Automated Market Makers (AMMs) are a staple of nearly every DeFi blockchain worth mentioning. Show me a DeFi chain without an AMM and I will show you a chain that needs an AMM. Where on a centralized exchange (CEX) a Central Limit Order Book (CLOB) pairs market-makers with market-takers, an AMM is the sole market-maker for all traders. AMMs are inefficient compared with orderbooks, because each trader experiences AMM slippage. I think of slippage as a "premium" you must pay for the benefits of decentralization.

The size of the premium you pay in slippage is a function of both your trade size and the amount of liquidity in the curve. Namely for any trade the slippage premium is large for (a) large trades and (b) low liquidity in the curve.

AMMs are well-understood, and the constant-product curve above is just one of many different flavors of AMM curve. One of the coolest things I know about AMMs is that a 2012 Minecraft plugin was the first use of a constant-product curve for pricing an item.

What are Perpetual Futures?

Perpetual Futures (perps for short) are derivatives which lack an expiry date and which grant exposure to the underlying by incentivizing traders to keep the price of the derivative in-line with the underlying asset. They are designed to mimic futures contracts which are continuously rolled over, thereby never reaching expiry. At no point does the trader need to actually custody the underlying asset: one can trade BTC.USD perpetuals without buying spot Bitcoin.

Perpetual exchanges have an internal "mark" price that is distinct from the spot price of an asset. The mark price is how much a representation of the asset is trading for on the futures exchange itself. If I tank the price on a perpetual futures exchange the price of the asset on the spot market is unaffected. To incentivize traders to bring the mark price back in-line with the spot price the protocol pays a "funding rate" to traders taking a long position. If the mark price were above spot price, funding would be paid to shorts. Thereby the price of a perpetual future product roughly tracks the price of the underlying.

And one important thing to remember about perpetual futures before we dig in further is that perps are ideally zero-sum: every 1 USDC that you make from a trade is 1 USDC that another trader lost. If a trader loses too much s/he is liquidated, meaning their collateral (USDC) is sold and their position is closed forcefully. If a trader owes more than the amount of USDC that is collateralizing that position then the position is underwater and the deficit is made up by the protocol. This is termed "bad debt" and is subsidized by an insurance fund. In Perpetual Protocol's case $PERP tokens are sold to cover the debt, and other vAMM exchanges do a similar thing to cover debt.

For instance if I leverage 100 USDC 10x then I am given 1000 vUSDC. If ETH is trading at 1000 USDC then I can buy 1 vETH. Should the market move 10% to the downside then my 1 ETH is now worth only 900 vUSDC. I have lost my 100 USDC and should be liquidated to pay the traders who went short.

Generally, a 10x leveraged long position with 0 profit + loss (PnL) should be liquidated when the market moves more than 10% to the downside. In reality it will be liquidated sooner because protocols often enforce a "safety margin" as liquidations will not happen instantly. Without a safety margin the protocol risks losing more money than it can collect from an overleveraged trader and thereby risks incurring bad debt.

Virtual AMMs

AMMs work great for spot markets. Can we use an AMMs market-making ability to build on-chain perpetual futures? Yes! That's exactly what Perpetual Protocol pioneered in their v1 by using a virtual AMM (vAMM) as their market maker. The idea is the same as an AMM except that both tokens are virtual and are minted solely by the protocol itself. In the case of Perpetual Protocol (v2) traders receive vUSDC representing their notional position (notional size is margin * leverage plus any profits / losses). Traders can then swap these vUSDC for vBTC (or vETH etc) on a Uniswap v3 AMM that is instantiated by Perpetual Protocol.

What makes these vAMMs inefficient compared to a pure orderbook model as you would see on a CEX is: slippage.

Recall that for a given trade slippage is determined by exactly two things:

1. The notional size of the trade
2. The amount of liquidity in the AMM curve

If I sell into an AMM I will cause the mark price to slip above or below the spot price. The more the price slips the less USDC I receive. If ETH trades for 1000 USDC, the most efficient perpetuals market allows me to sell 1 ETH for 1000 USDC.

Unlike with traditional AMMs we can mint as much vUSDC and vBTC as we like and provide this as liquidity. By increasing liquidity in the vAMM we decrease slippage. This is one way we can artificially control vAMM slippage. Exactly how much virtual liquidity to provide is a difficult problem, however, because traders can lever their capital as much or as little as they'd like: what is "acceptable" slippage for 100,000 vUSDC may not be acceptable for only 100 vUSDC. Some systems, like Drift protocol, dynamically adjust this liquidity in an interesting twist called a dynamic virtual AMM (DAMM).

Slippage is necessary in a vAMM because without it the price of the asset in the vAMM would not move. But if liquidity is too low large trades may move the market too much. Low liquidity also allows traders to manipulate the market easily. If I have 100,000 USDC and lever this 10x to make a notional size of 1MM vUSDC, and that 1MM USDC can move a market by 10%, I could easily wipe out all other 10x leverage positions by (1) buying vBTC with vUSDC (2) liquidating all now-overleveraged positions and (3) selling my vBTC. In addition to collecting liquidation incentives I have also profited by forcing traders to close their positions, allowing me to sell my vBTC for more than what I acquired it with.

This flow could be bundled into a single transaction, thereby making it impossible to sandwich any of these steps. With 100k USDC I now have access to risk-free, guaranteed profit at the expense of 10x leveraged participants. Poor you!

Manipulation is destructive for any market, so as a decentralized perpetuals exchange running a vAMM I want to prevent this. But who's to say 100k USDC is "a lot" of USDC? I could easily be a participant with 1MM USDC or more. Because this is a risk-free yield strategy I can borrow as much USDC as I possibly can and complete this flow as many times as I want to earn a stable return on my USDC for free.

Perpetual protocol "solved" this by introducing a price TWAP and a 10% rule: if the spot price of an asset and its "mark" (virtual) price diverge by more than 10% then the spot price is used for calculating if a position is liquidatable. And sure, this reduces the profitibility of such a strategy. But to understand why this is bad consider first that positions are liquidated when they are at-risk of having bad debt. If I close a position when I am underwater, the protocol loses money. Even better, if I cause the bad debt myself then I can profit from this by draining the protocol's insurance fund.

vAMM Initial Conditions

A direct consequence of forcing perpetuals to be a zero-sum game is that, should every position be closed, the mark price will return to its initial state. So if I bootstrapped a Bitcoin perpetual swap at 5,000 USDC per BTC, and the BTC price soared to 70,000 USDC per BTC, traders exiting their long positions will need to be replaced by new longs to keep the price at 70,000 USDC per. If no fresh capital arrives and every trader closed his / her long position, the mark price will plummet back to 5,000 USDC per BTC regardless of the spot price of BTC. As stated before, the protocol will pay (out-of-pocket, mind you) a funding rate to incentivize new traders to take the long position. If this continues then the protocol will bleed its insurance fund until it is empty, at which point the protocol is insolvent.

For an asset that trends up over time this means that if you want to exit a large position in profit you must convince someone to buy your bag. This is the definition of PvP trading, and such schemes often collapse when everyone runs for the exit.

You can think of the initial conditions of a vAMM as a pin, and the mark price as a rubberband wrapped around this pin. You can stretch the mark price out quite far, but eventually either the mark price must return to the pin or the pin must be moved closer to the mark price.

Considering all of this, it is clear that traditional vAMM perps cannot "unwind" safely when the underlying asset trends up with time. DeFi perpetuals either explode violently or quietly go bankrupt. There is no safe end-of-life for a pure vAMM perpetual swap as it must accomplish the impossible task of attracting more capital indefinitely. This is why they tend to topple over when put under stress, because everyone cannot redeem without returning to initial conditions, which bankrupts the protocol.

Drift protocol had the ability to repeg the stablepoint to the current mark price but this cost is subsidized by the protocol and is not very attractive, as you're simply providing exit liquidity to traders at the expense of the protocol, which is what happens even without repegging by way of funding payments.

For more thoughts about sustainability of traditional perpetuals check out this medium post

Safe, Open, Permissionless Perpetuals

The vAMM model produces a protocol that does not pass the test of being able to wind down slowly. Using a pure orderbook model would allow a protocol to wind down safely, but unfortunately running an on-chain matching engine is computationally complex. Off-loading the matching to a "private blockchain" is no better than running a CEX orderbook as it gives protocol insiders the ability to front-run orders.

Minimizing the need to trust a central authority is key. If you don't care about "trust" then just trade perpetuals on a CEX; the beauty of blockchain is its transparency and permissionlessness, both of which are destroyed if you allow one party to match orders behind closed doors.

Designing a new, safe, stable protocol that lets traders enter and exit the market freely, exchanging futures around the current spot price, and without fear of being forcibly liquidated or "stopped out" by a whale or a market-maker is one of the interesting problems I had the pleasure of working on with the Levana team.