liquidityAmount0, liquidityAmount1)$$ | *** ### Multiplier method Calculates estimated APR based on how much your price range overlaps with historical trading activity. **Assumptions** * Historical price data is used to extrapolate future price data (not the best indicator of future performance, but provides a decent estimate) * Price fluctuation within the historical range is assumed to be consistent across the time interval, resembling a periodic function with amplitude equal to the upper and lower price boundaries **Variables** | Variable | Description | | -------------- | ------------------------------------------------------------------- | | $$u\_{lower}$$ | Lower bound of user's concentrated liquidity price range | | $$u\_{upper}$$ | Upper bound of user's concentrated liquidity price range | | $$h\_{lower}$$ | Lower bound of historical price range across a specific time period | | $$h\_{upper}$$ | Upper bound of historical price range across a specific time period | **Retroactive range intersection** $$ r\_{lower} = \max(u\_{lower}, h\_{lower}) $$ $$ r\_{upper} = \min(u\_{upper}, h\_{upper}) $$ **Range definitions** $$ userRange = u\_{upper} - u\_{lower} $$ $$ histRange = h\_{upper} - h\_{lower} $$ $$ retroRange = r\_{upper} - r\_{lower} $$ Where $$retroRange$$ is the retroactive intersection between $$userRange$$ and $$histRange$$. **Multiplier calculation** Let $$m$$ = multiplier of rewards or fees that user will receive. | Condition | Multiplier | | -------------------------- | ------------------------------------------------------------------------- | | $$retroRange \leq 0$$ | $$m = 0$$ | | $$userRange = retroRange$$ | $$m = \frac{histRange}{retroRange}$$ | | $$histRange = retroRange$$ | $$m = \frac{retroRange}{userRange}$$ | | Otherwise | $$m = \frac{retroRange}{tradeRange} \times \frac{retroRange}{userRange}$$ | *** ### Important notes * These are **estimates**, not guaranteed returns * Actual returns depend on trading volume, price movements, and competition from other LPs * Narrower ranges earn more fees when in range, but risk going out of range more often * Out-of-range positions earn zero fees --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. 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