Rebase

A rebase is an automatic adjustment to the supply of a token in which a smart contract increases or decreases the balance held by every address at once. In the classic design, the contract compares the token's market price with a target price and expands supply when the price is above target and contracts it when the price is below. Each holder's share of the total stays the same, but the number of tokens in their wallet changes.

Tokens that work this way are known as rebasing or elastic supply tokens. The best-known early example is Ampleforth (AMPL), launched in 2019. The word is also used more loosely for tokens whose balances grow to reflect earned rewards, such as some liquid staking tokens. Rebasing is related to, but distinct from, the mechanisms used by an algorithmic stablecoin, which typically mint and burn a second token instead of changing everyone's balance. It is also different from a token burn, which removes coins from circulation without touching other holders' balances.

Imagine a pizza shared among friends. Instead of making each slice more or less valuable, the host simply recuts the pizza into more or fewer slices, and everyone keeps the same portion of the whole. If you had a quarter of the pizza before, you still have a quarter, but it might now be three slices instead of two.

A rebasing token does the same thing with coins. The aim is for each single coin to stay near a target price by changing how many coins exist. The value of what you hold still depends on what the whole pizza is worth, which is the part people often miss.

A simple version of the rule changes supply in proportion to how far the price is from target, often smoothed so the correction happens over several periods:

• $\Delta S$ is the change in total supply at the rebase.
• $S$ is the current total supply.
• $P$ is the market price and $T$ the target price.
• $\lambda$ is a smoothing factor that spreads the correction over several rebases.

Suppose a token has 1,000,000 units, a target of 1.00 dollar, a market price of 1.20 dollars and a smoothing factor of 10. The price is 20% above target, so the change is 1,000,000 × 0.20 ÷ 10 = 20,000 tokens. Supply rises to 1,020,000, and a holder with 1,000 tokens now has 1,020. Their share of supply is unchanged at 0.1%. Ampleforth reads its price from oracles, which report the average market price, and rebases once a day, using a target linked to the US dollar adjusted for inflation.

• Price-targeting tokens. Ampleforth and its imitators adjust supply to push the unit price towards a target, aiming for a unit of account whose supply, not price, absorbs demand changes.
• Staking rebases. Projects such as OlympusDAO (OHM) paid staking rewards as frequent balance increases, which produced very high advertised yields in 2021 and inspired many an OHM fork.
• Reward-tracking tokens. Lido's staked ether token, stETH, raises balances regularly to reflect staking rewards; because this complicates use in other protocols, a non-rebasing wrapped version is also offered. See liquid staking.

Changing balances causes problems for software built around fixed amounts. Decentralised exchanges, lending markets and wallets can mis-account for rebasing tokens unless they handle them specially, which is why wrapped, fixed-balance versions are common. Tax treatment is unclear in many countries, since each rebase may or may not count as income or a disposal. Rebasing tokens placed in a liquidity pool can also cause losses for liquidity providers, because the pool's balance changes while the other asset in the pair does not, and arbitrage traders take the difference. Users may also misread a rising balance as profit, even though their share of the network has not changed.

A rebase redistributes nothing: holders keep the same fraction of supply, so a price-targeting rebase does not create stability in the value of a holding. When demand falls, price and supply can both shrink, leaving holders with fewer tokens worth less each, a pattern some call a negative spiral. High rebase yields in staking-based schemes were frequently funded by new token issuance and collapsed when inflows stopped, as many OHM forks showed in 2022. Rebasing tokens can also be targets for oracle manipulation, since the price feed drives supply. Readers should treat advertised rebase yields with caution and check how a token's supply is actually controlled through its tokenomics.

• Ampleforth