Preconditions

• ETH price change: $r=1+x$

• Price of FLI $\sim\propto r^{2}$ (not proven yet)

• Price of ETH-USD LP $\propto r^{1/2}$

• Price of ETH-FLI LP $\propto r^{3/2}$

• $(1+x)^{-1/2}\sim1-\frac{1}{2}x+\frac{3}{8}x^2$

• $(1+x)^{1/2}\sim1+\frac{1}{2}x-\frac{1}{8}x^2$

• $(1+x)^{3/2}\sim1+\frac{3}{2}x+\frac{3}{8}x^2$

Case 1. LPing while keeping ETH exposure using loan

Start from 1 ETH

1. Borrow 1/4-ETH-equivalent USD using 3/4 ETH as collateral
2. LPing with ETH+USD (total 1/2 ETH)

Net value:

$\frac{3}{4}r-\frac{1}{4}+\frac{1}{2}r^{1/2}$

$\sim 1+x-\frac{1}{16}x^2$

$1+x=r$ is usual ETH exposure.

$-\frac{1}{16}x^2$ comes from Impermanent loss.

Case 2. LPing while keeping ETH exposure using FLI

Start from 1 ETH

1. Buy 1/4-ETH-equivalent USD for ETH
2. Buy 1/4-ETH-equivalent FLI for ETH
3. LPing with ETH+USD (total 1/2 ETH)
4. LPing with ETH+FLI (total 1/2 ETH)

Net value:

$\frac{1}{2}r^{1/2}+\frac{1}{2}r^{3/2}$

$\sim 1+x+\frac{1}{8}x^2$

$+\frac{1}{8}x^2$. Now it's plus sign.