Weighted Pools
Overview
Weighted Pools are an advanced implementation of the Constant Product Market Maker (CPMM) model, popularized by Uniswap, but with a customizable weight distribution. These pools are also referred to as Automated Index Funds in other DeFi ecosystems because they function similarly to traditional investment funds—but without the need for centralized portfolio managers.
Each Weighted Pool can contain up to eight different tokens, with each asset assigned a specific weight that determines its proportion in the pool. These weights dynamically influence trading behavior, allowing for strategic exposure to specific assets while ensuring efficient liquidity provisioning.
Mathematical Model
Mondrian Swap utilizes Balancer's generalization of the X * Y = K formula to enable: ✔ Unequal token weights, allowing for greater customization. ✔ Multiple assets per pool, increasing capital efficiency and diversification.
The formula for Weighted Pools is:
Where:
V is a constant invariant.
B is the balance of an asset.
W is the weight of an asset in the pool.
As asset prices fluctuate, traders and arbitrageurs naturally rebalance the pool by executing swaps that exploit imbalances. This ensures that the desired weightings are maintained, while trading fees are collected and distributed to Liquidity Providers (LPs).
Unlike traditional Index Funds, which require active management and fees, Weighted Pools flip the concept: instead of paying for portfolio rebalancing, Liquidity Providers earn fees from traders who rebalance pools through arbitrage.
Key Advantages of Weighted Pools
1. Exposure Control
Weighted Pools allow Liquidity Providers (LPs) to control their exposure to specific assets while still earning trading fees.
The higher a token's weight, the less impermanent loss it experiences if its price surges.
Example: A 70/30 ETH/MOND pool means ETH dominates the liquidity allocation, reducing impermanent loss compared to a standard 50/50 pool.
2. Variable Automated Index Funds
Unlike traditional portfolio management, Weighted Pools automate the rebalancing process, reducing manual intervention.
Traders, rather than managers, drive portfolio adjustments by capitalizing on arbitrage opportunities.
Mitigating Impermanent Loss (IL)
1. Customizable Asset Weights
Pools where one token has a significantly higher weight experience less impermanent loss than evenly distributed pools.
Example: A 90/10 ETH/USDT pool means ETH dominates, leading to lower IL than a 50/50 pool.
2. Trade-Off: Slippage vs. IL
Highly asymmetric pools (e.g., 95/5 ratio) reduce IL, but they also increase slippage for large swaps due to lower liquidity on one side.
Optimal Balance: Studies suggest that 80/20 pools offer an ideal trade-off between liquidity depth and IL reduction.
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