# Liquidity Provider Returns

### Overview

The returns to providing liquidity on Notional over the life of a liquidity pool come from a combination of trading fees earned, changes in the value of an LP's portfolio via market moves, and interest generated on an LP's net fDai holdings through time. To evaluate potential LP returns on Notional, the first thing to understand is how an LP's PNL (profit or loss) is calculated and how an LP's portfolio changes over time as trading occurs.

### LP PNL Calculation

An LP's PNL can be calculated at any time 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.

### LP Portfolio Changes

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. To calculate the LP's PNL, we need to know the Dai-value of their fDai.

### Trading Fees

Like other AMMs, returns on the Notional AMM are driven to a large extent by trading volumes. The more trading on a given liquidity pool, the greater the amount of fees that accrue to liquidity providers. Consider the following example where an LP initiates a pool with 500K Dai and 500K fDai and then a few lenders and borrowers arrive to the pool.

The prevailing interest rate stays relatively constant, the LP's net fDai position remains roughly neutral, and the LP collects a small fee on each trade.

### Impermanent Loss

Impermanent loss refers to the loss incurred by AMM LPs when the market moves away from the prevailing 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, impermanent loss is much smaller on Notional than it is for LPs providing capital to an ETH/DAI liquidity pool, for example, because cash/fCash exchange rates are **much less volatile** than ETH/DAI exchange rates. Consider the following adverse scenario for a Notional LP - they provide liquidity at a time when the pool's prevailing interest rate is 12% and then the interest rate subsequently spikes to 29%.

It would be difficult for the LP to experience a significantly worse PNL scenario and yet this loss still translates to only** .3%** of the LP's initial 500K Dai capital. The potential for impermanent loss will vary depending on time to maturity. Longer-dated fCash tokens will offer a higher potential for impermanent loss - but will compensate LPs with higher trading fees in absolute terms. Ultimately though, the risk profile for Notional LPs is significantly more conservative than for LPs on most other AMMs.

### Interest Rate Carry

Providing liquidity on Notional comes with a twist - cash/fCash exchange rates converge to 1 as fCash approaches maturity even if no trading occurs. Consequently, 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 the previous example, the LP accrued a net position of +275,000 fDai. Consider the effect on the LP's portfolio if a week passes and no trading occurs.

The Dai-value of the LP's fDai has increased by X, and the value of the LP's net holdings increases accordingly.

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

*for short. A net lending position gives an LP positive carry and a net borrowing position gives an LP negative carry.*

**carry**Over time, an LP's carry position can change in size or flip from positive to negative. The sum total of carry earned or paid over the life of a liquidity pool may contribute a significant portion of an LP's total returns.

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