Fragments Primer
In this primer we cover the core concepts behind the Fragments Protocol using a series of animated diagrams. We'll first describe the outputs of the system at a high level. Then we'll show how this is achieved from the bottom up.
1. Senior and Junior Perpetuals
Here we describe the high level inputs and outputs of the Fragments protocol:
describe fragments
The Fragments protocol works by reorganizing the volatility of an input asset (gold or BTC) into senior and junior perpetual tranches.
Sr∞ tranches are lower in volatility than their underlying asset; and Jr∞ tranches are higher in volatility than their underlying asset. Using the example of BTC:
- Sr∞ — the low volatility derivative
- Jr∞ — the high volatility derivative
Holding Sr∞ and Jr∞ together, in the right ratio, is like holding the underlying (gold or BTC); because volatility is conserved in the system.
Key Takeaway
Sr's and Jr's are low and high volatility derivatives of their underlying asset. As a convention we prefix the senior perpetual of a token with lv (ie: lvBTC); and the junior perpetual of a token with hv (ie: hvBTC). To learn how this works read on below.
2. Fixed-term Tranching
In this section we'll explain fixed-term tranching.
describe tranching --fixed
Tranching is the process of reorganizing an asset's volatility into two or more derivative assets with different volatility exposure.
The volatility of an asset, Ai can be separated into senior and junior fixed-term tranches simply and predictably:
- Sri — is affected by volatility last
- Jri — is affected by volatility first
At maturity both tranches mature into claims on the underlying asset (gold or BTC). Holding both [Sri, Jri] is equivalent to holding the underlying asset.
What's Special About This?
Fixed-term tranching simplifies the process of converting a medium risk asset into two derivative assets: one that is safe and one that's extra risky.
- Safe Asset — The senior tranche (Sri) can be held as a safe asset because it is only affected by volatility after its matching junior (Jri) has been depleted.
- Risky Asset — The Junior tranche (Jri) offers magnified volatility because all volatility accrues to it until it has been fully depleted.
Much of traditional finance works by some variation of this, but the methods used are complex, opaque, and difficult to implement without administrative oversight. Read on to learn about perpetual tranching.
3. Perpetual Tranching
Fixed term tranching, described above, is an extremely powerful building block. In fact you can use fixed-term tranches to create perpetual tranches; and reorganize volatility indefinitely.
describe tranching --perpetual
Perpetual Tranching is the process of reorganizing volatility into two or more derivative assets with different volatility profiles; indefinitely.
An input asset's volatility, A, can be separated into senior and junior tranches perpetually, by bundling multiple fixed-term tranches that are evenly offset by time.
And then systematically rotating maturing tranches out (left), in exchange for fresh tranches in (right):
- The Perpetual Senior (Sr∞) — is a proportional claim on a rotating basket of Sri tranches — it can be held as a safe asset.
- The Perpetual Junior (Jr∞) — is a proportional claim on a rotating basket of Jri tranches — it can be held for magnified exposure
Proportional Redemption
At any time, users can redeem the perpetual senior or junior tokens for underlying collateral on-chain.
Example: Let's say Alice owns 1% of the Sr∞ (or Jr∞) token supply; and wants to redeem all of it for underlying collateral. Upon redemption she would receive 1% of each fixed-term tranche in the collateral set, as well as 1% of any raw underlying collateral in the set:
Proportional redemption prevents bank-run scenarios because the composition of collateral remains the same before and after any given redemption.
What's Special About This?
Fixed-term tranching is great for temporarily reorganizing volatility, but fixed-term tranches aren't fungible across vintages because different vintages have experienced different market conditions over time. This makes them less perennially liquid. By bundling multiple vintages into rotating baskets of Sri's and Jri's we can solve for this problem in a simple and highly durable way.
4. Rotation
describe fragments --rotation
Rotation is the process of withdrawing maturing tranches and replacing them with fresh tranches. This process is automated and occurs weekly.
At the time of rotation (in the case of BTC), the junior perpetual contract initiates a process that:
- Mints fresh (Sr/Jr) tranches using assets in the hvBTC collateral set and moves the new seniors to the lvBTC collateral set (left arrows above).
- Withdraws the maturing Sr's from the lvBTC collateral set and merges them with maturing Jr's in the hvBTC collateral set, storing as BTC (right arrows above).
In the case where the BTC balance in the Jr vault does not cover the entire rollover, it rotates as much as possible.
Volatility Multiple
In the case where there is a target volatility multiple. Some amount of maturing Sr0's may be left in the Sr∞ collateral set to preserve the target ratio:
- Example: Let's say lvBTC is targeting 0.3x volatility. Because Sri can be approximated as a zero volatility asset, 30% of its collateral ought be raw BTC and the remaining 70% should be fresh fixed-term Sri tranches.
5. Rebalancing
Rebalancing is a process of periodic value transfer between the Sr∞ and Jr∞ collateral sets that aims to 1) ensure there's sufficient capital in the Jr∞ collateral set to complete rotations and 2) keep volatility multiples reasonably close to target.
Demand for stability (Sr∞ tokens) and volatility (Jr∞ tokens) come from different places. For this reason, the TVL of Jr∞ and Sr∞ collateral sets can grow out of balance.
Bidirectional Funding Rate
To help the system maintain balance, there is a funding rate mechanism that periodically transfers value from the overcapitalized collateral set to the undercapitalized collateral set. This has the added benefit of incentivizing users to hold whichever position there's less relative demand for; further encouraging balance.
- Example: let's say the system targets a 2/1 (Jr∞/Sr∞) ratio of collateral TVL. But at present there's excess demand for holding the Jr∞ vs the Sr∞ and the current TVL rato is 3/1. In this case the protocol looks at the deviation ratio ((2.5/1) / (2/1)) and computes an amount to transfer that directionally pushes the system towards the target ratio; based on this deviation.
Rebalancing occurs daily. Both the rebalancing frequency and the funding rate curve are configurable by governance.
6. Durability
The Fragments protocol was designed to bend rather than break under extreme market conditions. This means the system prefers temporary volatility over any condition that could: directly damage the broader ecosystem, lead to insolvency, or otherwise force the system to forever cease function.
Recall that the Fragments protocol works by splitting a medium volatility asset into a high-volatility derivative (hvBTC) and a low-volatility derivative (lvBTC).
- lvBTC and hvBTC are one-directional, proportional claims on baskets of collateral:
Similar to how a UNI-V2 LP token is a one-directional proportional claim on a basket of two assets. - The value of lvBTC (and hvBTC) is determined by the redeemable value of its collateral:
Similar to how the value of a UNI-V2 LP token is determined by the redeemable value of its collateral.
Additionally:
- lvBTC and hvBTC are collateralized by fixed-term BTC tranches.
- Fixed-term BTC tranches mature into raw BTC every 28 days.
Below, we'll cover the most extreme scenario to further illustrate.
Rotations Halting
In the most extreme scenario the tranched assets in lvBTC's collateral set matures into raw BTC (or gold) and the lvBTC token becomes a freely redeemable claim on the raw underlying asset. Although the system becomes more volatile, there are no bank-run conditions, insolvency, or cascading liquidations that take place along the way.
When rotation capital is insufficient, the fixed term Sri tranches naturally and progressively degrade into their underlying asset. The following shows the progression of lvBTC's collateral set that halts rotation for four consecutive cycles:
You can think of this as similar to ice and water. Imagine you have a voucher that's redeemable for a percentage of ice in a freezer. Continuing with this metaphor, If the refrigeration process halts (ie: rotations halt) your voucher (the lvBTC token) becomes redeemable for a combination of ice and water until the refrigeration process resumes, after which the water progressively freezes back into (and is redeemable for) ice.
Since each vintage of senior tranches in the lvBTC collateral set is offset by a fixed time-window, when rotations halt, the lvBTC token becomes redeemable for a combination of raw BTC and senior tranches. The longer rotations halt for the greater the fraction of redeemable collateral is raw BTC until rotations resume.
As more senior BTC tranches mature into raw BTC the price of lvBTC will become temporarily more volatile because BTC is more volatile than senior BTC tranches. Similarly, as rotations resume the price of lvBTC will become more stable again because senior BTC tranches are heavily insulated from underlying BTC volatility.
This process of degrading and resuming is continuous rather than discrete. The system “bends” safely rather than “breaking” catastrophically. More specifically, rather than triggering bank-runs, insolvency or cascading liquidations, when under extreme stress the lvBTC token simply becomes temporarily more volatile, and can resume stability in the future without bailouts.