Productive debt math

Guaranteeing a floor yield

In traditional onchain lending markets, the supply rate for lenders is simply:

$$supplyRate = borrowRate * utilizationRate$$

If the borrow rate is 5% and utilization is 50%, the supply rate is 2.5%. In Lotus, the math works differently.

The loan asset supplied by lenders intrinsically earns the base rate. For example, if the base rate is 3%, then the minimum a lender can earn is 3%.

Compressing the borrow-lend spread

With productive debt, the supply rate is calculated differently:

$$supplyRate = baseRate + (creditSpread * utilizationRate)$$

In our example, the borrow rate is 5% and the base rate is 3%. The borrow rate is simply the sum of the base rate and credit spread.

$$borrowRate = baseRate + creditSpread$$

As a result the credit spread is 2%. Using the calculation from above, if:

• the base rate is 3%

• the credit spread is 2%

• the utilization rate is 50%

This results in a supply rate of 4% which is significantly higher than the supply rate of 2.5% where productive debt isn't used.

In this example, all of the benefits of the productive debt are accruing to the lenders, but in practice the benefits are split between the borrowers and lenders.

The result is higher supply rates and lower borrow rates.

Reducing rate volatility

Because productive debt splits the borrow rate into a base rate and credit spread, rate volatility is reduced in most cases. Most markets use an IRM where an input to the credit spread is utilization. In markets without productive debt, a shock to utilization would have a large impact on the borrow rate because the IRM's logic doesn't have a concept of the base rate. With productive debt, utilization changes only impact the credit spread which is a portion of the overall borrow rate.

LotusUSD is used as the loan asset in markets denominated in USD, but it is mostly abstracted from the user experience for borrowers and lenders. Users are able to mint and redeem LotusUSD if they want low-risk yield.