# Zodiac Protocol

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**TLDR:**

- Zodiac Protocol deconstructs Liquidity Pool (LP) tokens into Principal only and Yield only tokens.
- Principal Tokens allow for investors to invest in LP tokens at a discount while removing the uncertainty associated with trading fees.
- Yield Tokens allow for investors to invest in a stream of trading fees generated by an LP and removes the Impermanent Loss risk inherent to LPs using a CFMM (Constant Function Market Maker) model.

**Summary**

Zodiac Protocol is a DeFi protocol that allows users to manage the risks associated with providing liquidity in AMMs (Automated Market Makers) by deconstructing traditional LP tokens into Principal tokens, which remove the risk of volatile trading fees, and Yield tokens, which remove Impermanent Loss risk inherent to LPs using a CFMM model.

Zodiac Protocol deconstructs LP tokens into Principal Only and Yield Only tokens. Principal Tokens allow for investors to invest in LP tokens at a discount while removing the uncertainty associated with trading fees. Yield Tokens allow for investors to invest in a stream of trading fees generated by an LP while removing the Impermanent Loss risk inherent to LPs.

One of the most popular crypto investment strategies is to earn yield by providing liquidity in AMMs, which exposes investors to three primary risk factors:

- Price fluctuations of the underlying cryptocurrencies in the liquidity pool
- Impermanent Loss Risk due to changes in the ratio of the prices of the underlying cryptocurrencies in the liquidity pool from the time the cryptocurrencies were deposited into the LP
- Uncertainty in future trading fees collected by the liquidity pool

Zodiac Protocol gives LP investors the ability to manage two of the three risks listed above. Zodiac users can utilize Principal Tokens and Yield Tokens to control the impermanent loss risk and trading fee risk of their crypto portfolios.

**Zodiac Protocol LP Yield Stripping**

The first step to use Zodiac Protocol is to take two or more tokens and combine them to create LP tokens. The LP tokens can then be deposited into a Zodiac vault to be used as collateral for yield stripping.

Zodiac uses LP tokens as collateral and creates two derivative tokens: a Principal Token and a Yield Token. LP tokens that get deconstructed must have a maturity date associated with the resulting Principal Tokens and Yield Tokens. The Principal Token’s composition will maintain the invariant (ex: the “k” for an xyk pool) from inception until maturity. In the illustration below, the price of the two underlying tokens change in value, which changes the composition of each LP token, but the invariant remains unchanged.

The valuation model of Principal Tokens takes the form of zero-coupon bonds, which is described by the formula below:

where:

P = Fair Market Price

F = Face Value at Maturity

r = Interest Rate Per Period

n = Number of Periods Until Maturity

When a user acquires Principal Tokens at price P and holds the Principal Tokens until maturity, the user has effectively acquired Principal Tokens at a discounted rate determined by the formula below:

where:

r = Annualized Discount Rate

n = Number of Years Until Maturity

F = Face Value at Maturity

P = Fair Market Price

Purchasing Principal Tokens and holding these tokens to maturity effectively creates a discounted LP token that does not receive trading fees but absorbs the impermanent loss inherent in Constant Function AMMs. This discount rate *r* is relative to the invariant of a CFMM. Principal Token holders are not guaranteed a return in USD terms. Instead, a Principal Token holder is guaranteed to earn a fixed rate of return of *r* relative to the initial invariant at the time the buyer acquires his Principal Tokens. Principal Token holders are still subject to the risks associated with the price fluctuation of the underlying tokens and Impermanent Loss.

Purchasing Yield Tokens entitles holders to the yield generated by trading fees and external incentives of the LP. Holders of Yield Tokens receive all of the yield from staked LP tokens until the Yield Tokens reach their maturity date. Unlike Principal Tokens, Yield Tokens are not subject to Impermanent Loss. At maturity, the value of Yield Tokens is zero. Before maturity, the value of Yield Tokens is dictated by the formula below:

where:

P = Fair Market Price

n = Number of Periods Remaining

C_i = Cash Flow Received from Trading Fees in Period i

r = Interest Rate

**Minting Principal and Yield Tokens Methodology**

Deconstructing LP Tokens result in two new tokens: Principal Tokens and Yield Tokens. Here is the general methodology of how the Principal and Yield Tokens work when a trader swaps tokens against the LP:

Deposit x $Token1 and y $Token2 into an LP.

Multiple AMM formulas can be used with Zodiac. For our example, we illustrate the methodology in the XYK AMM Model, the invariant k is equal to the product of x and y.

A trader swaps S $Token1 against the LP.

After a fixed trading fee percentage F is applied, the trader receives R $Token2 in the amount of:

Excluding the trading fee denominated in $Token1 and holding the initial invariant k_i as a constant, the LP now holds an amount of $Token1 equal to:

The LP will also consist of $Token2 in the amount of:

The trading fee applicable to this swap denominated in $Token1 is:

After applying the trading fee, the LP now holds $Token1 in the amount of:

The LP will also consistent of $Token2 in the amount of:

This will increase the final invariant k_f to:

After the swap, the Principal Token will hold a percentage of the LP tokens in the amount of:

After the swap, the Yield Token will hold a percentage of the LP tokens in the amount of:

**Conclusion**

Zodiac Protocol will enable users to obtain discounted liquidity, leverage exposure and stack yield. Zodiac allows for users to manage their Impermanent Loss risk and trading fee risk of their LP positions. With an LP consisting of two or more stablecoins (such as USDC and USDT), a Principal Token will share many similarities to a USD denominated zero coupon bond. The composability of Zodiac’s Principal and Yield Tokens will enable numerous future protocols.