AMO Overview

Frax v2 expands on the idea of fractional-algorithmic stability by introducing the idea of the “Algorithmic Market Operations Controller” (AMO). An AMO module is an autonomous contract(s) that enacts arbitrary  monetary policy so long as it does not change the FRAX price off its peg. This means that AMO controllers can perform open market operations algorithmically (as in the name), but they cannot arbitrarily mint FRAX out of thin air and break the peg. This keeps FRAX’s base layer stability mechanism pure and untouched, which has been the core of what makes our protocol special and inspired other smaller projects. 

Frax v1: Background
In Frax v1, there was only a single AMO, the fractional-algorithmic stability mechanism. We refer to this as the base stability mechanism. You can read about it in the Core Whitepaper. 
In Frax v1, the collateral ratio of the protocol is dynamically rebalanced based on the market price of the FRAX stablecoin. If the price of FRAX is above $1, then the collateral ratio (CR) decreases ("decollateralization"). If the price of FRAX is below $1 then the CR increases ("recollateralization"). The protocol always honors redemptions of FRAX at the $1 peg, but since the CR is dynamic, it must fund redemptions of FRAX by minting Frax Share tokens (FXS) for the remainder of the value. For example, at an 85% CR, every redeemed FRAX gives the user $.85 USDC and $.15 of minted FXS. It is a trivial implementation detail whether the protocol returns to the redeemer $.15 worth of FXS directly or atomically sells the FXS for collateral onchain to return the full $1 of value in collateral – the economic implementation is the same.   
This base mechanism can be abstracted down to the following: 
1.Decollateralize - Lower the CR by some increment xxx
 every time ttt
 if FRAX >$1   
2.Equilibrium - Don't change the CR if FRAX = $1 
3.Recollateralize - Increase the CR by some increment xxx
 every time ttt
 if FRAX <$1 
4.​FXS value accrual mechanism - burn FXS with minted unbacked FRAX, extra collateral, & fees  
At its fundamental core, the Frax Protocol is a banking algorithm that adjusts its balance sheet ratio based on the market's pricing of FRAX. The collateral ratio is simply the ratio of the protocol's capital (collateral) over its liabilities (FRAX stablecoins). The market 'votes' on what this ratio should be by selling/exiting the stablecoin if it's too low (thereby slightly pushing the price below $1) or by continuing to demand FRAX (thereby slightly pushing the price above $1). This decollateralization and recollateralization helps find an equilibrium reserve requirement for the protocol to keep a very tight peg and maximize capital efficiency of money creation. By definition, the protocol mints the exact amount of FRAX stablecoins the market demands at the exact collateral ratio the market demands for $1 FRAX. 
Frax v2: AMOs
We can therefore generalize the previous mechanism to any arbitrarily complex market operation to create a Turing-complete design space of stability mechanisms. Thus, each AMO can be thought of as a central bank money lego. Every AMO has 4 properties:
1.Decollateralize - the portion of the strategy which lowers the CR 
2.Market operations - the portion of the strategy that is run in equilibrium and doesn't change the CR
3.Recollateralize - the portion of the strategy which increases the CR 
4.​FXS1559 - a formalized accounting of the balance sheet of the AMO which defines exactly how much FXS can be burned with profits above the target CR. 
With the above framework clearly defined, it's now easy to see how Frax v1 is the simplest form of an AMO. It is essentially the base case of any possible AMO. In v1, decollateralization allows for expansion of the money supply and excess collateral to flow to burning FXS. Recollateralization mints FXS to increase the collateral ratio and lower liabilities (redemptions of FRAX).  

The base layer fractional-algorithmic mechanism is always running just like before. If FRAX price is above the peg, the CR is lowered, FRAX supply expands like usual, and AMO controllers keep running. If the CR is lowered to the point that the peg slips, the AMOs have predefined recollateralize operations which increases the CR. The system recollateralizes just like before as protocol liabilities (stablecoins) are redeemed and the CR goes up to return to the peg. This allows all AMOs to operate with input from market forces and preserve the full design specs of the v1 base case.
AMOs enable FRAX to become one of the most powerful stablecoin protocols by creating maximum flexibility and opportunity without altering the base stability mechanism that made FRAX the leader of the algorithmic stablecoin space. AMO modules open a modular design space that will allow for constant upgrades and improvements without jeopardizing design elegance, composability, or increasing technical complexity. Lastly, because AMOs are a complete "mechanism-in-a-box," anyone can propose, build, and create AMOs which can then be deployed with governance as long as they adhere to the above specifications. 

References and Resources/Links
1.​Original Announcement Post​
2.​Quick Twitter explainer thread​

Conclusion

Next - FRAX V2 - Algorithmic Market Operations (AMO)

FXS1559

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Frax v1: Background

Frax v2: AMOs