Il y a 2 j
Happy to share the slides from my talk at the CBER CtCe Conference last week, where I explain my work over the past 3 years about how we can go from
x*y = k
to
AMMs are effectively options clearinghouses
1/33 slides
The famous x*y=k formula defines how the exchange of tokens *have* to happen in an AMM.
The state of the pool before/after any swap has to satisfy x*y = L^2
That's a pretty powerful idea: abstract away all the market making and distill it in that simple invariant.
2/33
The inventory of Liquidity providers (LPs) will also follow that invariant.
Another way to also interpret LP positions in Uniswap is by tracking their value as the price changes.
The value V(P) of a LP position follows a sqrtPrice relationship
V(P) = 2L√P
3/33
Both frameworks are equivalent but are "transforms" of one another.
Both represent the same system, just with different value tracked.
4/33
Where this gets interesting is when looking at Uniswap v3's concentrated liquidity provisioning.
Choosing a range effectively moves the invariant curve towards the origin (0,0)
And where the price range determines where the curve crosses the x- and y-axes
5/33
The value picture makes it easier to understand what's going on.
The value of the LP position shifts from being 100% ETH below the lower price, to being 100% USDC above the upper price.
Between the price range, the LP position is smoothly going from 100% ETH to 100% USDC
6/33
Again, both frameworks are equivalent.
But while the invariant approach still works, I would argue it is more cumbersome than for v2 and hides some of the simplicity away.
The payoff approach is more WYSIWYG, which makes it easier to track PnL.
7/33
One thing we haven't touched is a *third* way to interpret LP positions: in liquidity space.
Uni v2 positions have liquidity spread out at all possible prices, from 0 to infinity.
Uni v3 positions only make liquidity available inside the range.
8/33
In UniV3, adding ranged liquidity creates a payoff that looks like a SHORT PUT payoff: 100% ETH below; 100% USDC above, smooth in between.
That payoff (also the same as a covered call) should be familiar to any options trader: positive delta, short gamma, short vol.
9/33
What happens if you *short* a LP position?
ie. borrow someone's LP position, unwrap it into its token constituents, and pay it back later?
This creates a LONG PUT payoff (!)
Let's work through an example:
10/33
A user:
1. Borrows an OTM LP position when the price is 4500
2. User gets 4000 USDC
3. Price decreases to 2500, position is ITM
4. User must pay back 1 ETH
5. User buys 1ETH at 2500, keeps the 4000 difference
Profits = Strike - Price
= 4000 - 2500 USDC
= 1500 USDC
11/33
Using put-call parity, users can also create SHORT CALL and LONG CALL payoffs:
- SHORT CALL = SHORT PUT + borrowing 1ETH
- LONG CALL = LONG PUT + BUYING 1ETH
12/33
And how much would that option cost you? We're used to options being paid upfront. We can't really do that in Uniswap.
Instead, we consider the fees collected over time as the options premium.
So the longer a position stays in range, the more value it generates.
13/33
We also look at the fees collected over time for buying options, with newly purchased options costing you zero (!)
To keep everything from blowing up, we make the fee paid by buyers depend on the utilization, attaching a spread to that cost (up to to 2x the Uniswap fees)
14/33
TLDR: this is how Panoptic repurposes LP positions as options
This options framework explains why most LPs get low fees:
- Arbitrage traders compress volatility and reduce returns
- Uninformed traders increase volatility and increase returns
Trade the vol, not the price
15/33
How to trade the vol?
If LPs aren't getting paid enough for the risk they take on due to a lack of uninformed flow...
...then the rational trade would be to short LP positions to buy CHEAP options.
16/33
If the purchaser dynamically hedges their delta, that creates a delta-neutral strategy called gamma scalping.
GS happens constantly in TradFi, but it is so overcrowded it has 0 alpha left to it.
But there's still alpha onchain, and here's how GS unfolds in Panoptic
17/33
The positive convexity of a long straddle means the position will increase in value faster than the underlying.
This is true whether the price goes UP or DOWN, and the expected profit from a change in price dP is
dV = 1/2 * gamma * dP^2
18/33
And once that price move has happened, the holder of the position would normally sell some shares to make the position delta-neutral again.
If you notice, the new position still maintains a positive convexity. And repeating this for every dP move UP or DOWN yields +dV.
19/33
To visualize this, we can consider a price that round-trips back to its starting point.
Holding any non-convex instrument would result in a net profit of 0.
But due to that convexity and dynamic hedging, the holder of that position collect +dV at every price move.
20/33
Doing this continuously results in profits that increase according to the REALIZED volatility of the asset.
The more volatile the asset, the more rebalances happen per unit time, and the larger the profits (minus the slippage/hedging costs).
Free money, right?
21/33
But everything has a cost, and in that case, the cost is known exactly: the buyer of that straddle will have to pay the fees collected in Uniswap to the original seller.
22/33
For a small price move dP, the fees generated by that amount of liquidity scale like the change in the square root of the price.
fees = -feeTier * L * ∆√P
In Panoptic, the spread means the buyer could pay anywhere between 1.01x and 2x that fee per trade.
23/33
Looking at a single trade, we can show the scalp will only be profitable if the fees paid are less than the profit generated from that scalp.
Specifically, any price move that's larger than TWICE the FEE TIER will be profitable.
And larger price move = even more profits
24/33
That's great for buyers because most price action in crypto can be extremely violent.
That -15% price move in a few hours is quite directional and has no reversal. So a gamma scalper could afford to not respond rapidly because the longer they wait, the more they profit.
25/33
But in real markets, the price does not go straight up/down.
There is some price microstructure that varies between Uniswap pools, with reversals every minute.
So while a one-shot price move is a guaranteed win, scalpers may wait several trades before they rebalance.
26/33
Performing that analysis shows the expected cost scales with the IMPLIED VOLATILITY of a market.
IV is shaped by the "quality" of the order flow and what happens inside a single block: eg. sandwich attacks with 3 trades generates 3x more fees for the same price action.
27/33
Notwithstanding the details of the flow, one can summarize the profit potential for a gamma scalper as the difference between the REALIZED and IMPLIED variances.
That formula is also known as the Variance Risk Premium.
28/33
You can of course do the same analysis for short straddles = LP positions.
There, the returns also scale with the variance risk premium, and LPs want SMALL moves and lots of REVERSALS.
Options lingo can also explain LPs' woes:
IL = Gamma Risk
LVR = low IV environments
29/33
How does gamma scalping perform in real Uniswap pools?
If we look at the ETH-USDC-30bps pool, it turns out the returns are very small: the fees are marginally lower than the gamma scalping PnL
So VRP = realized - implied is close to zero.
30/33
It gets more interesting in the 5bps pool: the gamma scalping returns are MUCH larger, close to 2x the fees generated.
Why do the two pools behave so differently? It's all about price microstructure.
If you remember, a profitable trade must have dP > 2*feeTier
31/33
For the 30bps pool, that means the price must move 60 basis points, compared to only 10 basis points for the 5bps pool.
Since most uninformed trades result in <60bps of slippage, those trades will get routed to the 5bps pool and give more opportunities for rebalancing.
32/33
So routing makes the trading patterns quite boring in the 30bps and 100bps pools since most trades find a better execution in the 5bps pool.
The ETH-DAI-5bps pool gets all the DAI-related flow, which translates to long-lived price spikes which make GS even more profitable.
33/33
That was the end of my talk, I'm giving everyone that made it to that point a sneak peek at the new improvements for Panoptic v2 🤫
Panoptic's thesis:
The LP side of AMMs
*is*
an options clearinghouse.
--
Please reach out if you're interested in running those strategies on Panoptic v2, either as a vault manager or a self-directed investor.
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