The formula that runs every liquidity pool.
Before you can hedge a liquidity mining position, you need to understand what is actually happening inside the pool. It is not complicated — but the consequences are.
An Automated Market Maker (AMM) is a type of exchange that uses a liquidity pool instead of an order book. There are no buyers and sellers matching prices. Instead, a mathematical formula sets the price based on the ratio of two tokens in the pool.
For the traditional AMM model used by Uniswap v2, Bybit LP, and most of the pools where yield is worth hedging, that formula is:
- x = amount of Token A in the pool
- y = amount of Token B in the pool
- k = constant that must stay the same
Whenever someone trades, the pool must keep k constant. Buy Token A from the pool and its supply drops — so to keep k the same, the supply of Token B has to go up (the buyer pays in Token B). The price of Token A rises as a mathematical consequence of its smaller supply in the pool.
A concrete example
Suppose a pool starts with 1,000 NEAR and 4,000 USDT. The entry price is $4.00 per NEAR.
k = 1,000 × 4,000 = 4,000,000
Now a trader buys 100 NEAR from the pool. The pool must end up with 900 NEAR. To keep k = 4,000,000, the USDT side must become 4,000,000 / 900 = 4,444.44. So the trader paid 444.44 USDT for 100 NEAR — an average price of $4.44 per NEAR, higher than the entry price. That price rise is called slippage, and it is the cost of trading against a curve.
Why this matters for your position
When you provide liquidity to an AMM pool, you don't deposit a fixed amount of each token — you deposit a share of the pool. That share is repriced continuously as the pool rebalances.
Concretely: if the price of NEAR falls, the pool automatically increases its NEAR holding (because traders are buying the cheaper token out of it — wait, the opposite). Let's be precise: if the market price of NEAR drops, arbitrageurs will sell NEAR into the pool until the pool's price matches the market. The pool ends up with more NEAR and less USDT. As a liquidity provider, your share of the pool now holds more of the coin that just dropped in price.
This is the core mechanic behind impermanent loss, and the exact reason why an unhedged LP position bleeds value in a downtrend — even while earning yield from trading fees.
The takeaway: an AMM is a price-taking machine. It will always follow the market, and it will always end up holding more of whichever token is currently cheaper. Understanding the curve is the first step to understanding what you actually need to hedge.
Next: how this translates into impermanent loss — with the numbers.
The primary risk of liquidity mining — in numbers.
Impermanent loss is not a bug. It is a mathematical consequence of how AMM pools rebalance themselves. Once you see the numbers, "impermanent" starts looking a lot more permanent.
When you deposit into a liquidity pool, you are committing to hold a 50/50 value split between two tokens. The AMM maintains that split for you — automatically. The problem: it maintains it by buying more of the token that just went down, and selling the token that just went up.
That is the opposite of what a rational investor would do. A rational investor sells high and buys low. An AMM pool, by design, buys low and sells low, and buys high and sells high. It is a counter-momentum machine.
The formula
For a standard x·y=k pool, impermanent loss as a function of the price ratio is:
This formula compares two outcomes: the value of your LP position at the new price, versus the value you would have had if you had simply held the two tokens in a wallet. The difference is impermanent loss.
What the numbers actually look like
| Price change | Price ratio (r) | Impermanent loss |
|---|---|---|
| +25% | 1.25 | −0.62% |
| +50% | 1.50 | −2.02% |
| −25% | 0.75 | −0.96% |
| −50% | 0.50 | −5.72% |
| −75% | 0.25 | −20.00% |
| +200% | 3.00 | −13.40% |
| −90% | 0.10 | −42.54% |
A few things stand out. First, IL is symmetric but not linear: a 50% move in either direction produces similar loss, but the loss accelerates as the move gets larger. Second, IL hurts on the way up too — a token that triples in price still costs you over 13% versus simply holding it.
Why "impermanent" is a misleading word
The term suggests that the loss disappears if the price returns to entry. Mathematically, that is correct — if the price ratio goes back to 1.0, IL goes back to 0.
In practice, that almost never happens. The token that dumped 50% rarely recovers cleanly to exactly where it started. By the time you withdraw, you are locking in whatever IL exists at that moment. And every day you stay in the pool, your hold-the-tokens alternative is accumulating or losing value independently.
The uncomfortable truth: if you exit a liquidity pool during a downtrend, you are selling at the worst time, holding more of the losing token than you started with. That's why unhedged LPs routinely underperform simply holding the same tokens — even when the pool pays 50% APR.
When does IL beat the yield?
A practical rule of thumb: at −50% price change, IL is about 5.7%. If your pool pays 60% APR and you stayed in for one month, you earned roughly 5% in yield. You are roughly break-even versus holding — after a month of risk and complexity. At −75%, you are 20% behind, and a full year of 60% APR only partially recovers that gap.
This is the calculation every serious LP does before entering a pool. It is also the calculation that makes hedging attractive: if you can neutralize IL mathematically, the yield stops being risk premium and starts being actual return.
The takeaway: impermanent loss is deterministic. Given the price path, you can calculate it exactly. That also means you can hedge it exactly — if you know how the AMM curve translates price into token exposure.
Next: how a delta-neutral short cancels the IL mechanically.
Cancel impermanent loss — with math, not luck.
If impermanent loss is deterministic, so is the hedge. A correctly sized short position offsets the LP's price exposure on every point of the curve. What you keep is the yield. What you lose is the IL risk.
The idea is simple. Your LP position holds a variable amount of the volatile token — more when the price drops, less when it rises. A short position on that same token has the opposite P&L profile. Size the short correctly, and the two cancel out as the price moves. That is what "delta-neutral" means: your total exposure to the token's price is zero.
How much of the token do you actually hold?
For an x·y=k pool, the amount of the volatile token in your position at price p is not a fixed number — it is a function of the price. The exact formula:
This derives directly from the pool invariant. If x·y = K and the pool's price is p = y/x, then solving for x gives x = √(K/p). For a single LP's share of the pool, we use a scaled constant k that represents just that share. The practical result is the same: your coin holding scales with the inverse square root of the price.
Starting position: 500 NEAR (value: $2,000, matched by $2,000 in USDT).
The position's constant: k = 500 × √4 = 1,000
So at any price p, your NEAR holding becomes 1,000 / √p:
| Price | NEAR held | USDT held | Total value | If held (no LP) |
|---|---|---|---|---|
| $2.00 | 707.1 | $1,414 | $2,828 | $3,000 |
| $3.00 | 577.4 | $1,732 | $3,464 | $3,500 |
| $4.00 | 500.0 | $2,000 | $4,000 | $4,000 |
| $5.00 | 447.2 | $2,236 | $4,472 | $4,500 |
| $6.00 | 408.2 | $2,449 | $4,899 | $5,000 |
| $8.00 | 353.6 | $2,828 | $5,657 | $6,000 |
Notice the pattern. When NEAR falls to $2, you end up holding more NEAR (707 vs 500) but the total value is only $2,828 — versus $3,000 if you had simply held 500 NEAR and $2,000 cash. That $172 gap is the impermanent loss.
The hedge: short whatever the pool gives you
At entry, the LP holds 500 NEAR. A naive short of 500 NEAR would be correct — but only at that exact price. As soon as the price moves, the LP's NEAR holding changes. A static 500 NEAR short would drift out of alignment immediately.
The correct hedge is dynamic. At every price, the short size should match the LP's coin holding:
When the pool gives you more NEAR (price down), the short increases to match. When the pool takes NEAR back (price up), the short reduces. The short and the LP holding track each other on the same curve — which is exactly what delta-neutral means: your net exposure to NEAR's price stays at zero.
What remains after the hedge
If the delta is neutralized, what does the hedged position actually earn? Three things, in order of importance:
1. Trading fees from the LP. These are paid by traders swapping through the pool and are independent of price direction. This is the primary yield.
2. Funding payments from the perpetual short. When funding rates are positive (the typical state in crypto markets), short positions receive funding. This is a second yield stream, often adding 10–20% annualized on the hedge notional.
3. Rebalancing slippage and fees, as a cost. Every time the hedge is adjusted to match the LP curve, a small cost is paid in trading fees and bid/ask spread. A well-designed rebalancing threshold minimizes this.
Net: yield minus rebalancing cost. No meaningful directional P&L on the underlying token. That is the mathematical goal of delta-neutral LP hedging.
Why most manual hedges fail
The theory is well known. The execution is where it breaks. Three reasons a manual hedge typically fails to hold delta-neutrality:
Static sizing. Opening a short equal to the entry coin count and leaving it there. This works at exactly one price. Any move and drift starts accumulating.
Discrete rebalancing. Rebalancing once a day or when "it feels off" leaves the position drifting for hours between adjustments. In a volatile market, that drift can dominate the yield.
Liquidation risk on the hedge leg. The short is on leverage. A strong upward price move shrinks margin on the short while the LP gains coin value — if the short liquidates before rebalancing, the entire hedge vanishes and the position goes long-delta at the worst possible moment.
The takeaway: delta-neutral LP hedging turns a directional bet into a yield product. The math is public; the execution is the differentiator. Continuous rebalancing, proper margin sizing, and liquidation protection are not features — they are requirements.
How TradeTechLiquidity implements this
Our hedge engine calculates k / √p for your specific LP position in real time, monitors the drift against your configured threshold, and executes rebalance trades through your exchange API. Margin safeguards close the short automatically before liquidation. You keep custody on your own exchange; we only hold trading permissions.
