Estimated APR for CLMM

How Raydium estimates APR for concentrated liquidity pools

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

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Overall pool estimated APR

Assumes trading fees and emissions are distributed across all liquidity in the pool, including out-of-range positions.

$$APR = \sum(d_{365}, h_{24}, s_{3600}, b_{0.5}) \times \frac{(perBlockReward \times rewardPrice) + totalTradingFee}{totalLiquidityValue}$$

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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 $i_c \geq i_l$ && $i_c \leq i_u$	$\Delta L = \min(liquidityAmount0, liquidityAmount1)$

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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	$m = \frac{retroRange}{tradeRange} \times \frac{retroRange}{userRange}$

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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