Thread by @tarunchitra

⚠️ New week, New Paper

Q: What was the best way to profit market volatility in DeFi over the last year?

A: @JupiterExchange's JLP pool

How does this pool work? Is this yield real? Is it safe?

@theo_diamandis, @RiskRinger, @perpsjesus, @ns_gauntlet, and I explain!

@weremeow @sssionggg Paper: arxiv.org/abs/2502.06028

Our journey begins by zooming out and asking, "why are centralized perpetuals exchanges so much more successful than decentralized ones?"

One aspect overlooked by 2020s era perps protocols is that centralized exchanges offer lending facilities to market makers and large traders

Such lending facilities:
- Improve capital efficiency for trading ✅
- Can lead to collusion between the exchange and particular market makers if they get preferential terms (e.g. Alameda) ❌

BUT DeFi lending protocols ameliorate the risk of this!

https://x.com/tarunchitra/status/1591087700379324417

Q: Can DeFi lending primitives build a more capital efficient perpetuals exchange?

First stab was @GMX_IO v1, which introduced the GLP pool to facilitate perps trades

One can view GLP as an "application-specific lending protocol": it lends pool assets to perpetuals traders

The flow is the following:
- Users who want yield deposit multiple assets into the pool
- Their assets are lent out to collateralize perps positions

e.g. Perps user opens up a 5x long position; user provides 1x collateral and the pool lends out the remaining 4x (+ charges a fee)

The loan is closed when either:
1. User pays back accrued fees and is returned their collateral
2. User is liquidated, returning pool's assets back

Unlike other DeFi lending, there is no discount/bonus paid to liquidate the position — collateral simply goes back to the pool

This is the sense that these loans are "application-specific" — lending protocol knows exactly *where* the borrowed assets are and can reclaim *exactly* what was lent out upon liquidation

Intuition: Risk/return of such loans should be way better than other forms of DeFi lending

TradFi analog: 'demand loans' to a market maker — often brokers or banks will do short-term loans to market makers so that they don't have to close open positions to quote on new markets (but are callable)

That's why we call such pools 'Perpetual Demand Lending Pools' (PDLPs)

How big are these markets?

The overall PDLP market size is ~$2.5B and has generated ~$897.93M in fees over the last 12 months, creating over 35%+ yields sustainably from trading fees (beating Bitcoin and Ethereum basis!)

@dYdX @HyperliquidX @JupiterExchange @GMX_IO Our paper does a few things:
1. Formalizes PDLPs in a manner general enough to include GLP, JLP, and @HyperliquidX's HLP, @dydx's MegaVault
2. What is funding rate arb in PDLPs?
2. Constructs a target-weight mechanism that describes how @GMX_IO/ @JupiterExchange's pool rebalance

3. Describes optimal arbitrage between the perps exchange and PDLP pool and shows that with high enough fees, E[PNL] > 0 for LPs and perpetuals traders
4. Describes LP losses in the pool that are analogous to @ciamac, et. al's LVR and shows that it is bounded in a way different to CFMMs

5. Lessened LP losses in PDLPs implies that pool shares are good collateral (c.f. @KaminoFinance / @DriftProtocol vaults) to borrow against (esp. when compared to CFMM shares)
6. Proves that these pools are easy to delta hedge via std. portfolio optimization

While there's a lot, let's go through them individually

== Formalizing PDLPs ==
PDLP users (like CFMMs) deposit 1+ assets in order to earn yield

PDLPs aim to stay near a target portfolio π* and provide creation-redemption incentives for arbitrageurs to keep the portfolio near the target

Depositors receive shares upon deposit

In HLP, the target portfolio is dynamically updated by an off-chain manager

In GLP and JLP, target portfolios are updated via creation-redemption arbitrage:
- Share Price < pool NAV: buy shares and redeem for pool assets
- Share Price > pool NAV: create shares from pool assets

You can see how well the pool share price tracks underlying asset price by looking at the difference between the market and "virtual" (i.e. the price if the NAV were distributed to the shares pro-rata) prices

$TRUMP caused a dislocation (see it?)

dashboards.gauntlet.xyz/protocols/jupi…

== Funding Rate Arb ==
Can both LPs + perps traders be profitable? Surprisingly, yes! We formulate perpetuals arbitrage where a perpetuals trader tries to close a funding rate gap while generating PDLP fees

We show they both can be simultaneously profitable at high enough fees!

== Optimal Arbitrage + Weights ==
If virtual and market prices deviate, what is the **optimal** arbitrage to choose?

Unlike CFMMs like Uniswap, PDLPs allow users to redeem many different portfolios provided they satisfy some weak constraints — what's the optimal one to choose?

What does 'optimal' mean?

GLP + JLP define π* via a target weight — e.g., if the pool contains (SOL, WETH, USDC), the target weight might be (25%, 50%, 25%)

PDLP provides "discounts" if you move the pool closer to the target weights — arbitrageur wants to maximize the discount

How does the discount work?

Suppose a PDLP has 100 outstanding shares and when the pool moves closer to the target weight, I receive an 5% discount

This means if I take 20 shares worth of pool assets and try to mint 20 shares, I will receive 21 shares (the 5% bonus)

How do I perform the arbitrage?

There are many portfolios I could use to maximize the discount — all USDC, all SOL, 1/2 SOL + 1/2 USDC — how should I pick the right one?

View the discount as a function of the portfolio → pair of optimization problems for creation, redemption

We show that these optimization problems can be solved approximately using, e.g. gradient descent, *even if you don't know the discount function f*

This explains why these pools have (generally) had low tracking error even though arbitrageurs may not have known the optimal arb!

An aside: If you look at the original @GMX_IO V1 code base, you can see that they had the right intuition in a comment about using discounts as a PID-like method to staying near a target weight

This is weirdly the key to approximate the optimal arb

github.com/gmx-io/gmx-con…

== Delta Hedging ==
There has been much written about how JLP seems to have "low delta" (e.g. low correlation to the assets held) which has led to the proliferation of leveraged and hedged JLP on @KaminoFinance and @DriftProtocol

How true is this?

https://x.com/y2kappa/status/1878853034035552612

We study this and show two things:
1. PDLPs have a bounded amount of extra delta rel. to the assets; this decreases as borrow fees go up
2. PDLPs are easy to delta hedge via Markowitz, improving the Sharpe ratio under broad conditions

Again, market intuition was (mainly) right!

The second result, in particular, is distinct from CFMMs — while there have been many attempts to hedge LVR/impermanent loss in CFMMs, none have been anywhere near as successful as delta-hedged JLP

Our results help explain when and why this is true for PDLPs but not CFMMs

The delta hedging result can be extended to study a question inspired by @GMX_IO V1 vs. V2: When should you use multiple pools vs. one big pool?

It turns out there's a nice Schur Complement condition for when to split pools (also: live V2 pools aren't optimally split)

tl;dr / recap:
1. PDLPs share similarities with CFMMs — creation-redemption arb and LVR — but they have low "wrong way" risk (they earn fees correlated to the direction of trade vs. CFMMs)
2. Allows us to bound their risk, partially explaining why JLP trades are so popular

But this opens a lot of new problems:
- How do we choose an optimal discount function F?
- How do we merge HLP-style pools (with single operators) with algorithmic weight mechanisms?
- Are there other types of application-specific loans in DeFi that could utilize this mechanism?

Thanks go out to a lot of folks for comments and feedback!