“Balancer: A Non-Standard Automated Market Maker” (Balancer Whitepaper v1, 2019) is by Fernando Martinelli and Nikolai Mushegian of Balancer Labs. It extends the Uniswap x·y=k constant product formula to an N-token, arbitrarily-weighted invariant:

$$V = prod_{i} B_i^{W_i}$$

where $B_i$ are token balances and $W_i$ are their weights (summing to 1). This allows Balancer pools to represent any portfolio allocation (e.g., 80% ETH / 20% DAI) that automatically rebalances to maintain those weights as prices change — funded by arbitrageurs who earn trading fees in return.

> PDF hosting: The Balancer whitepaper is at balancer.fi/whitepaper.pdf.

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Publication and Context

Nikolai Mushegian was a key contributor to the MakerDAO technical team and the original author of the DAI smart contracts before joining Balancer. Fernando Martinelli, a Brazilian physicist, co-founded Balancer Labs.

The critical observation: Uniswap’s 50/50 pools work well for symmetric market-making, but many protocols and asset managers want to hold non-50/50 portfolios. An 80/20 ETH/BAL pool lets a Balancer protocol provide liquidity while retaining 80% ETH exposure rather than splitting 50/50.

Balancer v1 launched in March 2020. Balancer v2 launched in May 2021 with a vault architecture separating pool math from asset custody.

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The Generalized Constant Weighted Product

The Balancer invariant is the constant weighted product:

$$V = prod_{i=1}^{N} B_i^{W_i}$$

For a 2-token pool with equal weights ($W_1 = W_2 = 0.5$), this reduces to Uniswap’s $sqrt{B_1 cdot B_2}$ = constant (equivalent to $B_1 cdot B_2$ = constant).

For non-equal weights (e.g., $W_1 = 0.8$, $W_2 = 0.2$):

• The price of token 2 in terms of token 1 is: $P_1 = frac{B_2 / W_2}{B_1 / W_1}$
• As $B_1$ is bought, $P_1$ rises, causing arbitrageurs to sell $B_1$ back in (rebalancing)
• The pool maintains the target weight ratio automatically through arbitrage

Self-rebalancing portfolio mechanics:

• If ETH price rises in an 80% ETH pool, ETH’s balance grows (relatively), shifting the pool above 80/20
• Arbitrageurs buy the cheap token (DAI) from the pool and sell ETH into it, returning the pool to 80/20
• The pool earns a trading fee from each such rebalance transaction
• Net effect: the pool maintains its target weights; LP holders effectively own an automatically-rebalanced index

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Pool Types (Balancer v2)

Balancer v2 introduced a modular architecture with pluggable pool types:

Pool Type	Description
Weighted Pool	N tokens, arbitrary weights (the original Balancer invariant)
Stable Pool	Curve-like StableSwap invariant for correlated assets
Boosted Pool	Idle LP assets deposited into Aave/Compound to earn yield
Liquidity Bootstrapping Pool (LBP)	Dynamic weights for token auctions / fair launches
Managed Pool	Discretionary portfolio management by a whitelisted manager
MetaStable Pool	For assets with a known rate relationship (stETH/ETH)

The Vault in v2 holds all pool assets centrally; pool contracts only define the math. This reduces gas costs (avoid multiple ERC-20 transfers per hop) and simplifies multi-hop routing.

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Liquidity Bootstrapping Pools (LBPs)

One of Balancer’s most used features: LBPs allow projects to do a fair token launch:

• Start with a high token weight (e.g., 95% project token / 5% USDC)
• Weight shifts dynamically to 50/50 over the launch period (e.g., 3 days)
• The shifting weight creates continuous downward price pressure
• Bots and price manipulators are discouraged (price naturally falls toward equilibrium)
• Users DYOR on timing rather than chasing an opening mempool race

Many projects used LBPs as an alternative to IDOs with better price discovery.

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veBAL and Tokenomics

BAL token launched June 2020. Balancer adopted the veBAL model (vote-escrowed BAL) in 2022, mirroring Curve’s veCRV:

• Lock BAL+ETH 80/20 BPT (Balancer Pool Token) for up to 1 year
• veBAL holders vote on gauge weights (which pools receive BAL emissions)
• veBAL wars emerged, with Aura Finance playing the role Convex plays in Curve

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Reality Check

Balancer has consistently been in the top 5 DEXes by TVL but has a smaller market share than Uniswap for volatile asset trading. The weighted pool model excels for protocol-owned liquidity (AAVE/ETH, BAL/ETH pools) but sees limited retail flow compared to Curve (stablecoins) or Uniswap (general tokens). Balancer v3 continued the modular architecture improvements, though adoption remains fragmented across multiple blockchains.

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Legacy

Balancer’s weighted pool demonstrated that AMM invariants are general-purpose mathematical tools, not just Uniswap’s specific formula. The concept of AMMs as self-rebalancing portfolios is intellectually significant: LPs don’t passively participate — they run an automated trading strategy (sell high, buy low via arbitrage). LBPs became widely used for fair token launches. The veBAL governance model added to the Curve Wars ecosystem.

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Related Terms

• Automated Market Maker (AMM)
• Liquidity Pool
• Curve Finance Whitepaper
• Uniswap v2 Whitepaper
• Impermanent Loss

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Research

• Martinelli, F., & Mushegian, N. (2019). Balancer: A Non-Standard Automated Market Maker. balancer.fi.

— Primary source. Section 3 derives the weighted product invariant; Section 4 the spot price formula.

• Angeris, G., & Chitra, T. (2020). Improved Price Oracles: Constant Function Market Makers. ACM AFT 2020.

— Taxonomy of constant function AMMs; Balancer occupies the “weighted geometric mean” category.

• Mohan, V. (2022). Automated Market Makers and Their Implications for Liquidity Providers. arXiv:2201.02516.

— Analysis of impermanent loss under different AMM invariants, including Balancer’s weighted pools.