DEX: Concentrated liquidity

In the world of finance, the concept of liquidity plays a vital role in the smooth functioning of markets. Liquidity refers to the availability of funds and the ease with which assets can be bought or sold. However, within the realm of liquidity, there exists a phenomenon known as concentrated liquidity. This intriguing concept unveils a scenario where a significant portion of available funds becomes intensely focused on a specific asset, market, or security. Let us delve deeper into the world of concentrated liquidity and explore its implications for investors and the financial ecosystem as a whole.

Concentrated liquidity overview

Concentrated liquidity refers to a scenario where a substantial portion of available funds or market liquidity is focused on a specific asset, market, or security. It signifies a situation where a significant number of investors or traders are concentrating their attention and resources on a particular area.

Concentrated liquidity can sometimes be advantageous, indicating a strong investor interest and confidence in a specific asset or market. This increased focus can lead to enhanced market efficiency, improved price discovery, and increased trading activity.

However, concentrated liquidity also carries certain risks. When a large portion of liquidity is concentrated in a single asset, it can amplify price volatility and create susceptibility to liquidity shocks. If investors abruptly exit their positions or rush to sell, it can result in reduced liquidity, making it challenging to find buyers and causing rapid price declines.

Market participants and regulators closely monitor situations of concentrated liquidity to assess potential risks and implications. Diversification and risk management strategies are often employed to mitigate the adverse effects of concentrated liquidity. These measures aim to promote stability, reduce systemic risks, and protect market integrity. Understanding concentrated liquidity is crucial for investors, market participants, and regulators alike, as it helps to identify potential vulnerabilities and implement appropriate measures to maintain a healthy and resilient financial system.

Concentrated Liquidity Operation

Concentrated liquidity operates through the aggregation of a significant portion of available funds or market liquidity in a specific area, asset, or security. This concentration can occur due to various factors and dynamics within the financial markets.

The operation of concentrated liquidity typically involves the following key elements:

• Investor Focus: Investors, traders, or market participants develop a collective focus on a particular asset, market segment, or security. This focus can arise due to factors such as positive market sentiment, perceived opportunities, strong performance, or specific events impacting the asset.

• Capital Allocation: As investors concentrate their attention and resources on the targeted area, they allocate a substantial amount of capital to investments within that area. This allocation can be driven by the desire to capitalize on potential gains, market trends, or a belief in the long-term prospects of the asset.

• Increased Trading Activity: The concentration of liquidity leads to heightened trading activity within the targeted asset or market segment. This increased trading volume can be driven by both existing participants and new entrants seeking to benefit from the concentrated liquidity.

• Price Impact: The concentrated liquidity can have a significant impact on the prices of the targeted assets. Increased demand due to concentrated liquidity can drive up prices, resulting in potential price inflation and elevated valuations.

• Market Efficiency: Concentrated liquidity can enhance market efficiency by facilitating improved price discovery, as increased trading activity and liquidity attract a broader range of market participants. This can lead to better alignment of asset prices with their underlying fundamentals.

• Vulnerability to Shocks: However, concentrated liquidity also brings risks. The heavy concentration of funds in a single asset or market segment makes it vulnerable to shocks and sudden changes in market conditions. If there is a sudden loss of confidence or a significant shift in investor sentiment, it can lead to liquidity shortages and price declines.

BaseBank Concentrated Liquidity Formula

The formula for Concentrated Liquidity in the context of BaseBank is:

$$(x_real + L/√P_b)(y_real + L√P_a) = L^2$$

1. Coordinate Systems:

BaseBank employs two different coordinate systems to analyze liquidity positions within an Automated Market Maker (AMM):

a. Liquidity/Price Coordinate System: In this system, the y-axis represents liquidity, and the x-axis represents the price (or logarithm of the price). It is useful for calculating slippage, fees, and comparing positions within the pool.

b. Amount of Tokens Coordinate System: Here, the y-axis represents the amount of "Y" tokens in the position, while the x-axis represents the amount of "X" tokens in the position. It is useful for understanding the amounts of tokens in a position and making decisions related to opening or closing positions.

1. Liquidity Calculation:

The liquidity (L) can be calculated using the virtual reserves x and y, based on the formula: x · y = L^2. This formula represents the relationship between the reserves of X and Y tokens and the liquidity in the position.

1. Concentrated Liquidity Position:

In the "amount of tokens" coordinate system, a concentrated liquidity position appears as a segment of a hyperbola between two points, A and B, with specific coordinates (ax, ay) and (bx, by) respectively. These endpoints determine the position's shape and relationship with the current price.

1. Real Reserves Formula:

To translate the liquidity position to the "amount of tokens" coordinate system, the curve segment between points A and B needs to be shifted to points A' and B'. The formula for shifting the function algebraically is given by:

$$(xreal + L/√Pb)(yreal + L√Pa) = L^2$$

Here, x_real and y_real represent the real reserves of X and Y tokens, respectively, while P_a and P_b denote the minimal and maximal prices of the position. The formula enables the translation of the liquidity position to the "amount of tokens" coordinate system, preserving the relationship between the position's liquidity and prices.

By using this formula, BaseBank can determine the real reserves of X and Y tokens required to shift the liquidity curve and accurately represent the concentrated liquidity position in the "amount of tokens" coordinate system.