foreign
[Music]
and today I want to talk about some of
the design work we did for our stable
coin that's called gyroscope and there's
a joint work with my co-founder Arya
clagasmond
so imagine you want to build a stable
coin
so you have a you have a cryptocurrency
and you want to keep it stable and in
some senses it's always going to look
like this you have some kind of reserve
of assets
and then people can mint and redeem
coins against that assets
um and that's going to stabilize the
price right if the price is too high
they can
um they can meet new coins if the price
is too low they can redeem coins it's
going to stabilize the market price
um and we call the primary Market
mechanism excuse me the primary Market
mechanism the thing that grants access
to these assets and that intermediates
between
mintus and redeemers which are basically
Upchurch and the asset Reserve
um now what are these assets well that
depends on your design
um it could be many different things in
a sanyaraj shared design
it could be it's basically an equity
share in a sense
for something like a basis design it's
something like a bond and in a reserve
back design at some portfolio of other
assets and by the way this is a design
we are using for gyroscope it's reserved
backed
um
now there are different situations we
need to look at
um the kind of boring case is when the
system is fully collateralized and all
the assets are perfectly liquid because
then this is just basically a pricing
problem price the reserve assets
um and the somewhat more tricky case is
the system might be 100 collateralized
but not all of these assets might be
liquid so you cannot necessarily pay
them out when people redeem
um and then there's the crisis situation
where the system actually becomes under
collateralized and then you need to
decide what to do and my talk is going
to be about the design of this component
that basically designs what to do in
such a situation
um
what we are implementing for gyroscope
is a reserve of only liquid assets so we
are not really considering this case but
it would be a maybe straightforward
extension of what we're doing
so let's look at some examples of this
um if you look at die
you have the PSM or plexibility
mechanism and it basically looks like
this that your reserve almost only
consists of usdc and this is what people
sometimes say that dye has become or is
going in the direction of wrapped usdc
um
the the numbers are like 60 or like the
PSM usdc then you have another 20 of LP
shares against usdc and of course in
that situation
um something you need to ask is are
there many risks associated with that so
for usdc for example there could be some
regulatory risk which may amount to
counterparty risk censorship risk and so
on
um kind of the goal of gyroscope was to
build something like a PSM 2.0
so how might you improve on this design
and I think there are like two ways the
first thing is you may want to diversify
your reserves you may not want to hold
only usdc
and the second thing is to implement
something like a programmatic risk
control that reacts autonomously to
market conditions so that that kind of
can be seen in two parts the first one
is if you have indicted different PSM
vaults are independent
um but you probably want to coordinate
them somehow to react in the same way to
Market strategies
and the other one is
um to price the stable coin depending on
market conditions especially when the
system should the system become under
reserved
and this is kind of where we're going
so kind of to to build such a system
there are like many different challenges
and I just want to give you like the
um the super quick overview
um basically we want picture right so we
have a reserve that consists of
different asset classes that are
probably structured in some way
and then you need to answer several
questions like which of these which
assets should that be which risks are
these exposed to how to structure the
whole thing so that the risks are
somehow contained
um how do you generate details on the
whole structure you probably want to
price these things with oracles and so
on these are all things I'm not going to
talk about but questions we still had to
answer for gyroscope and today I want to
answer
um this mechanism basically the question
is someone comes to your system the
system may be under reserved or illiquid
to some degree they want to redeem a
stable coin what is the amount of assets
you offer them
um and to do that we introduce a more
General tool which is what we call the
Redemption curve and this is a general
tool to analyze any stable coil design
basically
um so the Redemption curve is falling
curve you have two axes on one axis you
have the Redemption level which is
basically the amount of stable coins
that are getting redeemed and on the
other axis you have the Redemption price
that the mechanism offers to the
Redeemer and now we assume now we look
at what happens when people redeem more
and more in market conditions don't
change for the beginning so nothing
happens no prices change but people just
redeem more and more and ideally of
course what you want is this curve you
can always redeem at the dollar because
then you always stabilize your pack at
exactly a dollar
um and the higher your curvature here is
the less you support the peg as more and
more people redeem
um kind of the default that is also
happening for pack fiat currency is that
you try to support the pack as long as
possible until your reserve is empty and
then you don't support it anymore
and and kind of my argument will be that
maybe this Redemption curve is not ideal
and many other Redemption curves aren't
ideal either
so um we can see kind of this this type
of curve or that type of behavior in the
in the real world or in the Fiat world
um for example the attack on the British
pound in the 90s was basically
um a continuous outflow
um from the from the British pound
basically a continuous Redemption of
pounds against other assets until the
central bank was no longer willing to
support the peg
um and then you see this this kind of
drop where some people made a lot of
money
I think the recent crash of the pound is
probably not like that
I can't say anything about that
um if we look at if we look at stable
coins
we've seen similar behaviors the Strat
is a little bit outdated but there was
this period in like 2021 where like many
creative stable coin designs were
created and many of them crashed and in
a somewhat similar way very abruptly
um
I want to look at one like design case
study which would be Fey the original
design of Fae which was also not very
successful in its original form
um and so Faye had these direct
incentives which basically means
um the the more of Peck the whole system
is the worse the price you're getting
and that if you kind of look at it leads
to a Redemption curve that is very Steep
and that looks about like this which
means that your pack is not going to be
stabilized very long and then they
removed the direct incentives and then
their Redemption curve looked much much
less steep
um and we can see kind of the effect of
these like steep Redemption curve here I
hope this is kind of visible this is
like the price of a after launch
um and it had like a like a huge uh
price drop with a lot of volatility
um I should probably talk about the the
elephant in the room or maybe not
elephant anymore
um Sunny Road shares and the way I think
about Sanyo shares is essentially
um that you redeem at one dollar but
your backing is an endogenous asset
that's basically uh very very tied into
your project itself and this can lead to
some negative feedback spirals
[Music]
um
so essentially it's the same story as
from the Fiat world before
you provide Redemption at a dollar until
the willingness of the market to buy
your senior shares is exhausted and then
you basically crash very rapidly and I
should probably show this
um
right
um
the the Supply right here has this
Supply inflation at the same moment but
it doesn't really matter because people
don't want to the amount of senior
shares people want to buy doesn't
increase
of the amount of dollars people want to
put into senior chairs I should say
um I I should point out one thing about
this particular talk
this was when I gave the first version
of this talk this was not without
precedent we had a very similar system
uh called iron you may remember which
also crashed in a very similar way so
here you have the stable coin that
crashed at the same time the endogenous
collateral crashed also
um so so that that's not good and that's
why we made gyroscope Reserve pact
um
and
the basic idea of what I want to talk
about today is maybe we should think
about the Redemption curve as a design
problem and maybe we should choose a
Redemption curve that we think is useful
and reasonable and then we go and
Implement that in our primary Market
maker
um so the the basic design is going to
look like this right you remember this
picture
and we're assuming that the assets here
are exogenous so we don't need to worry
about these feedback effects but what do
you want to do if the system is under
collateralized or illiquid
um and we have like like I want to give
you these results in three parts
um first we thought about what are
actually disadrata for a good uh
Redemption curve what do we really want
and then I'm going to show you one such
curve that satisfies the Digital Data
and then I'm gonna talk to you about how
to actually Implement that because as
you remember the Redemption curve
assumes that no Market condition changed
over time and of course that doesn't
happen in reality so this step from
picking a curve and then implementing is
is making it Dynamic and this is going
to lead to this type of dynamic bonding
curve if you want to think about it like
that
um great let's first think about what we
would ideally want of our Redemption
curve
um first thing I want to I want to note
is that probably your collateralization
should be should stay above some lower
bound your Redemption shift Redemption
curve should not exhaust your reserve if
that's at all possible and the reason
for that is to enable the system to
recover later you if you exhaust your
reserve you're basically destroying your
your system
and that's bad and then you probably
also want the Redemption price to stay
above a lower bound if that's possible
to support the peg at least to some
degree
um of course this is Trivial we usually
want our stable count to be stable at a
dollar you probably want some kind of
continuity of that curve you probably
don't want these abrupt crashes and um I
would say that the main reason for that
is uh to prevent speculation because
these kind of discontinuous crashes are
something people could speculate on very
easily and that could also lead to like
all kinds of Market upheavals
um
and and then this is like a little bit
of a bonus but you want your Redemption
curve to be easy to use so probably what
you want is
um you want the execution if you redeem
a certain amount of a certain amount of
stable coins our stable coins can be
called dials I told you for that
um you probably want that to be easy and
especially you don't want there to be an
incentive to subdivide your redemptions
and to be somehow clever about the way
how people redeem
um we have like a few bonus desiderata
that are um with respect to like several
transactions or several blocks
um you probably want your the reserve
exhaustion to take a long time unless of
course you reserve just the scratches so
the system should uh also kind of think
about what what happens what happens
tomorrow what happens when the system
runs continuously
um you should be able to regain your
pack and of course you need to implement
the whole thing on chain
um ah yes the first math equation so
before I show you how we implement this
I have to introduce this nice equation
we assume that the Redemption pressure
is computed as a Time discounted some
if you don't care about that that's
totally fine
and now I'm going to show you one
simplified design that satisfies almost
all of the desireata
and this is a simplified Redemption
curve we're not using this but it's good
for explanation so what's a curve does
is that we support
a price of one dollar so people can
redeem at a price of one dollar
um
up until a certain amount of redemption
so on this axis we have redemptions
um
and then
we are gonna drop the Redemption price
so that the Redemption price is equal to
the collateralization ratio and this is
a sustainable way of doing it so for
example if your system is 80
collateralized the Redemption price
would be 80 cents and you can just do
that indefinitely and redeem the rest of
the money and of course this has all of
the nice properties almost all of them
um you don't run out of you don't run
out of Reserves
um you can actually configure a
trade-off that exists here of course the
longer you support a pack of one dollar
the lower your eventual
collateralization is going to be but
it's something that you can choose
um exactly so so we have like the
long-term survivability of the system
um because you might actually want to do
this like this would be like the
equation
um
but of course the problem is that this
is like this ugly discontinuous jump
that I mentioned before and so what we
really do is that we introduce a linear
segment there looks like this
um where the price would first be a
dollar then it would
decrease as more and more is redeemed
and then
um
if it if it has reached a point where we
have a sustainable collateralization
ratio it would just give you that price
um and if you want to do that the mouth
to do this looks like this
um but it's like it's fine right it's
fine they're like case distinctions and
fractions but it's not that bad
and one thing you you can see here is
that governance can configure this using
some hyper parameters so you can say
what is the minimum collateralization
that I want of my system
um and this is something that governance
would set because it's actually a
meaningful parameter you can say
um what is the steepness here that I'm
willing to tolerate another parameter
and then if you solve this equation it's
going to respond autonomously to these
type of parameters
um
now this curve is beautiful
but it has a problem it's not very
useful because it doesn't reflect
reality because we assume there is a
Redemption pressure of zero
um we have some kind of initial
collateralization of the system which we
call an anchor rate or we could we label
this like ra
um
and then you start from there the curve
tells you what happens when you start at
zero Redemption pressure at the anchor
rate nothing changes in the market
to implement that
we need to live in a situation where the
market will of course change and we can
still use this curve and this is what
I'm going to talk about today
so the goal is make the whole thing
dynamic
um make it react to the current market
state
and
I'm gonna show you how to do it
hopefully in a picture
and how we do it goes as follows
I showed you this curve
and if you know your anchor
collateralization which is on this axis
and you know a certain amount of
redemption pressure
and you can go and integrate the curve
from before and it's going to tell you
what your collateralization at that
point is going to be and that's up here
um
and now if we do that for all possible
sorry anchor values we get a
three-dimensional surface
um
and
what we just discussed was if you know
this and this you can compute this but
it turns out that you can also do it in
reverse so if you know the current
collateralization of the system on this
axis and the current Redemption pressure
here which is something that you can
just observe in in real time
then you can actually compute this
initial collateralization ratio which of
course at this point is a purely it's
purely a modeling tool but it tells you
if nothing had happened in the market
and we are now at the state where should
we have started if this model was true
okay so so many complicated words here
um and so basically this theorem says
that you can reconstruct that it's a
monotonistic argument
um it's it's fine
and and so then once you have the
initial State we can offer Redemption
prices
um based on uh based on this Redemption
curve as a model
um and that's pretty convenient because
it's a way to respond to current market
conditions it's completely autonomous
governance only has to set meaningful
hyper parameters it doesn't have to do
anything in the moment
and it's it's completely predictable for
other people so everyone knows what's
going to happen so yeah this you have
this huge transparency advantage over a
system where governance would just come
in and then make a vote and of course
other Market participants have no idea
what the outcome of this vote is going
to be
now I should probably talk about
implementation because you might be
looking at the theorem and you're like
yeah this is great if you're doing pure
math
but we're not doing that at all and I'm
going to talk a little bit about
implementation
and the implementation works in two
steps the first like core idea is that
um you saw you remember the scary slide
I showed you before with like many
formulas where everyone in the room
gasped so that had a couple cases
stations in it and if you do like the
cross product of all the case
distinctions you end up with a bunch of
regions and you can partition
your space into all of these different
regions and so you may believe me that
this is possible the theorem is that you
can actually detect in which region you
are based on only the current market
state
um and then it turns out that once you
know in which region you are
um Computing like this value on this
axis is very easy it's basically solving
quadratic equations then
um and that brings us to the algorithm
so we detect the region based on the
current state we reconstruct the anchor
State we take that as a model and we
compute our Redemption amount which is
basically integrating over this exact
curve I showed you before
and then when you like are being very
careful and you count all the things you
have to do to get this is actually very
cheap you just need to do some
arithmetic a little bit square root
um right so this system has a number of
interesting properties and I'm going to
show you just just like two
um
one result that you get like very easily
is that there's no incentive to split up
redemptions and like mathematically
that's because you're Computing an
integral and you can always split up an
integral in different parts and it
doesn't matter if you compute the parts
of the whole thing
so mathematically it's not very
interesting
[Music]
um
you have a path efficiency result which
is basically that and this is like a
little bit more interesting that the
protocol state is going to improve over
time so if you implement the system your
reserve does not crash
um completely to zero
um and people just come and redeem then
your system is going to recapitalize
itself over time and of course this is
exactly what we want we want long-term
survivability of the system
and
this is what this looks like
and now I want to conclude
so if you're taking away anything from
this talk it's that you can design your
Redemption curves when you're building a
stablecon system
and this is a very attractive way to get
good properties of your system it's also
a very useful tool to compare different
stable coins and to think about if the
stable coin design is actually solid
I showed you a design for one desirable
Redemption curve and then I showed you
how to make that Dynamic and make it
react to market conditions and if you
want to kind of be be involved into how
we actually do these things we have
implemented this in gyroscopes Dynamic
stability mechanism gyroscope is our new
stable coin launches planned towards the
end of the year
um and hopefully all these properties
are going to make a gyroscope very
robust if you're interested in the paper
and you should scan this QR code and if
you want to get in touch with us you can
go here or follow us here why did you
guys choose a like a piecewise linear
approach for example and not something
that's really smooth like a sigmoid or
something like that are there nice
properties that you get out of the this
then you would not get otherwise yeah
let me just just jump back to the slide
so the
[Music]
should I give the honest answer or the
line no I'm going to get the answer so
if you're honest answer is because it's
easy to implement
um because and like the reason is that
this is linear so it's integral it's
quadratic and solving quadratic
equations is easy and solving anything
else is is hard so I have more of a
philosophical question in the last let's
say two or three centuries the tenancy
in the state-backed currencies has
always been to leave Beijing to go
toward the free voting money why do you
think that in the crypto economy we are
seeing a Resurgence of Peg money that
seem to be quite prevalent
yeah
yeah that's that's a deep question I
wasn't expecting that uh
um why why do we have a Resurgence of
packed coins
um
I think my intuition is that
people think in USD or in some other
fiat currency that is not really
represented in crypto maybe at some
point we have a crypto native currency
um that that doesn't need a pack because
it's very stable against other Fiat
currencies
but I think we're not there yet and
that's why we need to represent some
some kind of measure some kind of
numerator that people are familiar with
and that matters in people's lives yeah
let me just add a little bit to that so
uh it's a common strategy when you're
kind of like developing a new economy to
do something like a currency Peg and it
seems to work well in those situations
because people want to use a more
trusted unit of account like a dollar
and so I think that's has a large
influence here but I also just want to
note that the uh the autonomous monetary
policy that we've been developing can be
more General than just maintaining a a
currency Peg you can choose parameters
in different ways to do more arbitrary
monetary policy too
I would want to know how do you think
about once the system gets under thrust
and you you get to the Redemption price
like what would be the the mechanisms or
the incentive to because it's kind of a
uh I think there is some loss of trust
in the Market at that point
how do you how do you think about how to
regenerate a system and and getting back
to the pack
like this
yeah so that
the gyroscope design contains a number
of other uh like lines of defense and
sort of ways that uh that the reserve
could replenish over time and so
basically this monetary policy the idea
is to buy the system time so that those
other mechanisms might be able to kick
in some examples of that is basically
like reserve assets are deployed in Risk
segregated ways but they can still
potentially earn some yield and so
there's sort of a tendency to increase
collateralization over time because of
that and then there's also sort of this
idea of forward guidance from the the
the monetary policy itself like
basically the as the out level of
outflows this like time discounted sum
that Stefan was saying decreases over
time then there's upward pressure on the
peg from the reserve assets again kind
of according to this uh this policy and
then there's other mechanisms too you
can check it out in our docs and happy
to talk more after after this as well