Balancer: A non-custodial portfolio manager, liquidity provider, and price sensor

01 Claim ledger

What the paper is allowed to say

Each row is a sentence already in the study. The status is the same on every row: a model claim, not a live measurement.

1. Claim 01 · Paper model

   Weights are the portfolio

   A pool that is 80 percent one asset and 20 percent another will buy and sell in a way that pulls inventory back toward those weights. The weights are a target, not a decoration.

2. Claim 02 · Paper model

   More than two assets share one invariant

   The paper's value function multiplies balances raised to their weights. A trade must not decrease that value, before fees.

3. Claim 03 · Paper model

   Liquidity provision is index management

   Someone can hold a weighted basket and earn fees from people who use the basket as a market. The paper's pitch is that these are the same object.

4. Claim 04 · Paper model

   Prices fall out of the weights and balances

   The spot price between two tokens is a function of their balances and weights. As with Uniswap, that spot is movable inside a transaction.

5. Claim 05 · Paper model

   Smart pools can change weights

   The paper allows a controller to shift weights over time. That is a strategy layered on the invariant. A static pool and a moving one should not be described alike.

02 Three cuts

Observation, model, falsifier

A desk does not stop at the summary. Each claim is cut three ways, using only this study's own assumptions and checks. Nothing here is a new figure.

1. 01 Weights are the portfolio

   Observation

   What the study says

   A pool that is 80 percent one asset and 20 percent another will buy and sell in a way that pulls inventory back toward those weights. The weights are a target, not a decoration.

   Model

   What has to hold

   Weights are positive and sum to one in the normalisation the contract uses.

   Falsifier

   What would retire it

   What are the weights, and can a controller change them?

2. 02 More than two assets share one invariant

   Observation

   What the study says

   The paper's value function multiplies balances raised to their weights. A trade must not decrease that value, before fees.

   Model

   What has to hold

   Weights are positive and sum to one in the normalisation the contract uses.

   Falsifier

   What would retire it

   What are the weights, and can a controller change them?

3. 03 Liquidity provision is index management

   Observation

   What the study says

   Someone can hold a weighted basket and earn fees from people who use the basket as a market. The paper's pitch is that these are the same object.

   Model

   What has to hold

   Providers know whether weights are fixed. A moving weight is a different product.

   Falsifier

   What would retire it

   Does a provider expect their deposit mix back, or a rebalanced basket?

4. 04 Prices fall out of the weights and balances

   Observation

   What the study says

   The spot price between two tokens is a function of their balances and weights. As with Uniswap, that spot is movable inside a transaction.

   Model

   What has to hold

   All tokens behave as standard transferable balances.

   Falsifier

   What would retire it

   Is the spot price being consumed by another contract inside the same transaction?

5. 05 Smart pools can change weights

   Observation

   What the study says

   The paper allows a controller to shift weights over time. That is a strategy layered on the invariant. A static pool and a moving one should not be described alike.

   Model

   What has to hold

   Providers know whether weights are fixed. A moving weight is a different product.

   Falsifier

   What would retire it

   What are the weights, and can a controller change them?

03 Sequence

One action, as an operating tape

1. 01A creator sets tokens and weights. Providers deposit the basket and receive pool shares.
2. 02A trader sends one token in and takes another out. The contract checks the weighted product.
3. 03Balances move. The pool now holds a different mix, and subsequent trades see a different price.
4. 04If a controller is shifting weights, it does so under the paper's rules, and liquidity follows the new target over time.
5. 05A provider who exits receives a slice of whatever the basket has become, not of what they originally deposited.

04 Load-bearing

The argument, and where a pitch drops it

1. A portfolio that is a market will be arbitraged

   The cut

   If the outside world prices an asset differently from the pool's weight-implied price, arbitrageurs trade until the pool agrees. The provider is systematically selling what went up and buying what went down, relative to the target weights. Fees are the hoped-for payment for being that counterparty.

   Why it carries weight

   If this cut is skipped, the paper's name is being used without the mechanism that makes the name mean anything.

   Where it is dropped

   A manager who can move weights can move value. The paper's non-custodial claim depends on which powers the controller actually has.

2. Unequal weights change impermanent loss, they do not repeal it

   The cut

   An 80/20 pool loses less to divergence than a 50/50 pool on the same pair, and earns fees on a different shape. The paper gives the geometry. It does not give a free rebalancing service.

   Why it carries weight

   If this cut is skipped, the paper's name is being used without the mechanism that makes the name mean anything.

   Where it is dropped

   A manager who can move weights can move value. The paper's non-custodial claim depends on which powers the controller actually has.

3. Controllers are fiduciaries the math will not supervise

   The cut

   A smart pool whose weights can be moved can be a useful strategy or a way to dump one asset into passive providers. The invariant will not judge the controller. Governance of the dial is the risk.

   Why it carries weight

   If this cut is skipped, the paper's name is being used without the mechanism that makes the name mean anything.

   Where it is dropped

   A passive basket is not a hedge. Providers still hold the assets.

05 Register

What has to be true

• Model · Not re-measured

  Weights are positive and sum to one in the normalisation the contract uses.

• Model · Not re-measured

  All tokens behave as standard transferable balances.

• Model · Not re-measured

  Providers know whether weights are fixed. A moving weight is a different product.

• Model · Not re-measured

  Anyone using the pool as a price feed understands a single trade can set the spot.

06 Divergence

What happened after the paper

Balancer shipped multi-asset weighted pools and later versions added stable-like and managed pools. The 2019 paper is the weighted invariant and the portfolio reading. Later fee switches, gauges and ve-token politics are protocol economics on top, not pages of the white paper.

A later client, parameter set, or reward formula is a different object. Cite this paper for the mechanism. Cite a primary release for the network. This desk has not re-run the proof.

07 Pre-mortem

What to check before you use the idea

1. Kill test 1What are the weights, and can a controller change them?
2. Kill test 2Does a provider expect their deposit mix back, or a rebalanced basket?
3. Kill test 3Is the spot price being consumed by another contract inside the same transaction?
4. Kill test 4How many tokens are in the invariant, and what does one illiquid member do to exits?
5. 0 of 4 marked on this browser. A mark is a reading note, not a pass, a rating, or a recommendation.

08 Anatomy

The paper, in the order a builder needs

09 Lexicon

Terms, opened into the record

Weight

The target share of a token's value in the pool. Trades pull balances back toward it.

Weighted invariant

The product of each balance raised to its weight, which a trade must not reduce.

Smart pool

A pool whose controller may change weights or other parameters over time.

Pool share

A claim on the current basket, fees included, under the current weights.

10 Repository

Every linked record on this page

Underlined words open a page that already exists: a concept, a protocol profile, a failure record, or another paper. If a word is not underlined, this desk does not have a record for it.

11 Related

The next papers, as theses

• Uniswap · 2020

  Uniswap v2 Core

  The 2020 core paper for Uniswap v2: a constant-product automated market maker, with arbitrary ERC-20 pairs, price accumulators, and a flash-swap callback. It is the clearest short specification of the pool that much of later DeFi either forked or assumed.

• Curve · 2019

  StableSwap — efficient mechanism for Stablecoin liquidity

  Egorov's 2019 invariant for pools of assets that should trade near parity. The curve is flat around the peg, where most stablecoin trades happen, and bends toward a constant-product tail when the pool is pushed off parity.

• Uniswap · 2021

  Uniswap v3 Core

  The 2021 paper that replaces the uniform reserve curve with concentrated liquidity. A provider chooses a price range. Inside the range their capital acts like a constant-product pool. Outside it, their position is entirely in one asset.