Understand the principles and profit calculation of DeFi leveraged mining in one article

Written by: Francium Protocol, a leveraged yield aggregation protocol on Solana

Leveraged Liquidity Mining (LYF) is a mechanism that allows users to increase their mining positions, meaning that users can borrow external liquidity to increase their own liquidity for mining.

For example, Alice has earned a good return by growing and selling corn. Alice wants to expand her farming, so she proposes to borrow some money from her neighbor Bob and use the money to buy more corn seeds. In return, part of the harvest will be paid to Bob.

This is the beginning of leveraged liquidity mining (LYF). Now suppose Alice has 1000 USDC at the beginning. Alice uses her 1000 USDC and 1000 USDC borrowed from Bob to buy rice seeds for planting. The 1000 USDC borrowed from Bob will generate 10% interest and return to Bob. In this case, Alice can enjoy the benefits of nearly 2000 USDC, provided that she only has 1000 USDC.

This is mining with 2x leverage.

Not every investment will have a good return. When Alice asked Bob to borrow USDC, Bob made this trade-off: if he did not lend those USDC, then he would always have 1,000 USDC assets; if he used USDC to take out a loan, he would enjoy 10% (100 USDC) interest per year, but if Alice failed to plant snacks or the price of snacks fell, the worst case scenario was that she would not be able to repay the principal or even the interest. In order to ensure the safety of their assets, Bob and Alice reached an agreement that if the value of Alice's snacks dropped to a certain price, Alice would sell all the snacks and return Bob's 1,000 USDC.

This is leveraged liquidity mining with a liquidation mechanism.

But what if Alice doesn't borrow money, but borrows cash from Bob? What if the value of Alice's assets doesn't just depend on cash?

Use LYF to go long/short

From the above examples, we can see that the most intuitive function of LYF is to amplify the income from mining. In order to study the performance of LYF when we use LP mining (which is the most common case in the DeFi world), let's build a stable token model.

There are two tokens in this model: Token A and stablecoin USDC. Let P be the price of A in terms of the amount of USDC. Initially, Charlie holds N USDC and the price of A is P₀. When he participates in LYF with leverage Y:

1. Borrow N(Y-1) USDC from the lending pool

2. NY/2 USDC (half of the total USDC) will be exchanged for A

3. Deposit A ​​and USDC to get LP tokens

4. Pledge LP tokens for Farming

When closing a position, it follows these steps:

1. Convert all LP tokens to Token A and USDC

2. Sell ​​all tokens A (convert to USDC)

3. repay

4. Get the remaining USDC

According to the AMM formula, when P changes, the amount of USDC we can withdraw by redeeming LP tokens is

So when you close your position, your profit is

In traditional long positions, the profit we can get by going long on XA is X(P-P₀). Without loss of generality, let the initial price P₀=100. Initially, Charlie holds MA, and its initial price is P₀. When he participates in LYF with leverage Y, the long performance of lever mining is as follows:

USDC earnings using 1x/2x/3x leverage vs. regular long positions

But LYF does more than that. If you are a keen trader, you might think that if the price of a token is going to drop over a certain period of time, the best way to profit from it is to short the token. The usual steps are: when the price of token A is P₀, borrow X tokens of A, immediately sell X tokens of A for Y tokens of B, and when the price of token A drops to P, buy back X tokens of A, so that you get a profit of X*(P₀-P) tokens minus the interest on the borrowing of B. With LYF, it is slightly different. If you hold X tokens of A and open a 3x leveraged position, you will automatically borrow 2X tokens of A from the lending pool, and half of the total number of tokens of A, i.e. 1.5XA, will be immediately exchanged for token B. 0.5X tokens are shorted immediately. In traditional shorting, you can only profit from price drops, but in Farming, in addition to the income from price drops, you can also earn LP tokens. Since the LP price and token price have a square root relationship, this is a safer way to short an asset. You may wonder if this is a good shorting method, so next we will use the same model to show you the performance of shorting using LYF.

Initially, Charlie holds MA with an initial price of P₀, when he participates in LYF with leverage Y:

1. Borrow M(Y-1) A from the lending pool

2. MY/2 A (half of the total A tokens) will be exchanged for B

3. Deposit A&B and get LP

4. Pledge LP tokens for mining

When closing a position, it follows these steps:

1. Convert all LP tokens to tokens A & B

2. Sell ​​all B tokens and exchange them for A tokens

3. Repaying lending pool debt

4. Get the remaining tokens A

According to the AMM formula, when P changes, we can withdraw the amount of A by redeeming LP tokens. Without loss of generality, we set the initial price to 100 (due to the similarity solution, you can get the same performance at other initial prices)

The total value of LP tokens is

When you close your position, your profit is

In traditional short selling, the profit we get from short selling is

Without loss of generality, we set the initial price to 100 (due to the similarity solution, you can get the same performance at other initial prices)

Token A 1x/2x/3x leveraged income, USDC as principal

Token A 1x/2x/3x leverage income, Token A as principal

From the above chart, we can see that the LYF curve is much smoother. Comparing 2x LYF with traditional short and long, it starts to approach the profits of traditional long/short within a certain range, but the risk will be higher when the price drops/rises more. It may not look as good as a simple long/short strategy, but there is an important factor that we have not taken into account: liquidity mining income, or what we can call self-adjusting leverage. Our LP tokens are constantly rewarded, and these rewards are reinvested into our LP tokens. The ratio of borrowed tokens to capital will become lower and lower, so our leverage ratio will decrease. For example, if token A will not fluctuate in a short period of time, then LYF long/short can make it more resistant to future market fluctuations. In the constant APR automatic compounding model, the profit can be illustrated as follows:

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