How the Index Works

This page explains, more precisely, how a Bush Weighted Pool of tokenized stocks on Robinhood Chain stays balanced, what a "weight" actually means, and what you receive when you add liquidity to one of these pools.

What's in the Pool

The tokens in these pools are tokenized stocks, on-chain representations of real equities that are live on Robinhood Chain. A pool might hold tokenized shares of, say, AAPL, TSLA, and NVDA side by side, the same way a traditional index fund would hold a basket of equities. The difference is that the basket lives in a single smart contract, and anyone can trade against it or provide liquidity to it directly.

Weights Are Value Shares, Not Token Counts

The most common misunderstanding about a Weighted Pool is thinking a "40/40/20" pool means the ratio of token quantities. It doesn't. Each token has a normalized weight (all weights sum to 1), and the pool's invariant is:

where is the pool's balance of token . As long as the pool's internal spot price for a pair matches the external market price, a token's weight equals its share of the pool's total dollar value, not its share of token count:

So in a 40/40/20 AAPL/TSLA/NVDA pool, 40% of the pool's value is held in AAPL and 40% in TSLA, regardless of how many shares of each that works out to. If AAPL trades at $220 and TSLA at $250, the pool will simply hold fewer AAPL tokens than TSLA tokens to keep both at 40% of value. The weight is a target value share, not a target unit count.

This value-share definition is also what makes the pool behave like an index: a 40/40/20 Weighted Pool is functionally a self-custodied, self-executing version of a 40/40/20 index allocation.

How Rebalancing Actually Happens

The pool never "decides" to rebalance; it has no keeper and no manager. Instead, rebalancing is a side effect of arbitrage:

  1. An external event moves the market price of one of the underlying stocks (e.g. AAPL rallies 10%).
  2. The pool's internal spot price, determined only by its balances and weights, is now stale and cheaper than the market.
  3. Arbitrageurs buy the underpriced AAPL out of the pool (paying with TSLA/NVDA) until the pool's spot price matches the market price again.
  4. That trade reduces the pool's AAPL balance, but since each remaining AAPL token is now worth more, AAPL's value share moves back toward its 40% target.
  5. Every one of these arbitrage trades pays the pool's swap fee, which accrues to liquidity providers.

The pool is always being pulled back toward its target weights by anyone trading it toward the correct market price. There's nothing to schedule or trigger.

Adding to the Index

Adding liquidity means depositing the underlying tokenized stocks into the pool, either proportionally (matching the current 40/40/20 split) or as a single asset, which the pool internally swaps to fit the target weights (incurring normal swap pricing on the imbalanced portion).

What You Get Back: The Index Token

In return, you receive Bush Pool Tokens (BPT), an ERC-20 that represents your proportional claim on everything the pool holds. Holding the BPT is equivalent to holding a slice of the whole index:

  • It's the index token. One BPT represents a fixed share of the pool's basket of tokenized stocks, at whatever the current 40/40/20 (or however the pool is configured) weighting is.
  • It earns the trading fees. Every arbitrage or organic swap that passes through the pool pays a fee, which flows back into the pool's balances, so the value of your BPT grows relative to the underlying basket over time, without you doing anything.
  • It's redeemable any time. You can burn your BPT to withdraw your proportional share of the underlying tokenized stocks, either proportionally across all tokens or as a single asset.

Put together: you deposit tokenized stocks, get an index token back, that index token auto-rebalances via arbitrage and earns fees while you hold it, and you can redeem it for the underlying basket whenever you want out.