Hedging AMM Risk. It works

There’s a view out there that it’s very difficult to hedge your AMM exposure, and that doing so may simply lock in losses. That’s not the case, and it’s not the case in many scenarios, but I feel compelled to highlight one particular subset, where an effective hedge can be achieved with the simplest of instruments.

Firstly, let’s put the complexity to the side. You won’t need butterflies, or more bundled structures to achieve this. And you definitely won’t need to use options, it can be effectively done with the same futures and spread products available on Alpha5!

[Credit to Dmitriy Berenzon who helped fact check some AMM claims. For those of you looking to get a better grasp of AMM models, check out some of his work, including this helpful article https://medium.com/bollinger-investment-group/constant-function-market-makers-defis-zero-to-one-innovation-968f77022159]

The AMM pool

There are various types of pools. We’ll assume for now we’re dealing with a basic constant function variety, and we categorize the pools based on the assets it has as:

The ‘stable’ category where it is often USD-equivalent stablecoins (USDT/USDC, USDT/DAI, etc.).

The majors, where the likes ETH or another major currency in its ERC-20 format is paired against a stable coin (ETH/DAI, ETH/USDC etc.)

Then you have your really weird frontier-stuff, such as LINK/UMA etc.

Let’s focus on the second one, because it can produce a juicy yield, and still lends itself well to a simple hedge.

A lot of AMM pools run a constant market function, whereby the total value of the pool at anytime will be subject to the infamous x*y = k formula. When we understand and accept how this works, we come to this notion of ‘Impermanent Loss’. It’s debated, with some saying the loss is actually quite ‘permanent.’ Hmm…

Let’s see what it actually looks like

In fact, to put it into words:

If one of the assets:

went up 25%: IL = .6%

went up 50%: IL = 2%

went up 75%: IL = 3.8%

went up 100%: IL = 5.7%

(Of course this works on the way down as well, but for illustrative purposes we’ll just run with positive returns).

For you to lose 5.7% in the above, the asset must DOUBLE…Let that sink in.

Now where the intellectualism forks from the highly probable range of distributions is calling this exposure as short optionality. In theory, this is definitely true. In practice, if you treat it as such, especially to hedge, thinking the best thing to do is sell a straddle or strangle, you’re probably fucked. Why? Because as you can see from above, you really need something to move a great deal to lose any material amount of capital.

In fact, let’s run the numbers. Let’s take the price of ETH to be $350 and assume that in 1 month, ETH can go up and/or down by 50%, or have a ‘standard deviation’ of $175. That’s a lot. It would make the annualized 1-month implied volatility for ETH:

approx. [175/(SQRT(30/365)]/350 = 174%

In actuality, 1m ETH vol is usually roughly half of that, and the short-gamma position is quite small, relative to the potential yield (especially as markets mature). From a pure optionality perspective, in most market conditions, [for this subset we are looking at], you should be happy to be short this option.

The Parameters

To evaluate the hedging profile, we’ll need to figure out what our gains and liabilities are likely to be. Though it’s not perfect, it’s not a guessing game, and there are statistical models to help.

Firstly, let’s look at the yield source. There’s 2 components:

1. AMM liquidity providers will receive a fee for providing liquidity

2. They may also receive another incentive (an additional interest/savings rate or a farmed token that has some value on the open market). This isn’t always the case, but it’s definitely the bedrock for the mid-higher double-digit APYs.

The total then contributes to your APY.

Coming to a real example then, assume the following prices/parameters:


Liquidity: $50,000,000

Your contribution: $1,000,000

Your share: 2%

Fees charged in pool: 0.3%

Pool volume/month: $100,000,000

As a 2% shareholder (assuming no material move in liquidity added or removed):

You would have collected: 100,000,000*(.003)*.02 = $6,000 in 1 month

Now that alone is only an APY of 7.2% — not something for which you may stake $1m (as you take on rug-pull and broader smart contract risk)

Instead, what’s likely is that by contributing that liquidity, you will have probably gained some rights to an alternative yield, be it in the form of a farmed token with some USD value, or some passive dynamic yield (as some exchanges are now offering).

If we assume the APY to be say 40% (a reasonable number in the current market), then we know that the majority of the APY value is being driven by this extra incentive, not by the gross fees for liquidity. It also means that as the market-price of that extra incentive changes (as it does violently at times), the APY will fluctuate dramatically.

So how do we hedge and is hedging effective?

We already determined that labelling this as a short-gamma profile is likely over-estimating volatility. So if not options, then what? Perps or futures!

So, in this case, assume the $1,000,000 in contribution you made was in equal parts USDT and ETH. With ETH at a price of $400, you contributed $500,000 and 1,250 ETH to the pool.

Now, also assume you didn’t simply own 1,250 ETH, you had to buy it. There was a cost for that. Assume that was 10bps (high end of costs these days).

Once that was done, you put both into the liquidity pool.

Not being a native ETH holder, you thought about the market-risk on the ETH leg.

You notice on Alpha5, the following prices for ETH:

ETHUSDT (perp): 401.50

ETHZ20 (dec future): 403

ETHH21 (mar future): 405

You say, okay I’ve got about $500,000 worth of ETH risk here, and I don’t want it. I have some capital on Alpha5 (say $100,000), and I’m happy to lever 5:1 and manage some margin risk to hedge out my ETH exposure.

(There is a common misconception here. That you need some complex structure to hedge out the bulk of your risk. However, as we noted from the overkill with optionality, the 1-standard deviation of distributions is so vast, a pure linear instrument like a future is highly effective for more established assets).

Remember, despite the constitution of the pool at any given point in time — whether it has X or Y amount of ETH — it’s the total value of your share that you are concerned with. And that will largely emulate the price of ETH sans the IL)

So you decide to sell ETHUSDT (perp) at 403. In doing so, you pay Alpha5, 0.055%.

Your total transaction cost on the way-in thus comes to: 0.155%

Say the APY starts moving (people like this trade of yours, and think you’re onto something). Say, you come back exactly 1 month-later, and notice that the actual APY averaged throughout the month was 30%, or 2.5% for the month (because your farmed token or other incentive was highly volatile).

And let’s say that the price of ETH went up 25% during this time (as a function of popularity etc.*). Now you want to close out the entire thing, you’re just done. How did you fare?

(*The correlation between APY and price of the asset [ETH], is likely to be strong. This is to be supplemented by the correlation between the rise in ETH price and the funding rate of the perpetual swap and/or the futures premium. And by the translative property, the correlation between APY and the funding rate/futures premium is likely to be strong and positive, which has good implications for picking hedging strategies)


1. Transaction costs of purchasing ETH and hedging on Perp = .155%

2. Transaction costs of selling ETH and unwinding Perp = .155%

3. IL (relative to a HODL) on ETH after a 25% appreciation = 0.6%
(this is consistent with a ~80 vol)

4. Blockchain costs for approving/adding/removing liquidity = *approximation of .25%

5. Cost of selling any farmed token (if any) for APY purposes = .1%

Total Costs ~ 1.26%


1. APY of 30% for a monthly yield = 2.5%

2. Sitting short the perp in a rising ETH market likely leading to at least .03%/day gains = .9%

Gross Gain ~ 3.4%

Net Gain ~ 2.14%, for an APY of 25%.

However, if we want to be very specific, the $100,00 you used as collateral for the perp, also counts towards the cost of capital, so your APY is lessened by 10%

The gain from sitting short a leveraged hedge actually made more money than the IL. Few pay attention to this.

Actually, when you take note of pools in a CFMM, with large established assets on one-end with a stablecoin on the other:

1. The risk of IL is materially lower

2. If there is risk for IL, the derivatives market is likely to bid the asset through leverage (in the same direction), and in a hedge you would be shorting that leg, to earn an additional “buffer- yield”, further mitigating IL.

This of course addresses just one subset of the AMM pool-types. But it is still relevant enough to notice; there are approximations out there that drive you closer to a higher risk-free rate in the space and help you side-step the overly complex minutia.

When you get to pools where the assets have a tremendous propensity for volatility, the game changes, and it becomes necessary to emulate a long optionality position. In those instances however, it is entirely possible (if not likely), that the net APY (as a function of that instability), is high enough to warrant a strangle purchase as a hedge, as the yield accrued from the pool outweighs the premium outlay for the options (especially if you can trade your 3rd order Greeks).

The Bottom Line is this:

Hedging AMM exposure definitely can be profitable.

It is not a guarantee of locking in of a loss,

The short gamma exposure is not uniformly punitive across all assets

Sticking to known/larger currencies, allows for greater odds of realization of a strong yield.

What we saw above was a simple ‘ETH’ futures hedge. In a follow-up piece, I’ll try and highlight more advanced hedging techniques using spreads.

And remember, all of these instruments are on Alpha5 for your perusal!

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