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What does this mean for the future of Instrumental?

Written by 0xMoonscraper

While much has been made about farming strategies across different blockchains, other aspects of Instrumental are novel to the DeFi landscape. In this piece, I introduce the concept of trading Liquidity Pool (LP) tokens as enabled by Instrumental. Hence beyond Instrumental being a cross-chain strategy hub, liquidity providers can get additional utility unlocked for the LP-native tokens tradable directly on Instrumental.

Let’s run through a refresher.

Automated market makers (AMMs) make token swap Decentralized Exchanges (DEXs) possible. They do this by building LPs through liquidity providers who add their assets to a pool. These assets are locked in for a pre-determined period, and the liquidity providers are paid for the fees generated from token swaps in this period.

The AMMs price the assets in the pool according to the above formulae. X and Y represent the amount of tokens, which are assets being traded, in the pool.

When a liquidity provider provides their assets to a pool, they are given a new token in return. This is referred to as an LP token (LPT). This token functions as a receipt of provision to a pool and a means for a liquidity provider to gain the rewards of mining and token swaps fees accurately, according to the proportion of their assets within the pool. The value of these LP-native tokens is decided by the aggregate value of the entire pool, and then the number of LP-native tokens that represent this supply. A larger pool with fewer LP-native tokens is worth more, and vice versa.

The above indicates the value of the LP position in terms of token Y, where Y is being traded for, X and Y represent two tokens within the pool, and y is inclusive of any trading fees (through a separate pricing formula).

LP-native tokens are then burnt to get users the reward for their provision, which comes in the underlying token native to the pool. Taking a small digression, it is interesting to note that when the liquidity provider burns their LPTs, the rewards are automatically obtained simply from the returned tokens. In other words, there is no need to keep track of exactly when the LPTs were minted, or what has happened in the meantime that the provider has been in the pool. Also, it is not that the fees collected from the trades in the pools are “set aside” to some other vault that we need to go query to get the returns made by the liquidity providers. Everything is in a sense automated — and it works in this creative way mainly due to the high gas cost of Ethereum. The liquidity provider claims (aka burns) their LPTs for the underlying tokens and, by doing so, automatically receives all of their initial capital and their rewards.

What Instrumental allows users to do, however, is to sell these LP-native tokens themselves. Consequently, users can sell the actual liquidity in a pool itself, and those seeking liquidity can buy it.

This enables the monetization and ownership of liquidity, creating new financial incentives for liquidity tokens and enabling new structures like protocol-owned liquidity.

This functionality is neither straightforward nor simple. There are multiple factors at play when enabling the exchange of LP-native tokens, which is part of why it is novel to Instrumental:

Different LPs have different aggregate values and different supplies of LP-native tokens, which means one LP-native token is not directly tradeable for another.

LP-native tokens fluctuate in value as

In the above equations, QA and QB denote the share of the LP-native tokens (fraction of pool ownership) of the two different parties, A and B, respectively. LPA/LPB, represents the number of LP-native tokens given to liquidity provider A/B, and NA and NB represent the respective supply of total LP-native tokens within each pool.

The above figure denotes swap prices of the tokens, where x and y represent the amount of tokens, and A and B represent the different LP-native tokens being exchanged.

Different LPs may not have a common token between their pools, making it difficult to compare prices. In such a scenario, we use an oracle and swap according to a different common token

After swapping to a common token Z, and calculating the exchange rate to this token using rates rA and rB (again from a chosen, commonly a global, oracle) the above are used to determine the value of the different LP-native tokens in terms of the common token Z.

Normalizing LPA and LPB value to 1, the above formula is used to calculate a fair price for LP token swaps.

The above equation is similar to the previous example, except the common token is now denoted with C, and there are weights, represented by wA and wB, according to the specifics of the LBP.

The above is an example of how this plays out.

Users want to optimize for their needs, such as AMMs with low slippage. This requires more complicated AMMs, who then have more complex LPs. In these scenarios a separate equation determines the relationship between LBP tokens and pool parameters, introducing an additional wrinkle of complexity in price calculations.

The above is an indication of how token swaps would occur for AMMs that use more complex algorithms for its price determination, building on the specific formulae used by one such major DEX and its unique invariant.

With the complexities peculiar to each LP-native token, it is important that they are addressed before Instrumental can allow the sale of LP-native tokens. Instrumental is able to do this through mathematical price calculations that factor in these different models for the price calculation required.

At a high level, what is ultimately relevant for this pricing to take place is the distribution of tokens within a pool, the overall supply of LP-native tokens, and the pricing for conversion to a common token. With these understood, Instrumental is able to tackle these challenges through a common basic strategy, irrespective of the individual pool type:

Instrumental pushes the boundary even further through “LP-native” token swaps as a cross-chain strategy hub facilitating optimized yield. This is powered by integrating with AMMs already integrated into Mosaic, thereby unlocking greater utility for liquidity provisioning (LPing). This has significant implications for strategies like protocol-owned liquidity (POL). The ownership permanence of LP-native tokens is crucial for the growth and sustainability of other functions like treasury deployment a protocol might choose to implement. Moreso, native LP-native tokens swaps on Instrumental allow liquidity providers to leverage it without facing the cost and time-related barriers they encounter if using dedicated DEXs for that purpose. Chain and layer agnostic swaps become more profitable to LPs, improve convenience, and further drive DeFi adoption.

The framework discussed in this article covers the basics of LP token swaps. In the future, we also aim to solve the more complicated case of having different reward options on various networks. For example, if an LP token on one network is also staked in a yield generating activity, this reward also needs to be accounted for. More on this in a later post.

LP-native token swaps are made possible through Mosaic’s technology and an extensive list of AMMs. As Mosaic expands its list of integrated AMMs, Instrumental can continue to build an interconnected layer and chain agnostic network for seamless LP token swaps. By Q4 of 2022, users can leverage this technology across different chains and start swapping their LP-native tokens.

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