# Why does Zircon work?

In this section we’ll answer a question that many people might have about Zircon: why does it work? Why should I trust that this works? After all, so many teams tried and failed to solve impermanent loss, what makes Zircon different?

The explanation deals with options, so it can be a bit complex if you’ve never heard of it. We’ll try our best to explain all the relevant concepts.

First off, let’s define impermanent loss. There are a lot of ways you can interpret it, but the one most relevant for our purposes is in option terms:

Impermanent loss describes the loss occurring from a liquidity provider’s natural negative gamma position.

In option trading, Delta and Gamma are some of the most important “greeks” that every trader should understand deeply. Delta describes your degree of exposure to the market: how much does your portfolio change in value for each change in price of the underlying token.

Gamma describes how much your Delta changes for each change in price. So negative gamma means that your Delta decreases when the price goes up, and increases when it goes down. That’s, in a nutshell, impermanent loss — gain less when it pumps, lose more when it dumps.

If you know calculus, then all this should be familiar: Delta is the derivative of the value of your portfolio with respect to price, and Gamma is the second derivative (or it's the first derivative of Delta).

### Understanding AMMs and impermanent loss with math

The xy=k AMM offers us a very convenient way to calculate impermanent loss, since it’s an extremely easy function that defines every trade.

This formula can be rearranged to provide the value of a liquidity pool for any given price (defined in one of the assets, USD for simplicity):

$f(x) = 2\sqrt{kx}$

Where x is the price, and k is the pool’s constant (which never changes if no liquidity is added/removed).

This formula is key to impermanent loss. If the price doubles, the value of your portfolio goes up by sqrt(1+1.0) = 1.41, a 41% gain. To remove the effects of having half of the pool in USD, we can double the % change, making it an 82% gain vs. 100%.

IL is as simple as that: there are no evil arbitrage traders, toxic flow, markups or whatever fancy terminology you could come up with to explain it.

The specific way that traders interact with the pool will affect the fees it collects, and hence the k part of the equation. However, the linear changes of fees will be tiny compared to the enormous effect of a square root applied to any price change. After all, the fees you obtain also suffer impermanent loss.

Impermanent loss is just a result of the way the AMM is set up, which has the mathematical consequence that liquidity pools are o(x) (i.e. the function describing them is of lower degree than the function describing your portfolio in your wallet).

The complexity of IL arises with order-book like constructs, different types of formulas or other novel AMMs. For xy=k, it's very simple.

### How Zircon deals with impermanent loss

It’s worth mentioning that xy=k is among the least “impermanent lossy” types of AMMs you could have. Concentrated liquidity will often increase your impermanent loss, requiring active management to stay in range.

The basic idea behind Zircon's IL mitigation is simple. Instead of trying to be liable for the entire loss of a liquidity pool compared to an ideal portfolio (which grows with the square of the price change), you act on the derivative of the liquidity pool, or its delta.

In practice, this means that Zircon Pylon pools have a shared impermanent loss position. This is unlike regular AMMs, where each LP counts impermanent loss from the price at which they join the pool.

A Zircon pool can be balanced, so that nobody has impermanent loss. It can be imbalanced towards the Float side, which might suffer heavy impermanent loss during price gains. It may be imbalanced towards the Stable side, which might make them suffer impermanent loss if the Float asset goes down.

The goal of the Zircon protocol is to ensure that each side is balanced: hence it will redirect fees and rewards to the weaker side, so that new LPs come in to rebalance it, or LPs from the strong side leave.

This rebalancing action is what helps reduce impermanent loss and keep it manageable. Each time a new LP joins or exits the pool, they will change its delta. If they do so perfectly, the pool will have no IL at all. But in practice, nothing is perfect.

### What are the drawbacks?

The biggest drawback of this system is that impermanent loss is now path-dependent. So if Alice supplies liquidity when ETH is worth $10, ETH goes up to$1,000, and then it dumps back to \$10 again, Alice's position is very unlikely to be the same that she started with.

Alice could have more ETH, or she could have less — it all depends on the path that the price took, and how the different LPs adding and removing liquidity changed it.

The motto for the Pylon system is that you control your impermanent loss. The system gives you all the tools to maximize your returns by adding or removing assets at key moments.

But you’re a passive liquidity provider, you still benefit from Zircon: the actions of the active LPs will help bring down your total IL.

All of our products will be designed to benefit passive and active players alike: we're not making a DEX just so that large market makers would dominate decentralized trading as well.

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