ARC: Update AMPL interest rate curve to account for over-approximation in compounded interest

Dear all,

My apologies in advance for the length of this post, but I’d like to present a different case and need to contextualize it a bit. Let’s take a step back and see what really the goal is with Ample on Aave.

We want a set of parameters that maximize borrowing/lending activity during most of the year (as with any other coin). Ample doesn’t typically spend all that much time in positive rebase, and certainly not above certain values. In other words, the time spent above 1.5 is very minor and negligible in my opinion. With the shorting activity allowed by Aave it is expected that Ample will spend more time around its target price than before. People will take loans at 10-20% above target and close those loans below target which will lead to greater stability.

As far as I can see there are four types of borrowers:

(1) Those who borrow because they actually need a loan to purchase something else (car, house, other crypto). These will sell ample, pay back after a longer amount of time.
(2) Those who borrow because they want to short sell and profit soon after.
(3) Those who borrow because they want to go long (without liquidating other assets)
(4) Those who borrow to profit from rebase arbitrage. They will try to enter and leave the market closer to rebase time.

The first three types of actors are clearly the most important ones, who help create a healthy system. The last type of actor is the most selfish actor that causes some risk.

Now two solutions are possible:

a) An astronomical high fee that disallows 100% utilization even during short periods of time as some have suggested. This still allows rebase arbitrage to happen, but only guarantees that utilization will not go to a 100% around rebase, and if it does, lenders are made whole due to the astronomical interest paid. Yet, at say 80% utilization, lenders are still losing most of the rebase, and the solution really only caters for avoiding 100% utilization. The problem, however, is that borrowers of type 1, 2 and 3 now get hurt when utilization increases by 1 or 2%. Each percentage point up now represents a huge increase in interest by hundreds or thousands of percent (somebody can do the math), so when unsuspecting new borrowers step in, the previous long term borrowers will constantly get hurt by this.
This will happen irrespective of whether we are in positive rebase or equilibrium and thus can hurt borrowers more frequently. As soon as utilization goes above 80% the lending market becomes unstable and serious borrowers (type 1) will stay away. I am afraid this will make the product unfeasible for any serious investor.

b) A lower fee, which allows 100% utilization at peak times, but is sufficiently high to keep lenders happy when they cannot withdraw their funds during certain hours or even days (worst case). At the same time, the lower max interest allows for a more predictable increase in interest rate for each percentage increase of utilization, and borrowers of type 1, 2 and 3 are less damaged every time that new borrowers arrive and utilization grows.

So even though there is no perfect solution that fits the bill in all scenarios I am convinced that solution b will cater for a more healthy lending market in the long term. Therefore I support the current proposal and think it is unwise to raise the interest any further. If anything, I am afraid that it may be too high already, but that remains to be seen. I hope the proposal goes live soon.

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Glad to read this… and I 100% agree with Peyman here on his option B. The point shouldn’t be to directly optimize to the rebase. There will be different actors with different risk appetites, not necessarily folks seeking to maximize their share % of the Ampl network. Going forward I would also like to see this

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I think 1, 2, 3 are best served by rebase being taken into account by the market.

4 is best served by rebase not being taken into account by the market.

The desire to make this market interesting by not taking rebase into account, is what is causing problems for the first 3. Not considering the impact on how you chose to setup the market around the actor most optimized to profit from that market is silly imo.

This isn’t a typical borrowing market. You have made a specific choice to ensure this is not a typical borrowing market. Why treat it like a typical borrowing market and ignore the impact of the Choice to have distinct functionality.

To me, it reads like you just want to be able to typically borrow and lend, which is not the product being built here.

@BlockEnthusiast @Peyman

I think 1, 2, 3 are best served by rebase being taken into account by the market.

1 and 3 can only work if rebases are not taken into account. For example, in the current AMPL lending market where a borrower is not exposed to rebase, if I take a loan of 10,000AMPL at a price ~$1 to purchase a car or to Long ETH. And let’s assume that after a year AMPL supply has increased by 20%. I still owe 10,000 AMPL + interest, If I buy them back at ~$1 and then repay them then I had to repay the $10,000 + interest.

In these use cases AMPL borrowing behaved in a similar way to stablecoins even though it is not pegged to $1 but oscillates around ~$1.

In the alternative you suggest in which borrowers are exposed to rebase. Now I am owed 12,000AMPL + interest which at price of ~$1 are $12,000 + interest
In that case borrowing AMPLs doesn’t make sense for 1 and 3.

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and let’s assume that after a year AMPL supply has increased by 20%. I still owe 10,000 AMPL + interest, If I buy them back at ~$1 (because sooner or later AMPL will converge to ~$1) and then pay them then I had to repay the $10,000 + interest.

Yes but you owe significant interest due to actor 4 in such a way where it never makes sense to do this over borrowing typical stables without this added risk.

Yes my alternative is they treat AMPL like a volatile asset when borrowing and shorting it. If short ETH, and borrow ETH to buy a house, same problem if ETH spikes in price. Typical behavior.

Here I am trading any expectation around AMPL MC rise with demand for borrowing AMPL in a market designed to be exploited.

Lets model 10k APR as a max and how many days it would take of paying that interest to recoup losses.

At $1.03 a borrower paying 10k% APR ( no compounding) could be in the pool for 3.48 days paying interest at that rate before lenders break even. This will result in 100% utilization for the entire time a positive rebase is expected to occur. You are welcome to remodel in APY if you prefer that model.

As a borrower in your scenariio, I would be ill advised to borrow from such a pool to pay for a car, as positive rebases will ensure I’m paying a far higher interest rate than had I just borrowed stables.

So again, who is this market really for if we can all acknowledge entity 4 has incentive to extract value from 1-3, and why would 1-3 ignore 4 when deciding to use this market?

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Yes my alternative is they treat AMPL like a volatile asset when borrowing and shorting it. If short ETH, and borrow ETH to buy a house, same problem if ETH spikes in price. Typical behavior.

Such behavior can be added to AAVE or other lending platform, one way is by listing a wrapped AMPL. For users who seek that market they can use such lending market. For Users 1 and 3 above the current lending market on AAVE is what is most suitable.

Yes but you owe significant interest due to actor 4 in such a way where it never makes sense to do this over borrowing typical stables without this added risk.

You are making the assumption the utilization will be 100% all or most of the time which is not a realistic assumption considering the proposed curve and the history of AMPL price

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You are making the assumption the utilization will be 100% all or most of the time which is not a realistic assumption considering the proposed curve.

You are making the assumption that positive rebase will occur so infrequently it will have NO EFFECT on borrower behavior, which is not a realistic assumption considering the proposed curve.

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Those pushing for this have already acknowledged utilization for even days worst case is possible, so why would that not impact the decision making of borrowers. One day of potential 10k% is worse than any stable rate imo.

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There are some benefits to borrowing ampl for type 1 borrowers (Those who borrow because they actually need a loan to purchase something).

While the high apy in positive rebase could negatively impact the borrower, the borrower also has a chance of repaying their loan at a significantly discounted rate by repaying when price is below peg. This could offset the extra apy paid from positive rebase.

The value of lending markets for elastic assets is that they act differently from floating price assets and stablecoins, we shouldn’t try to make the lending market for ampl act like that of a volatile asset’s lending market

Sorry previous chart overcharged so had deleted that post.

I have now backtested the data with the assumption of a neutral market. 10k% APR will be charged for however long it takes to break even and no longer.

Else on 0 or negative rebase assumption is 0.5% is being charged per day.

No compounding has been performed.

I feel this is reasonable, without getting overly complex but feel free to suggest alternative parameters.

While I do feel borrowers can exist in such a model, certainly not long term illiquid purchases.

The value of lending markets for elastic assets is that they act differently from floating price assets and stablecoins, we shouldn’t try to make the lending market for ampl act like that of a volatile asset’s lending market

Yes it is different and therefore I think its prudent to consider what makes elastic lending unique. Ignoring the ramifications of Short Time Borrowing actors is to launch a market purposefully blind to the effects of new features you are adding on purpose. If I was shown why such impacts are mitigated, I’d be open to hearing it, but all I’ve heard in response is “Short Timer Borrowing doesn’t impact behavior in a way that we need consideration to.”

I’m the only one I can see even trying to model this.

Edit: Just to add rebase at $1.06 is as low as ~ 30 min of max utilization to break even
Rebase at $1.56 is ~ 294 minutes of max utilization until break even.

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Thanks to everyone for sharing your views and analysis of the AMPL interest rate. Its one of the best debated subjects on the forum

It seems we have consensus around the need for the Aave UI to reflect the approximation of the interest rate compounding

With regards to the AMPL interest rate parameters, while the community seems to agree on the need for an update, there are two main views:

  1. Maximise utility for borrowers with “reasonable” borrowing costs with a lower slope 2 parameter and lower borrowing rates at high utilisation
  2. Protect liquidity for depositors to enable Aave withdrawals at any time requiring a higher slope 2 parameter and overall higher borrowing rates at high utilisation (to cover the rebasing arbitrage opportunity)

An interest rate model with 3 slopes might be able satisfy both perspectives but for the time being we need to adapt the current model

@Naguib it would be really great to have the Snapshot cover the various views of the community (showing the slope parameter but also rate projections) to gauge not only support but also preferred outcome

For example:
a) Do not change AMPL interest rate model with slope 2 = 10,000%; leading to 2.69E+43%APY at 100% utilisation
b) Change AMPL slope 2 to 750%; leading to 186,210.38% APY at 100% utilisation
c) Change AMPL slope 2 to 1,500%; leading to x% APY at 100% utilisation
d) Changel AMPL slope 2 to 2,500%; leading to x% APY at 100% utilisation
e) …

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Given the above backtesting, do you still think this market serves someone wanting to buy a car?
If no, is that the intention of the market?

I’ve shown at max utilization at only 2.47% of the year makes it so a 1 year loan faces 250% APR no compounding. With compounding its worse. Far less than near 100% of the time you felt it would require to impact the decision imo.

You are making the assumption the utilization will be 100% all or most of the time which is not a realistic assumption considering the proposed curve and the history of AMPL price

Can we acknowledge your making the unrealistic assumptions now.
Else can you give me new parameters that might better serve car guy.

More data for funzies cause I have it.


Higher max rates has the same effect on our car borrower, but lower time of the pool 100% utilized to reach neutral.

However higher rates means lenders can attack borrowers by reducing lending capacity in advance. Already at 10k% this is a risk not being discussed.

The fact that all the AMPL folks in this thread upvoted that quote tells me none of you have even considered the data or have your own data sources modeling this. And that’s not good from my perspective that all of you were under such a false impression about basic mechanics of new functions your introducing.

Edit here’s a model with the rates proposed above when backtested :

Max : 750%
% of year 32.98%

Max: 1500%
% of year 16.49%

Max: 2500%
% of year 9.89%

Max: 5000%
% of year 4.95%

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You did a good job! Let the data speaking. I didn’t thought it’s only need 2.47% of a year make the APR reaching 250%… if true, that’s really terrible…

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But in other words, 2.47% equals 9 days a year, it’s quite impossible to reach 9 days a year of full utilization… IMO, one day a year will be at most…

I’ve been a long-term AMPL supporter from the early days. One of the strongest shipping arguments and use-cases was that it will be very flexible and useful in borrow and lending markets, like Aave.

Now after almost 2 years we’re finally at the stage where we can see AMPL lending and borrowing on Aave, yet last week I had to borrow USDC instead of AMPL (I’m car guy), simply because of the new implementation.

AMPL might very well borrow like a stablecoin, but with the borrowing rates potentially going to astronimical numbers with these slopes, no sane person in the world would ever risk their collateral in Aave to take out 20,000 AMPL in order to buy a car, when they have to pay back 20,000 AMPL + a multitude of the borrowed amount of interest 5 years later.

I vividly recall the strongest argument came from the core dev team themselves, where such a transaction was highlighted, it being thus vastly superior to Bitcoin in this regard. However, with this implementation, it doesn’t matter if I owe 20k AMPL + 200k interest or 1 BTC that was worth 20k back then, and is now worth 200k.

Thus, in my humble opinion, the current implementation and way forward in this current iteration completely defeats the core use case and purpose of the AMPL token, and it can no longer sustain this argument for being a useful asset class in lending and borrowing markets for everyday users, and instead be the same highly volatile dynamite it has been since it’s inception for a different group of investors & users.

It is a stable contract, but with an undisclosed small print for new borrowers that they might very well wreck and completely liquidate themselves borrowing from Aave within days, if unlucky.

Not saying this is necessarily a bad thing, but the whole mission statement of Ampleforth would and will need to change if this does not get addressed in the coming months.

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@BlockEnthusiast @Shubiwubi

I disagree with this being framed as a black and white issue (bad for lenders or bad for borrowers). No one is forcing anyone to borrow or lend. The goal is to try to design a healthy market where the most actors can come in participate in a meaningful way.

I also don’t think this is going to be the one and only AMPL pool. This is a AMPL pool with a certain risk-return trade off. There will be others with different trade offs in the future. There will be ways to borrow AMPL with a stable interest rate.

I think what you are pointing out is a broad issue with all variable rate lending pools. APYs of other pools have been high for periods of days, thus affecting longer term borrowers. Longer term borrowers who prefer variable rate loans over stable rate ones sign up for the risk.

I do agree that in the case of AMPL there will be a lot of fluctuation in interest rates in the early stages and that coupled with the higher ceiling will make longer time frame borrowing prohibitive. I also agree that it’s unrealistic to think AMPL will be strictly as good or better than borrowing stable coins in all scenarios on day one.

However it is important to note, the market has a mix of borrowers who want to borrow over a wide spectrum of time frames. When AMPL’s price and the pool interest rate is stable in short time frames (hours/days), one could imagine pragmatic borrowers to choose AMPL over stables if the interest rates are appealing. Maybe that’s the only kind of borrower we need to be looking to attract in the early stages and thats completely fine IMO. Considering the size of the DeFi stable coin lending market I’m pretty sure that population is quite significant.

The big picture here is AMPLs utility as a denomination asset does feedback into the protocol and fundamentally changes the movement pattern of AMPL.With more MC stability the borrower market will get safer over time. It’s just unreasonable to expect it to happen in the early stages.

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Been following along here closely and I have a few thoughts and would ultimately like to propose to “keep 10,000%” as the top end, but to “keep” it as it should have been working, ie true fee is 10,000%. I think the original intention works and is fair balance. Logics:

  • A jump to 182k% is too much too soon: We havent seen it “working” or “broken/stuck” (people locked in for days on end) at 10k% (the lock in was at 38% which was of course too low).
  • 182k% is too volatile: I think 182k% will be too volatile as it jumps 10s of 1000s of %s in minutes - especially around rebase - and varies from 500% to 182k% and everything in between - going from 98-99% utilised is just a HUGE jump of 10s of 1000s of %s. This makes ampl UNPREDICTABLE, it goes AGAINST one of the principles, or things that ampl is KNOWN for - that every day, at the same time there is the rebase, we know when it is and what it will be and it creates certainty, confidence, and results in trades around it. Fluctuating apy in the 10s of 1000% of % is too much and makes things unpredictable, could flash liquidate people who borrow, puts extra risk on the other side - it *might be what’s needed ultimately but I think we need to SEE It at 10k% , and I think 10k% can work and is enough.;
  • “Lock in argument”: Lenders will not get “locked in” in it as badly as we fear. We are already seeing trades in and out around rebase - there will be higher utilisation near rebase and paybacks afterwards. Paybacks will need to occur due to profit being high and worry of liquidation. Paybacks will occur constantly as every trader has different risk ratios, profit targets, expectations. People will also borrow the ampl to SHORT it so it might not be sky high 10k locked interest forever, and as it gets shorted to come back to $1 then again Paybacks. Also at a 10x higher marketcap, when/if there is $2billion in tvl in aave then there is room for most actors to get in and out, the lockins are a product of smaller marketcap and should mitigate at higher caps.
  • “10k% is not enough argument”: Yes this is MUCH less than the rebase when it is positive, but not everyone wants to spot long hold an intense ampl position. People have different risk profiles, some “institutions” or just professionally managed funds/”farms” just have ROI targets - 10,000% roi is a LOT. There are other ways that a 10,000% lender can retain exposure to positive rebase even - simply buying/holding 100k ampl say, but only lending out 20k of it for the 10k% apy and keeping the rest as spot. This is not black and white, and already we have seen some fair deposits at low APY, 10k% is a lot higher and will get more tvl , and it being high and even “locked in” at 10k% will attract more people into the pool. It will become known/expected that a risk of this could be being locked in for days (not months, I don’t think it is as bad as this)
  • “Expansions and lockins will be cyclical”: I expect lockins and expansion phases to be cyclical - there might be semi lockins where large players can’t get in or out (but as mentioned above periods around rebase where liquidity comes and goes and smaller entrants can get in), but I think this will last days or a week at the most - not a scenario where the lender is locked in for months on end - this would be TOO big a supply increase and traders will earn profit and take profit and pay back their loans along the way, this is just 1; human nature, or just an extension of the rebase itself - rebasers earn profit and take profit and it brings ampl back to peg - ampl has not been infinitely rising and neither will it with lending now.

Ultimately. TLDR: It is a 3 way balance between:

  1. Giving enough apy that lenders don’t get locked in [a) I don’t think this is as bad as people are worrying , and b) if it is 10k% locked 24.7 and there ARE lockins then at least this is KNOWN, we will get historical data and models to work from like “ok over the last 3 months ampl has had 1 explosive upcycle week each month where lenders were locked in - so we as a fund/lender should consider than and do X and Y to protect ourselves and/or retain ampl exposure additionally
  2. Giving enough apy volume to be fair and needed for lenders (imo 10k% is more than enough, it will bring some, which will bring others, and being stable professional lenders who will figure out their risk profile and decide if/how to retain exposure or not - but again importantly they have predictable rates to work with)
  3. Giving a fair rate so that borrowing ampl can make sense for a simple borrow to buy a car with. This I didn’t touch on above. This is tricky for sure. I believe that this is NOT POSSIBLE at all while ampl is at a lower marketcap and that we shouldnt focus on it in the short term - HOWEVER that “only 10k% is the best shot at making it closer to fair/reasonable. But this just will not work in the short term, ampl needs to grow up to be billions in marketcap. Then it can work and we wont get “lockins” when there is $2billion deep tvl and wont be so much explosive cycles where the supply 10x increases in short timeframes anymore - ampl will only borrow like a true stable coin at this higher limit and the debate on it being unable to be borrowed to buy a car with is all just assumptive that 10-182k% is the reality forever, but the explosive growth and crazy fees only happen most intensely at this lower marketcap level and become more manageable and predictable - and imo likely slower growth at higher marketcaps.

TLDR: 10k% is enough, it is a perfect amount. #10200

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Thanks @Alex_BertoG for the sum up.

Thanks everyone for reading and participating, specially @BlockEnthusiast

@BlockEnthusiast I truly appreciate the angles you are exploring but your interest rate computation formulas are incorrect. Happy to review your interest rate formula in DMs to get the numbers for the scenarios you are exploring properly, see corrected numbers below.

One day of potential 10k% is worse than any stable rate imo.

One day at 10k% from the table above is 1.3% daily and if we assume the rest of the year is at 2%. Then the total effect of the one day will be an APY of (1.013*1.02)-1= 3.326%

I’ve shown that max utilization at only 2.47% of the year makes it so a 1 year loan faces 250% APR without compounding.

at 186k% for 2.47% (9 days) of the year and 2% interest for the rest of the year will result in 22.76% APY not 250%

186k% APY equates to 2.08% daily, so for the whole year it is (1.020844^9*1.02)-1=22.81%

There is no such thing as “APR without compounding.” so don’t know what do you mean by that.

Yes but you owe significant interest due to actor 4 in such a way where it never makes sense to do this over borrowing typical stables without this added risk.

If actor 4 causes 100% utilization for a minute at every single positive rebase day(as you suggested). This will only raise APY from 2% to 2.13% assuming 90 days of positive rebase a year.

It seems your arguments are pointing to that the APY is too high for 1 & 3, This ARC is suggesting lowering the APY from the current astronomically high (2.69E+43%) one due to the over-approximation explained in the original post. It is very unclear from your points if you are trying to make the case for even lower APY than this proposal or for keeping it as is in the current astronomical state.

If your intention is to make the case for a completely different behavior then the best way is to discuss that in https://forum.ampleforth.org/, Ampleforth Official or another AAVE ARC if it is ready for that stage. As that is outside the scope of an interest rate curve adjustment.

@Shubiwubi @unkindthrone13 @zhoujerryhao
Please check the corrected numbers for the scenarios above.

@danbainbridge Reasonable argument for simply correcting to true 10,000% APY, will likely add a similar option in snapshot vote options. One thing to bear in mind is as mentioned in the previous ARC that a nonlinear (referring to logistic or exponential) curve is more suitable. The reason is the linear curve 10,000% from 2% to 186,000% is so steep that it will make the APY value too sensitive to utilization ratio once it gets to the optimal utilization. And the plan was to implement that to raise the 100% utilization APY more without a curve that’s too sensitive to utilization. The over-approximation in a way made that possible without implementing a new InterestStrategy contract. And thus raising the max from 10,000% to 186,210% significantly reduces the concern for being stuck at 100% utilization while avoiding extreme sensitivity to utilization.

Stay tuned for the snapshot vote!

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When is it expected to start?

Your free to review the data and have at. Your numbers are not correct because you have numerous false assumptions. Feel free to DM me to go over privately if you’d like and I can walk you through. I’m fine posting here personally.

As it stands, you are proposing APY’s with no reference to impact, so I don’t know how anyone in here can be expected to make an informed choice. Seems more, pick a number that feels good and figure out your own impact. (Thus my actions)

I’d like to state again, I’m using APR. I don’t know the frequency of compounding and haven’t gone about calculating it. If you do, maybe you would like to put out numbers to your liking. This is how I put out numbers.

Ok so lets return again to the discussion now that we’ve had that out of the way.

__

Let me contextualize what we can learn from knowing rebase earned and using APR despite being aware that compounding will reduce time:

  • it will accurately reflect the targeted amount to be paid to achieve equilibrium.
  • it will project a greater amount of time to reach equilibrium than is necessary.

But here we have a few things going for us.

  • The time frame we are gauging is one year.
  • The time frame of attacking rebase < 1 day.

So i don’t care if I get time wrong, as I’m getting the daily amount needing to be paid correctly and that is the most important part which impacts our friend the car buyers choice, coming from a place as conservative as possible to appease to you. No compounding.

If actor 4 causes 100% utilization for a minute at every single positive rebase day(as you suggested). This will only raise APY from 2% to 2.13% assuming 90 days of positive rebase a year.

We’ve moved on from the debate from this. Keep up.

Actor 4 causes 100% utilization for as long as needed to match rebase. It would be 1 minute at the initial rates I provided but since we are capping rates, it floats outward for a longer period until equilibrium is reached.

Last charts posted demonstrated increasing max rate reduces time at max utilization, but does not affect the total amount charged.

It seems your arguments are pointing to that the APY is too high for 1 & 3, This ARC is suggesting lowering the APY from the current astronomically high (2.69E+43%) one due to the over-approximation explained in the original post.

My point is that interest will be to high for actors 1-3 due to actor 4 because actor 4 will make real amount charged equal to that as rebase gained regardless of max interest rate.

So 1-3 are actually invested not in a stable borrow within a price peg channel, but have abstract exposure to positive rebase, and negative rebase acts reduce the likelyhood they can sell low on a crash.

Thus rebase means Debt has exposure to volatile gains, but reduced exposure to volatile losses.

Net worse for actors 1-3 than borrowing AMPL without the fancy rebase takes.

And while actor 4 wins out, its still not a good product for them. Thus not a good product for anybody.

It is very unclear from your points if you are trying to make the case for even lower APY than this proposal or for keeping it as is in the current astronomical state.

My initial point was that 10k APY does not match interest needed to reach equilibrium. This pushed us to the understanding that it will reach equilibrium by pushing outward to slim margins. What’s that affect on borrowers. Very high realized costs. Thus the conversation shifted towards borrowers. We were given 4 types of borrowers,

This market seems intended for types 1-3, but we can show 4 wins while 1-3 are negatively affected.

I think its important to note an APY’s effect on time at 100% utilization since my current work has shown rates impact time but not amount paid.

If your intention is to make the case for a completely different behavior then the best way is to discuss that in https://forum.ampleforth.org/ , Ampleforth Official or another AAVE ARC if it is ready for that stage. As that is outside the scope of an interest rate curve adjustment.

My intention is to make the case that we are picking interest rates blind with no visibility into how they will affect the market, and as proposers, you have a responsibility to consider the impact of your discussions and make sure voters can make informed decisions.

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