## Intro

The experiments described below are designed to show how LP profitability is impacted by volume, fees and timing in the market. The first expirement establishes the baseline relationship between roi to fees and volume and answers the question: "what size fee creates the highest ROI for LPs?" The second experiment is intended to understand the impact of LPing when the market is in an irrational state (e.g. the fixed rate is much higher/lower than the variable rate). Essentially, we want a good rule of thumb to follow when adding liquidity.

Once we are comfortable with this initial analysis, we can use smart agents to get an idea of how fees impact rational trading given a yield source like stETH. It should help us identify at what point the fee level creates a hysteresis that starts impacting volume and value for the LP.

Ultimately it would be good to use this type of analysis to help us prioritize integrations like Flow Carbon and Fixed Borrow. For example, let's say we want to put a value on a fixed borrow integration with Morpho. We could run a version of experiment 1, where there is a slight volume bias towards shorts. We can sweep different biases that represent additional volume in the form of shorts generated from fixed rate loans on Morpho (remember, in order for a user to get a fixed rate, they have to open a short on hyperdrive). The additional short volume generated by a Fixed Rate Borrow provides an opportunity for bots to arb the rate back down and LPs will profit from the fees generated. Ideally, we could begin to quantify what these integrations could potentially be worth to LPs.

### Profitability Analysis
Configure the trading agents s.t. the market rate is rational. Assume that the yield source is steth and the smart bot knows that the variable rate will average out to 3.5%.

### Experiment 1:

Use a random agent (rob) and a smart agent (sally) to trade X% of the TVL per day and plot how profitable it is for LP (larry). The experiment will be a full factorial run matrix sweeping:

- Daily volume as % of liquidity: 1%,5%,10%
- Curve Fee: 1%, 0.5%, 0.1%

while observing the impact on ROI.

#### What did we learn?
1. LPing is profitable and predictable if the fixed rate is steady
Rule of thumb: your return goes up by 9bps for percentage point increase in

### Experiment 2:

This is identical to Experiment 1, but I want to see what happens when LP Larry adds liquidity when the fixed rate is too high/low relative to the variable rate. To perform this experiment, execute a full factorial run matrix sweeping:

- Percent of TVL traded per day: 1%,5%,10%
- Curve Fee: 1%, 0.5%, 0.1%
- Initial Fixed Rate: 2% to 5% incremented by 0.5%

while observing the impact on ROI.

#### What did we learn?

## Stylized facts