Appendix 3

Impermanent Loss explained

Impermanent Loss (IL) originates from within the crypto sub ecosystems classified as liquidity provisioning and liquidity pools, as a service to crypto DEXs. And at its core revolves around the prevailing market price of a single asset and the price of that same asset as part of a liquidity pool and involves the concept of Arbitrage. Liquidity pools enable DEX users to trade coins and tokens almost instantaneously across blockchains because liquidity providers make it possible.

Arbitrage is critical to maintaining parity of the price of assets in a liquidity pool and the prevailing market price of that same asset on its own as determined by DEX Aggregators (these protocols collect information on all DEX order books and compile a prevailing market price of an asset).

Liquidity pools are structured in trading pairs and investors contribute pairs of coins in a 1:1 ratio to the pool, for example and investment of $200 000 in the following quantities:

Liquidity Pool of ETH/USDC pair				USD Val of each component	Ratio
100 ETH	@	$1000	=	$100 000	50%
100 000 USDC	@	$1	=	$100 000	50%
Total				$200 000	100%

DEXs are structured as Constant Product Automated Market Makers (AMMs) and how they function creates an arbitrage event when price changes happen in the open market

Using our example above, let’s assume that the prevailing price from DEX Aggregators of ETH rises to $1100. Remember that the price of ETH inside our liquidity pool is still $1000. This typically triggers an Arbitrage event where traders will be wanting to buy ETH @ $1000 out of our liquidity pool and resell the same ETH at the prevailing market price, thereby benefiting from price differences of the same asset in different marketplaces.

At this point awareness is drawn to the engine driving AMMs and the mathematics that power these engines. AMM algorithms use arbitrage to maintain parity between asset prices across DEXs. Also when traders buy assets out of a pool each individual unit bought is subsequently more expensive than the previous unit until the price of the asset in the liquidity pool is equal to the prevailing market price of the asset.

In our example above, with the market price of ETH @ $1100 and our liquidity pool price of ETH @ $1000, traders will buy ETH from our pool using USDC (the other part of the ETH/USDC trading pair) meaning that the proportion of ETH: USDC will change by the amount of USDC put into the pool to release an algorithmically calculated amount of ETH.

We will be using the constant product formula, employed by liquidity pools to maintain the 50:50 ratio of value (calculated at prevailing market prices of assets). The formula is stated as follows:

x	*	y	=	K

Where : x = quantity of Token A

: y = quantity of Token B

: K = constant to keep Token weights in balance

In our scenario, our metrics look as follows:

ETH (x)	*	USDC (y)	=	K
100	*	100 000	=	10 000 000

This means that x and y are variable and will change, however as their proportions change the value will remain the same.

For illustration purposes and taking our assumptions into consideration lets say a trader was able to purchase roughly 5 ETH for an average price of $1050 (total USDC spent on ETH = $4 200 before the ETH price in the pool was equal to the ETH market price @ $1100).

After applying the constant product formula we are able to determine our new coin proportions, market price and value as follows:

Liquidity Pool of ETH/USDC pair				USD Val of each component	Ratio
94.728 ETH	@	$1100	=	$104 200	50%
104 200 USDC	@	$1	=	$104 200	50%
Total				$208 400	100%

From the above table we see that the liquidity pool has made a profit of $8 400 with a yield generated of:

ETH Val	+	USDC Val	=	Total Liq pool Val	-	Original Val of pool	/		*		=	Yield Generated %
$104 200	+	$104 200	=	($208 400	-	$200 000)	/	$200 000	*	100	=	4.2%

This is actually the point at which IL becomes evident. Since, had the investor maintained his holdings as follows:

100 ETH

100 000 USDC

His asset value would be as follows:

Asset	@	Mkt price	=	Total USD Val
100 ETH	@	$1 100	=	$110 000
100 000 USDC	@	$1	=	$100 000
Total				$210 000

The 2 calculations above illustrate IL and the scenarios that it could result from.

Impermanent Loss calculation

Single Assets Combined Val	-	Liquidity pool Val	=	Impermanent Loss
$210 000	-	$208 400	=	$1 600

Impermanent loss is classified as such because the loss only becomes permanent once the investor sells his holdings in the pool.

The most significant risk metric for impermanent loss whilst providing liquidity is if the trading pair chosen contains 2 assets with high volatility. The rule when deciding on risk tolerance and potential investment is that the more closely correlated the pair of assets, the lower the probability of IL.