[Music]
thank you for the introduction
um hi everyone my name is Theo um I do
research at B capital crypto and I'm
also going to talk about decentralized
exchanges um I want to kind of focus
this conversation around the liquidity
providers and this talk is really going
to be a call to action for some research
and then also product development I
think would be quite
interesting um so let's look at the
value of an LP position in an amm I'm
going to say that we have two assets one
is a numerar and the other is some asset
whatever you want with Price p valued in
terms of the numerar so you can think of
maybe the first asset is ethereum the
second asset is uh some other uh some
other token and P is the price of that
other token in terms of ethereum and uh
this amm has a set of allowable States
so we can think about it as having some
set of reserves and it says I will let
the reserves change in particular ways
so what's the value of the liquidity
provider position well if we assume
there's one Arbitrage or at least one
arbitrageur who's going to try to
extract as much value as possible from
the amm we get this minimization
function or sorry this minimization
problem which essentially says the value
of an LP position is the minimum value
uh among all the sets of allowable
Reserves reses so for what's most common
which is the constant function market
makers that set of allowable reserves is
just going to be essentially some
invariant uh evaluate the reserves that
has to be greater than or equal to some
constant so just to make this very
concrete with an example let's take a
constant product amm uh so things like
Unis swap V2 and for that we're going to
have this square root in variant if we
plug this in and kind of go through
everything we get the value of the
liquidity provider position at time T So
at t uh amount of time after this
position was opened is essentially
proportional to the square root of the
price plus a term that depends on the
fees so we look at this and there's a
few questions that one might ask or a
few kind of considerations uh first is
do I want this derivative uh do I want
this product second is what rebalancing
cost am I going to pay Arbitrage ORS to
maintain this uh position's value for me
and then third is can I hedge the price
movement let's say I just want fees I
just want fees for providing my
liquidity I don't want to be exposed to
the price movement how easy is it to
hedge this so I'll review some of the
current research which is mostly on this
first question do I want this derivative
and there the question is okay well
let's say there's something I want so
some portfolio value V that I want how
do I get to an invariant for a constant
function Market maker that gives me said
value um we see some examp examples in
practice I'm using this Loosely but uh
things like zero coupon bonds at
maturity some of the yield token pools
look kind of like this uh we also see
things like weighted portfolios so
things like balancer pools geometric
mean market makers uh some of the
Perpetual exchange lending pools look
kind of like these weighted portfolios
uh we've seen covered calls on chain and
other people build options on top of amm
and then we've also seen recent
proposals uh for things like prediction
Market amms there's a recent blog post
from Dan and CMAC on that the general
theory for the static case so for the
case where the time te doesn't matter uh
from replicating market makers papers in
uh 2021 2023 says that if that portfolio
value function is some concave
homogeneous increasing function we could
figure out the cfmm that gives us said
function however this doesn't really
tell us why some of this stuff works in
practice some of the stuff doesn't seem
to have worked in practice how do we do
it in the dynamic case that was only in
the static case and there's a few things
that I think at least are key factors
here for that uh I think the ease of
hedging the price movement essentially
if LPS desire some delta neutral
strategy so they're not taking uh risk
on the price of the underlying asset how
do they do that with an amm so they just
essentially want the exposure to the
trading fees
second is the amount extracted by
Arbitrage so if you've heard lever
thrown around or we can think of these
as rebalancing fees that you have to pay
to Arbitrage ORS how much is that and
like essentially how much leakage is
there from uh my portfolio value third
is just how useful is it to have one of
these custom portfolio value functions
like what are essentially derivatives
that I might want to have is the
portfolio value actually useful or
not so the reason that I think that
looking at this is exciting is there's
over 10 trillion dollars of Assets in
ETFs there's a lot of passive liquidity
out there clearly people are doing stuff
in kind of the financial world with this
and I think there's a lot of opportunity
to bring this liquidity on chain so if
you're interested in collaborating on
these types of questions on the research
side or on the Practical side please
reach out thank
you thank you so are there any questions
no questions raise your hand so I
can send you the
mic
okay okay all
clear H there's a question
here
yep uh you didn't talk uh uh you didn't
expand in detail but uh um can you uh is
there um a brief uh introduction about
uh what are typical ways of
hedging the directional move it it
depends on the actually I think this is
kind of a issue in a lot of amms because
for instance if you wanted to uh hedge
like say a like a constant product
position you have that square root uh
function that's your long exposure to
the asset and most places to get short
exposure are giving you a linear short
exposure and so what that means is the
amount that you need to be short that
asset is going to change as the price
changes um and that makes it very
difficult because you have to constantly
be managing this uh the short position
the hedge of the short position um which
means that it's like no no longer uh
passively providing liquidity and
there's um there's a number of blog
posts if you um message me I can send
you from kind of a few years ago that
talk about this but in terms of the
question of like how do I design a
portfolio value that is easy to hedge um
I I I think this is a pretty interesting
area of research moving forward
especially the dynamic case where the
cfmm or the aade market maker might be
changing over
time there's another question over there
in the center how do you how do you
think about concentrated liquidity
provision in particularly regards to
hedging as you described so if I'm an LP
and I want to you know only provide
liquidity within certain bands you know
how do you think about that in regards
to the rest of the formula
um those also actually do fit in kind of
the standard constant function Market
maker framework even the constant
liquidity pools um there's a there's a
paper that I wrote with a number of
colleagues called the geometry of
constant function market makers that
shows that connection um essentially the
the high level idea is one way to think
about all of these things is there's
like some set of reserves that's
allowable kind of that first slide that
I had and that set has particular
properties for let's say like the things
that you want to hold so even say a
concentrated liquidity position whether
that's like the Unis swap V3 hyperbolic
type concentrated liquidity or if it's a
linear concentrated liquidity you can
even in some ways think of an order book
as linear concentrated liquidity
positions uh because for whatever you're
selling it's just kind of a linear
amount um so this all falls into similar
framework and actually I think that's
one of the things where kind of the more
we can bring this all into a common
framework we can start to use more
interesting mathematics and then really
push forward um our ability to like
understand the stuff and build end
products happy to talk more offline
thank you for the
question there's time for one final
question over
here what do you think is like the the
right way of thinking about these
portfolios for users because crypto is
quite quite a unique place you need to
put like these two tokens in in the AML
and traditional Market making market
makers are looking for optimizing USD do
you think we are looking at maybe the WR
metrics when we are measuring this kind
of performances should we build
portfolios for this on two kind of
tokens what's your take on on that um so
sorry if I understand the question
correctly it's like what types of
portfolios should we be what what kind
of products are we trying to design I I
think that's a good question I I think
right now there's the the first kind of
step to answering that question is to
figure out you know what might we care
about and then how do we design for
those types of uh for those metrics I I
think there's a question of to like what
the metric should even be and then after
that we can kind of you know look into
what actually how to actually construct
those portfolios um but that I think the
exciting part is the design space is
pretty wide open right now and of course
we can look to finances along history
that we can look for inspiration to
thank
you well thank you very much please have
a nice round of app place for you