Providing Liquidity

Liquidity Providers capitalize Notional’s liquidity pools. They contribute currency and fCash to the liquidity pools and act as counterparty to the lenders and borrowers that arrive to the protocol. In exchange for their service, liquidity providers earn fees every time a lender or borrower trades between currency and fCash.

Liquidity Tokens

When a user provides liquidity to a liquidity pool, the user receives liquidity tokens. Liquidity tokens represent their proportional claim on the currency and fCash tokens in that pool.

Liquidity tokens are redeemable for these underlying assets at any time.

Depositing Liquidity

First, an LP specifies a liquidity pool and an amount of cash they wish to supply as liquidity. Then, the liquidity provider mints a pair of fCash tokens.

Then the liquidity provider deposits the cash and positive fCash into the liquidity pool and receives liquidity tokens in return.

Now the LP has liquidity tokens alongside an obligation that is offset by the positive fCash their liquidity tokens entitle them to.

Revenue Dynamics

A liquidity provider's PNL (profit or loss) gives a snapshot of the amount of money they have made or lost at any given time. The LP's PNL can be calculated as the difference between their net current holdings and their initial deposit. At inception, a liquidity provider's PNL is zero because their net current holdings equals their initial deposit.

But the liquidity provider’s PNL and net current holdings will change upon trading. Imagine that a lender has just sold Dai for Dec 1 2020 Dai and now the LP’s liquidity tokens are worth 105 Dai and 101 Dec 1 2020 Dai.

The liquidity provider now has a net fCash position. If they were to withdraw their liquidity now, they would hold an extra 5 Dai but would also be a net borrower of 4 Dai. The LP's PNL will depend on the Dai-value of -4 Dec 1 2020 Dai (in other words, the LP's PNL depends on the exchange-rate between Dai and Dec 1 2020 Dai).

Example Time Series

Action	Pool Dai	Pool fDai	Exchange Rate	Interest Rate	LP fDai Position	LP PNL (Dai)
Provide Liquidity	500,000	500,000	1.01	12.00%	0	0
Borrow	495,056	505,000	1.0102	12.28%	5,000	5
Lend	496,047	504,000	1.0102	12.22%	4,000	7
Lend	505,962	494,000	1.0097	11.66%	-6,000	19
Borrow	491,131	509,000	1.0104	12.51%	9,000	38
Borrow	486,188	514,000	1.0107	12.79%	14,000	40
Lend	510,975	489,000	1.0095	11.37%	-11,000	79

Returns Breakdown

The returns to providing liquidity on Notional come from a combination of trading fees earned and changes in the value of an LP's net holdings.

Trading Fees

Like other AMMs, returns on the Notional AMM are driven to a large extent by trading volume, total liquidity in the pool, and the fees charged on trading. The more trading on a given liquidity pool, the greater the amount of fees accrue to liquidity providers.

Position PNL

The difference between the Notional AMM and other AMMs comes in the calculation of an LP's position PNL, or what is commonly known as "impermanent loss". Impermanent loss refers to the loss incurred by LPs when the market moves away from the exchange rate at which they provided liquidity - LPs get shorter when prices go higher, and longer when prices go lower. This concept applies to Notional LPs as well. However, the effect is much smaller on Notional than it is for LPs providing capital to an ETH/DAI liquidity pool because cash/fCash exchange rates are much less volatile than ETH/DAI exchange rates.

Interest Rate Carry

Impermanent loss on Notional comes with a twist - cash/fCash exchange rates converge to 1 as fCash approaches maturity even in the absence of trading. This means that an LP with a net positive fCash position will consistently make money over time if nothing happens because the dai-value of their fCash will gradually increase. Conversely, an LP with a net negative fCash position will consistently lose money over time for the same reason.

In fact, this shouldn't be surprising. Remember that a net negative fCash position is equivalent to borrowing, and a net positive fCash position is equivalent to lending. The money that an LP earns or loses over time reflects the interest they are accruing or paying via their fCash holdings. This effect is known as interest rate carry, or just carry. A net positive fCash position results in positive carry for an LP and a net negative fCash position results in negative carry.