Protocol math
In Lotus, unutilized liquidity from junior tranches can be used by borrowers in more senior tranches. As a result, there is a unique logic to Lotus markets that is not present in other lending markets. If you want a complete understanding of how Lotus works, it is critical to understand these terms and how they fit together.
Supply / Borrow
Each tranche has lenders that supply to it and borrowers that borrow from it.
Supply — the amount of loan assets supplied to the tranche
Borrow — the amount of loan assets borrowed from the tranche
Junior Supply / Borrow
A tranche's junior supply is the cumulative sum of supply (and pending interest) for the tranche and all tranches more junior. Junior supply is the liquidity that is available to the tranche ignoring borrowing activity.
Similarly, the junior borrow of a tranche is the cumulative sum of borrows for a tranche and all tranches more junior.
Junior Net Supply
Junior Net Supply represents the amount of unutilized liquidity cascading from junior tranches. It is the difference, between junior supply and junior borrow.
Below, we'll pause for an understanding check, using an example. Note that in tranche 1, the borrow amount is larger than the supply amount. In typical lending protocols this is impossible, but in Lotus, it is because of cascading supply. At tranche 1, there is 800 of junior supply and only 700 of junior borrow. Effectively, the excess liquidity from junior lenders is being used by senior borrowers.
0 (Senior)
200
100
1,000
800
200
1
200
250
800
700
100
2
200
100
600
450
150
3
200
150
400
250
150
4 (Junior)
200
100
200
100
100
Free Supply
Free supply is the amount of loan token that can be:
borrowed from a tranche by a borrower
withdrawn from the tranche by a lender
A tranche's free supply is the minimum of junior net supply in it's own tranche and any tranches more senior.
The free supply in tranches 2 and 3 is 100, because there is a lower junior net supply in tranche 1 which is more senior.
0
200
100
200
200
1
200
250
100
100
2
200
200
150
100
3
200
150
150
100
4
200
100
100
100
Available Supply
Available supply is the amount of liquidity that was available to this tranche before any of this tranche's borrowing. The available supply is used for calculating a tranche's supply utilization in the next step.
The available supply is the sum of junior net supply and borrows.
Supply utilization is the share of a tranche's supply divided by the available supply. As a result, the most junior tranche always have supply utilization of 100%. Supply utilization is used in interest and bad debt allocation.
Tranche Supply Utilization
0
200
100
300
66.67%
1
200
250
350
44.44%
2
200
200
350
57.14%
3
200
150
300
66.67%
4
200
100
200
100%
Tranche Borrow Utilization
Borrow utilization is the amount borrowed from a tranche out the total that was possible to borrow. It is calculated as 1 - freeSupply / jrSupply . Borrow utilization is used by interest rate models.
0
200
100
200
1,000
80.00%
1
200
250
100
800
87.50%
2
200
200
100
600
83.33%
3
200
150
100
400
75.00%
4
200
100
100
200
50.00%
Dynamic Loan Mix
Unutilized liquidity in a junior tranche can be borrowed by more senior borrowers. Therefore, supply deposited to a tranche ultimately is allocated to it's tranche and the tranches more senior creating a dynamic loan mix.
For example, tranche 4 lenders have supplied 200 units, but there is only 100 units borrowed in tranche 4 directly. Because tranche 4 lenders are the only ones that can support tranche 4 borrowers, 100 units of the tranche 4 liquidity is directly utilized.
The remaining 100 units cascades to tranche 3. This is why the available supply in tranche 3 is 300. It is the 200 units directly supplied to tranche 3 plus the 100 units cascaded from tranche 4. Since there is 150 units of borrows out of the 300 in available supply each unit of available supply is 50% utilized.
Tranche 4 (200 units total) = 100 to tranche 4, 50 to tranche 3, ...
Tranche 3 (200 units total) = 100 to tranche 3, ...
0
200
100
300
66.67%
200
1
200
250
350
44.44%
100
2
200
200
350
57.14%
100
3
200
150
300
66.67%
100
4
200
100
200
100%
100
The end result of the cascading process leaves a dynamic loan mix to each tranche:
T0
33.33%
9.52%
4.08%
2.04%
1.02%
T1
71.43%
30.61%
15.31%
7.65%
T2
57.14%
28.57%
14.29%
T3
50.00%
25.00%
T4
50.00%
Capital Allocated
33.33%
80.95%
91.83%
95.92%
97.96%
The table above show how much of each tranche's supply is allocated to each tranche. For example, tranche 4 is allocated:
50% to tranche 4
25% to tranche 3
14.29% to tranche 2
7.65% to tranche 1
1.02% to tranche 0
Tranche 4 has a high capital allocation percentage of 97.96%. In fact, it's even greater capital efficiency if you account for the fact that 100% of the capital is earning the productive debt rate. However, this doesn't mean that tranche 4 lenders are unable to withdraw their capital. The free supply of tranche 4 is 100, which means that tranche 4 lenders can withdraw up to 50% of their capital instantly.
Since more junior tranches have increased risk, they will also have higher credit spreads. Suppliers to these tranches are getting the highest possible yield subject to the demand for risky credit. Senior tranche lenders get less capital efficiency, but this impacts them much less given that what is not being utilized is still earning the productive debt rate.
Bad Debt Allocation
Lotus's cascading logic ensures that there is symmetry between a lender's risk and reward by using the same process for allocating bad debt as interest.
The supply utilization formula is how the protocol allocates interest in a tranche to all of the tranches that ultimately provide liquidity to it. The same method is used to allocate any bad debt.
In the example, below we will allocate bad debt based based on the supply utilization.
Case: Bad debt of 10 units in tranche 2
0
200
100
66.67%
200
1
200
250
44.44%
100
2
200
200
57.14%
10
10 * 57.14% = 5.714
3
200
150
66.67%
(10 - 5.714) * 66.67% = 2.857
4
200
100
100%
(10 - 5.714 - 2.857) * 100% = 1.429
The example has 10 units of bad debt in tranche 2 which is supported by liquidity from tranches 2, 3, and 4. As a result, all of these will see some share of the bad debt. The supply utilization in tranche 2 is 57.14% so tranche 2 will be allocated that proportion of the bad debt. The remaining bad debt (10 - 5.714) cascades to the next more junior tranche (3). The supply utilization there is 66.67% and so (10 - 5.714) * 66.67% = 2.857 units of bad debt. Now, at the most junior tranche the rest of the bad debt is allocated. Of the 10 units, 5.714 units was allocated to tranche 2 and 2.857 to tranche 3, leaving tranche 4 with 1.429 units.
Interest Allocation
Interest allocation works the same way as bad debt allocation. Starting from the most senior tranche, the interest accrued there is allocated to tranche 0. The remainder cascaded to the next more junior tranche (1) and is combined with any pending interest there. The sum of cascaded interest and pending interest is multiplied by the supply utilization. The process continues until all of the interest has been allocated.
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