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Overview

BEX LP tokens represent a share of a liquidity pool. Accurately valuing these tokens is essential for displaying balances, calculating rewards, and for on-chain operations like collateralization and liquidation. There are several methods to value LP tokens, each suited to different use cases.

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Methods of valuation

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Informational (sum of balances)

This calculation is for informational purposes only and should NOT be used on-chain as it can be easily manipulated.
This method is suitable for off-chain, informational, or UI purposes. It is not manipulation-resistant and should not be used for on-chain or critical financial operations. Formula: PriceLP token=∑i(Balancei×Pricei)SupplyLP TokensPrice_{LP\ token} = \frac{\sum_i (Balance_i \times Price_i)}{Supply_{LP\ Tokens}} Where:
  • Balancei: balance of token ii in the pool
  • Pricei: market price of token ii
  • SupplyLP\ Tokens: total supply of LP tokens
Example: Suppose a $BERA/$HONEY pool contains the following:
TokenBalancePrice (USD)Value (USD)
$BERA1,000$10$10,000
$HONEY10,000$1$10,000
Total Pool Value$20,000
LP Token Supply1,000
  • Pool Value: 1000 $BERA ×\times 10 USD + 10000 $HONEY ×\times 1 USD = 20000 USD
  • LP Token Price: 20000 USD // 1000 $LPTOKEN = 20 USD

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Weighted pools

Weighted pools use a constant product invariant with custom weights. This method is manipulation-resistant and is recommended for on-chain or robust off-chain use.
Calculation StepsFormula
Step 1: Pool Invariant where ∑iwi=1\sum_i w_i = 1x1w1x2w2⋯xnwn=kx_1^{w_1} x_2^{w_2} \cdots x_n^{w_n} = k
Step 2: Token Weighted Valuesp1x1w1=⋯=pnxnwn=k^\frac{p_1 x_1}{w_1} = \cdots = \frac{p_n x_n}{w_n} = \hat{k}
Step 3: Calculate k^\hat{k}k^=k⋅∏i(piwi)wi\hat{k} = k \cdot \prod_i \left( \frac{p_i}{w_i} \right)^{w_i}
Step 4: Final LP Token Price where ss is the LP token supplypLP=k^s=ks⋅∏i(piwi)wip_{LP} = \frac{\hat{k}}{s} = \frac{k}{s} \cdot \prod_i \left( \frac{p_i}{w_i} \right)^{w_i}
Example Imagine an 80 $BAL/20 $WETH Pool with the following:
Calculation StepsValues
Step 1: Token Weightsw1=0.8w_1 = 0.8 ($BAL)
w2=0.2w_2 = 0.2 ($WETH)
Step 2: Oracle Pricesp1≈p_1 \approx $4.53 ($BAL)
p2≈p_2 \approx $1090.82 ($WETH)
Step 3: Pool Parametersk≈2,852,257.5k \approx 2,852,257.5 (from pool.getInvariant())
s≈5,628,392.26s \approx 5,628,392.26 (from pool.totalSupply())
Step 4: Final LP Token PricepLP=ks⋅∏i(piwi)wi≈p_{LP} = \frac{k}{s} \cdot \prod_i \left( \frac{p_i}{w_i} \right)^{w_i} \approx $11.34

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Stable pools

Stable pools are optimized for assets that trade at or near parity (e.g., stablecoins). They use the StableSwap invariant and often expose a getRate() function. StableSwap Invariant: A⋅nn⋅∑ixi+D=A⋅D⋅nn+Dn+1nn⋅∏ixiA \cdot n^n \cdot \sum_i x_i + D = A \cdot D \cdot n^n + \frac{D^{n+1}}{n^n \cdot \prod_i x_i} Where:
  • AA is the amplification parameter
  • nn is the number of tokens
  • xix_i are token balances
  • DD is the invariant
LP Token Price (using getRate): Most stable pools expose a getRate() function, which returns the value of 1 LP token in terms of the pool’s base asset (e.g., USD or a stablecoin): pLP=getRate()×(price of base asset)p_{LP} = \text{getRate()} \times \text{(price of base asset)} Manual Calculation (if needed): pLP=∑ixi⋅piSp_{LP} = \frac{\sum_i x_i \cdot p_i}{S} Where SS is the actual supply (use getActualSupply() for pre-minted pools). Example: Suppose a USDC/DAI/USDT pool with getRate()=1.01getRate() = 1.01 and USD as the base asset:
  • LP token price: pLP=1.01×1=1.01p_{LP} = 1.01 \times 1 = 1.01 USD per LP token

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Linear pools

Linear pools are designed for pairs where one token is a yield-bearing or wrapped version of the other. They use a simple linear invariant and expose a getRate() function. Linear Pool Invariant: xmain+r⋅xwrapped=kx_{main} + r \cdot x_{wrapped} = k Where rr is the rate between the wrapped and main token. LP Token Price (using getRate): pLP=getRate()×(price of main token)p_{LP} = \text{getRate()} \times \text{(price of main token)} Manual Calculation (if needed): pLP=xmain⋅pmain+xwrapped⋅pwrappedSp_{LP} = \frac{x_{main} \cdot p_{main} + x_{wrapped} \cdot p_{wrapped}}{S} Where SS is the virtual supply (use getVirtualSupply()). Example: Suppose a wstETH/ETH pool with getRate()=1.05getRate() = 1.05 and ETH at 20002000:
  • LP token price: pLP=1.05×2000=2100p_{LP} = 1.05 \times 2000 = 2100 USD per LP token

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Special considerations

  • Pre-minted Supply: Some pools (especially stable pools) pre-mint the maximum possible LP tokens. Always use getActualSupply() or getVirtualSupply() as appropriate.
  • Protocol Fees: Some pools accrue protocol fees, which may affect the actual value of LP tokens. Weighted and stable pools account for these in their supply functions.
  • Manipulation Resistance: For on-chain or critical use, always use invariant-based or rate-based pricing, not simple sum-of-balances.
  • Re-entrancy Protection: When evaluating on-chain, always check for Vault re-entrancy using ensureNotInVaultContext(vault).
  • Staked LP Tokens: If LP tokens are staked, include both wallet and staked balances in your calculations.

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References