Below I explore the relationship between equity and obligations.
I take a view of this relationship from the perspective of path independent AMMs as they provide a point of comparison for exchanging risk profiles.
Quick Review of Prior Concepts
Impermanent Loss (aka Divergent Loss)
Automated Market Makers (AMMs) run trading strategies on assets deposited into their custody. This involves automated pricing of assets vs each other and adjusting balances accordingly. This allows losses and gains from trading to be formally assessed.
These generally acquire the falling asset and sell the rising asset such that if current price moves away from your deposit price, the units you initially held will be less valuable than the units you currently hold. However if the price returns to the original deposit price you will hold the same, therefore the loss is impermanent. It lasts only so long as the price has diverged from entry.
Ideally any impermanent loss is offset by fees accrued for the service.
Path Independence / Path Dependence
Uniswap V2 AMMs are full range and Path Independent.
Uniswap V3 AMMs are Path Independent until a rebalance occurs in which assets held by the strategy are shifted to a new range. Often this is realized through a swap. At such a point it becomes path dependent on where these rebalances occurred.
An Individual LP may be path independent in a Uniswap v2, but they can become path dependent if they withdraw liquidity wait for the price to change, then reenter the LP, perhaps swapping some assets to max capital usage in the strategy.
Summary
Impermanent Loss
Difference in currently priced value between Initial Units deposited and Current Units withdraw-able.
If you don’t rebalance returning to the same price
Path Independence
Predictable value at any given price
Path Dependence
Difficult to predict value dependent on the historic pathing
Combined
Impermanent Loss in an AMM range which does not rebalance is Path Independent
Impermanent Loss is made Path Dependent when rebalancing occurs, which makes adjustments in asset supply, and pricing range along the curve.
Volume between start and end price impact revenue generated which gives some aspect of path dependence to if a positions is in profit.
Path Independent Equity
In some cases Equity is path independent, but not fixed share. These are cases where the relative portion of the product owned changes at predictable rates given certain metrics.
Fixed Equity (Cryptopunks)
There are 10,000 Cryptopunks that exist and there will only ever be 10,000 cryptopunks. Therefore owning 100 punks guarantees you 1% ownership of the total supply.
Constant Emissions (BTC)
BTC issuance is defined over over a long time frame.
Over time each Bitcoin represents less and less percent ownership of the total supply. This binds your equity to time.
Continuous Token Sale (SOCKS)
Lets take Unisocks for example. These are sold on a full range bonding curve. The more demand, the higher the price, and the available liquidity to purchase still locked in the bonding curve.
This means that if you own 1 SOCKS today, and I buy one of the remaining 20 pairs in the pool, your relative share of circulating SOCKS will go down. However if someone sells a pair back into the pool your relative share of circulating SOCKS will go back to what it was.
This is True impermanent Equity. As demand scales you own less of the total supply but the relative value of your supply has gone up. At any price you can derive circulating supply and vice versa.
Weighted Continuous Token Sale (GMX)
GMX has a weighted continuous token sale at present. Rather than using a Uniswap v2 curve to sell more Equity into circulation, they use a Uniswap V3 set up spread across many different tick ranges. This still allows them to cover the full range, but breaks up the continuous liquidity available, allowing them to add stronger support at particular price ranges.
I think this is a really interesting phenomena which when left static can be as Path Independent as a Uniswap v2 curve, while expressing confidence in more selective price ranges as though it has multiple Curve Finance A Factors.
I am very much inspired by this framework. While the project itself is trying to avoid introducing complexity, in a broader context, I could see protocols injecting Rolling Hills like structures into this framework to earn more revenue for the DAO while marketmaking across a fuller range.
Further, if the project chooses to rebalance its weights, each rebalance of distribution along the curve would be a path dependence, but once rebalanced would remain path independent until the next decision to rebalance.
Dabbling in limited Path Dependence
Coverage (MKR)
Lets take Maker for example. Of late the MKR token is repurchased off the market by way of revenue reducing MKR supply as a function of fees.
MKR also gets issued in times when its liquidation system fails, covering losses.
Its equity is a backstop for failing to meet its liquidation obligations. This limits new equity being minted, but when it is minted its after a large market downturn. To combat this Maker has a delay before new MKR is auctioned to reclaim debt.
As long as Maker governors make the right collateral choices and stimulate strong liquidation markets, their equity is relatively path independent, but should they be wrong, path dependence may come strongly knocking.
Stress Test: Passed
The best example of the risk faced by MKR equity holders is that of Black Thursday. Maker has time between deficits arising and MKR being auctioned to the public. This buffer allowed for a DAI Backstop Syndicate to quickly form.
Since Maker is most at risk after a large crash where its equity is already at a relatively low price as well as market confidence more broadly, the MKR auction must find buyers. Holders also want to limit dilution. To this end a contract was spun up to backstop the MKR auction where entities could pool funds together to signal a bottom and limit equity dilution.
I think were a few key factors which prevented the system from imploding here
dilution was limited.
the system otherwise performed as expected
the issues which caused dilution were not core to the design and could be addressed by external coordination centers.
Projects such as KeeperDAO and B Protocol were launched to address a lack of liquidators.
the issues around lack of liquidity could be addressed with additional vaults
Overflow vaults like USDC-B were created to generate DAI at high interest for shorter term arbitrage opportunities around liquidations
The PSM was created to create a low friction way to access liquidity when needed.
Path Dependent Equity
In some cases Equity is path dependent. These are cases where the relative portion of the product owned changes at unpredictable rates, depending on when certain actions took place.
Impermanent Loss Protection (BNT)
In the case of Bancor, Equity acted much like a continuous token sale with two big exceptions.
The buyback was powered by loans instead of protocol owned assets.
The protocol offered excess equity to cover these sales at the time depositors wished to exit. Going as far is to mint if the excess is not enough.
In this scenario the single sided LPs of Tokens paired with BNT were in fact lending Bancor liquidity to market make, as they are dependent on Bancor to get them back any liquidity of their which is sold.
When LINK is sold from single sided LP’s it accumulates as BNT but the lender only has a claim on LINK. Its up to the system to the protocol to manage its loans and ensure the above 47 BNT owed to LINK holders is returned as LINK in addition to the IL faced.
While sales still followed a the path independent nature of an X*Y=K pricing curve, the loans were path dependent in when they were called by the lenders.
If a lender wishes to exit when their deposited token is at a higher price vs the systems equity token, then the system needs to either give them other lenders liquidity, or buy back with the protocol token at a loss.
If a lender wishes to exit when their deposited token is at a lower price vs the systems equity token, then the system can repay them with the balance on hand, but may need to buy back lost equity with the excess token at a loss.
The hope would be that revenue generated from demand from the protocol outweigh not only the impermanent loss, but this must also counter the price impact of selling BNT at a low to secure assets.
A key problem is when all that protocols activity is mostly self contained. To sell BNT to buyback USDC, largely needs to do that on chain, and that means creating more debt for itself. This puts the protocol in a position where it can’t close loans by selling BNT without creating even matching levels of debt.
Stress Test: Undecided favoring death spiral
When too many users try to exit at once while BNT is at a low price relative to most trading pairs, then Bancor needs to sell BNT into its own pools which increases its debt as its trying to repay it. Each pool just inflates with BNT which pushes down the price of BNT which then requires more BNT to be sold to reclaim debt. This problem is compounded when too many users enter when BNT is at a relatively high price.
A key problem faced in holders organizing to backstop BNT is there is no clear image of what they are saving. If the core function of the protocol can’t properly hedge, how can that be resolved without a complete redesign. Is it better to try that without the baggage of debt owed to all current LPs?
For now Bancor has chosen to freeze incentives and deposits. Withdrawals not only do not pay IL insurance but do not facilitate the withdrawal of the value held by the pool in BNT. Users could choose to exit at steep loses, or remain at risk of further BNT sell pressure reduces the assets available to exit with.
If enough folks exit at a loss that the debt can be rebalanced, will there be anything left standing anyway?
AlgoStables (LUNA)
In the case of Luna, Equity acted much like a weighted continuous token sale with two big exceptions.
The buyback issued synthetic debt instead of protocol owned assets.
The buy or sell pressure at any particular price is determined by the sellers, not the protocol.
This creates debt which is owned by the system but can be selectively created and redeemed by individuals.
The protocol would issue $1 worth of Luna equity in exchange for UST obligations, and generally sensible to complete the arb by selling the Luna.
The protocol would issue 1 Luna worth of UST obligations for each Luna burned.
Like Bancor, we face path dependence in the form of granting individual autonomy to impact the prices these acts occur, which can cause the phenomena eloquently described by MonetSupply below. (I can’t unsee this tweet)
Because of this relationship, the sustainability of the ecosystem was heavily dependent on how unstructured actions take place.
Stress Test: Death Spiral
When push came to shove there were not enough buyers of Luna when it became obvious the system itself incentivized these behaviors and would need to be entirely restructured. Given this was the core feature of the chain, there was little demand to try to save the system, and take on the debt accrued which became far larger than the equity available.
Anything worth saving is better to fork and start fresh without the existing obligations hanging over their head.
Its all a confidence game.
Without debt, its all gravy.
With debt, equity value is strongly tied to if people believe you can cover your debt.
With IOU’s, people trust you have the asset to be repaid on hand.
With collateral, people trust in liquidation mechanisms.
With pure equity, things get tricky. Mint/burn mechanics are a hoot, with powers only exceeded by their mystery.
Comparing Stress Tests
MakerDAO
Core functionality worked
Outside capital organized to sustain a floor price
Existing holders did not sell in anticipation
Obligations were restrictively generated in case of failures, and impacted by collective liquidation demand
Bancor
Core functionality failed
Outside capital remains to be organized
Can’t solve issues selling into external markets and internal markets retain debt
Existing holders are in a standoff, will they sell or will they wait for a resolution?
Obligations were programmatically generated and further impacted by individual activity.
Luna
Core functionality failed
Outside capital tried to organize but were not enough
Existing holders panic sold
Obligations were programmatically generated and further impacted by individual activity.
I think what’s interesting is we’ve seen the largest problematic outcomes occur when socialized debt is drawn and closed at the whim of individuals. The system needs a way to hedge that bet.
Further, outside capital needs to be available to back the system when necessary. This means holders must have other investments they can liquidate in emergencies to maintain system security.
Reflecting on Synthetix
One of the more interesting phenomena this draws my attention towards is Synthetix.
Here debt is socialized, and the impact of that debt is determined by individual bets, but its managed to survive. A key to its survival in my mind are
Conservative obligations relative to equity. Initially requiring an 800% C-ratio and slowly lowering that over time
Assigning individuals responsibility for hedging shares of system debt.
As we’ve seen with DAI Backstop Syndicate, attempted with Luna, and needed for Bancor, having outside capital hedging protocol equity ready to swoop in when needed is an important part of backing a system with equity. It needs outside capital to sell that equity into, and not overly dilute current holders.
Synthetix leads the way on this front in a way that is in my mind becoming pivotal to any system which collectivizes debt purely with equity.
Synths allow equity holders to collectively approve which assets can be synthesized.
Synths allow equity holders to individually increase or decrease the systems total debt in exchange for taking on a share of the obligations.
Synths allow any individual to allocate what assets the system debt is exposed to.
Every death spiral so far has had
Socialized obligations with collective exposure to the debt pool
socialized hedging with external capital
While Synthetix has remained strong due to slight changes to the model:
Socialized obligations with individual choice of exposure to the debt pool
Individualized hedging with DAO provided capital
While there is much path dependence introduced by individual allocation rebalancing, countering that with individual equity holders hedging outside of the system allows the protocol to maintain value despite heavy exposure to path dependence.
Diverse counter trading allows individual equity holders to profit by merit of out managing debt. This binds their individual ability and contribution (maintaining system backing) to their profit in a way that is participation neutral in other protocols.
Allowing the user to trade out of system debt allows individuals to choose their risk exposure levels through debt drawn and investment choice without actually needing outside capital. Whereas Bancor/Luna need individuals to protect it with external assets, Synthetix grants equity holders with capital in the form of sUSD, its debt note, which they can then save the system with that capital by resupplying that capital back to the system.
Of late, I keep coming back to the chefs kiss maneuver of binding system risk to individuals. Its a fantastic way to allow those most productive to your DAO to grow in equity share with assessments based on objective merit. Mad props.