# Tranche Math

> The targets of about 9% for Senior and about 32% for Junior come from the model on this page. Here is the model, then what happens in weaker and stronger weeks.

Canonical: https://spout.finance/docs/tranche-math/

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The targets of about 9% for Senior and about 32% for Junior come from the model on this page. Here is the model, then what happens in weaker and stronger weeks.

## The model's assumptions

- A $10m pool: $8.5m Senior (85%) and $1.5m Junior (15%).
- $30,000 of gross option premium in a week, about 15.6% a year gross on the pool.

- The protocol fee at 20%, because the Insurance Fund is below its target.
- Treasury bill yield on idle cash left out, for simplicity. In practice it adds to the pool's yield.

## A normal week, step by step

| Step | Senior | Junior |
| --- | --- | --- |
| 1. Gross premium $30,000; protocol fee 20% ($6,000); $24,000 remains |  |  |
| 2. Senior priority: 7% a year on $8.5m, divided by 52 weeks | **$11,442** |  |
| 3. The excess of $12,558 split 25% / 75% | **$3,139** | **$9,418** |
| Total for the week | **$14,582** | **$9,418** |
| Annualized (the week's income × 52, divided by the tranche's balance) | about 8.9% | about 32.7% |

## Weak, normal and strong weeks

Same pool, different premium. The Senior rate and Junior rate columns annualize the week: its income times 52, divided by the tranche's balance.

| Week | Gross premium | After 20% fee | Senior gets | Junior gets | Senior rate | Junior rate |
| --- | --- | --- | --- | --- | --- | --- |
| Weak | **$12,000** | **$9,600** | **$9,600** | **$0** | about 5.9% | **0%** |
| Normal | **$30,000** | **$24,000** | **$14,582** | **$9,418** | about 8.9% | about 32.7% |
| Strong | **$45,000** | **$36,000** | **$17,582** | **$18,418** | about 10.8% | about 63.9% |

These are illustrations of the model, not forecasts. Real premium varies week to week with market conditions.

In the weak week the pool earns less than Senior's 7% priority, so Senior takes everything and Junior earns nothing. In the strong week, most of the extra goes to Junior. That is the trade: Junior's income swings much more than Senior's.

## When the Insurance Fund is at target

While the Insurance Fund holds at least 2% of the pool, the protocol fee drops to 10%. In the normal week, $27,000 would remain after the fee instead of $24,000, and the extra $3,000 would be split 25% / 75% like any other excess.