# Good Pools and Bad Pools on Uniswap V3

Why are some pools good 🐶 and other pools bad 😈?

The answer comes from breaking down LP profits into:

• Price changes 📈
• Fees collected 🎟️

By comparing LPs to options, we discover parallel insights — let's explore!

### Price changes​

• ⬆️ Price up: positive return
• ⬇️ Price down: negative return
• ⤵️ Payoff determined by delta (Δ) & gamma (Γ) of LP position

Why use options terminology (Δ & Γ) for LPs? Hint: that payoff looks awfully like a short put option!

### Fees collected​

Fees collected are determined by the theta (Θ) of the LP position.

• 🕒 Θ: Rate of time decay (dV/dτ)

• 💰 dV = fees collected

• 🧊 dτ = 1 block → Θ = fees per block 🤯

• ✅ Near the money: Θ > 0

• ❌ Far the money: Θ = 0

### Implied Volatility vs. Realized Volatility​

In TradFi, options selling is more profitable when Implied Volatility (IV) > Realized Volatility (RV). Can we compare IV-RV for LPs?

Yes! But let's use fees instead of IVs since:

• Easier calculation 🧮
• Fees collected ⇔ options premia 👇
• ⬆️ options premia ⇔ ⬆️ IV

• 🐶 Good pools (green dots): lie below the line, compensated by high fees given volatility ("IV > RV")
• 😈 Bad pools (pink dots): lie above the line, not compensated enough ("IV < RV")

(Dot values are summed returns from LPing)

### How do price changes and fees affect returns?​

• ⬆️ Price → ⬆️ LP returns (since fees are always positive)
• ⬇️ Price → ⬆️ LP returns if Θ dominates
• ⬇️ Price → ⬇️ LP returns if Δ & Γ dominate

Let's define "dominance" so we can analyze pool returns! 👇

We define a metric to measure how much fees dominated LP returns:

$Θ\text{ dominance} = \frac{\text{fees}}{\text{fees } + \text{ |payoff|}}$

(fees & payoff expressed as percentages)

Meaning:

• 💪 100% Θ dominance → fees drove 100% of LP returns
• 🤕 0% Θ dominance → price movement drove 100% of LP returns

Previously, we found that LPing on ENS was highly profitable (+124%), but UNI was not (-28%). By graphing Θ dominance next to cumulative returns, we find:

• 😔 Bad days (negative returns) driven by price movement
• 🥳 Good days (positive returns) driven by fees

Breakdown of positive & negative returns confirms that good pool Θ dominance > bad pool Θ dominance:

• 😔Bad days: 28% (ENS) > 22% (UNI)
• 😊Good days: 59% (ENS) > 50% (UNI)

The good pool also had a higher proportion of good days:

• 🤩ENS: 63% (272/433)
• ☹️UNI: 55% (335/608)

• Fees: 466%
• Payoff: -371%
• Return: 95%

The bad pool's fees weren't enough to compensate (UNI):

• Fees: 309%
• Payoff: -332%
• Return: -23%

(All values are summed)

### Summary​

📣 Key Insights:

• LP = short option payoff
• Δ, Γ, and Θ affect LP returns
• LPs compensated when IV > RV
• Good days/pools driven more by fees than by price changes

Disclaimer:

• 📢 None of this should be taken as financial advice.
• ⚠️ Past performance is no guarantee of future results!