LESSON 9 · NOTES · PRACTICAL TRACK, LESSON 1
What Arbitrage Really Is: Delta Neutrality
Arbitrage comes with or without directional risk. We’ll walk through the numbers to show how two opposite positions remove that risk, where the profit comes from then, and what neutrality does not protect you from.
Three takeaways
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Arbitrage can carry directional risk or none at all. Spot-spot with a transfer carries it: while the transfer is in progress, you are long. Two opposite positions held at the same time carry none: that is delta neutrality.
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Zero delta: price direction doesn’t matter. Up or down, the result is the same, as long as both legs are closed together. Along the way, the gap between the legs can drift.
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Neutrality removes directional risk, but not every risk. The legs must be equal in number of coins, not in dollars; leg divergence, liquidation of one leg, ADL and exchange risk all remain.
1. Arbitrage with directional risk
You buy on exchange A, transfer, and sell on exchange B. While the coin is in transit, you are holding it — you are long. If the price drops 2%, a 2% spread is gone (lesson 7, the “time” cost). This is still arbitrage, one of the strategies, but with directional risk: while you are transferring, you are a trader. This lesson is about removing that directional risk.
2. Delta
Delta is how much your result changes when the price moves by one unit. Buy 1 coin — delta is +1: price +$1, you +$1. Open a short on 1 coin — delta is −1. Hold both positions at once on the same number of coins: +1 and −1 = 0. Zero delta means that wherever the price goes, your result does not depend on it. That is what delta neutrality means.
3. Checking it with numbers
A hypothetical coin (the math on bitcoin is the same, the numbers are just longer): spot 10.00, perp 10.02. We buy 100 coins on spot and short 100 on the perp. The gap at entry is $2. No fees.
| Scenario | Long spot | Short perp | Total |
|---|---|---|---|
| Price → 9.00 (−10%) | − 100 | + 102 | + $2 |
| Price → 11.00 (+10%) | + 100 | − 98 | + $2 |
Up or down, the outcome is the same: the gap between the legs at entry. With one caveat: this holds if both legs are closed together. Along the way, the gap between spot and perp can swing either way — how to gauge that is covered in the practical track.
4. So where does the profit come from
$2 on a thousand invested is 0.2%. You can’t live on that. In delta-neutral arbitrage, profit comes from two sources:
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Funding. Every few hours the perp pays one side to stay close to spot (lesson 4). If you are on the side being paid, that is income for as long as you hold the position. More on this in the following lessons.
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The gap between the legs. On liquid coins like bitcoin it is pennies; on others it can be several percent. Which coins and how to find them is covered in the practical track.
Delta neutrality is not income in itself. It is a way to remove directional risk so you can collect profit from other sources without guessing.
5. Trader vs. arbitrageur
A trader holds one position — the result depends on direction. An arbitrageur holds two opposite positions — the result depends on the difference between them. Neither better nor worse: just different work.
6. What zero delta does not protect you from
- The legs are not equal in number of coins — delta is not zero. Count in coins, not dollars: $1,000 on spot at 10.00 is 100 coins, $1,000 on the perp at 10.02 is 99.8. Not equal. The right way: 100 and 100.
A caveat: this applies to spreads from fractions of a percent up to a couple of percent. With spreads in the tens of percent, equal coin amounts give a fixed result when the spread converges, but while the spread persists, the position is effectively short by its size; in such cases it sometimes makes sense to size the legs equally in dollars — there is a separate lesson on this in the practical track.
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The gap between the legs widened further. The outcome at close is the same, but along the way it puts pressure on your margin. How to estimate how far the legs can diverge is covered in the practical track.
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One leg gets liquidated — the other is left naked. You are a trader again, not by choice (lesson 4 — leverage; lesson 8 — where your capital sits).
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ADL — auto-deleveraging. The exchange forcibly closes your profitable leg to cover someone else’s liquidation when its insurance fund isn’t enough. Not your mistake — someone else’s. And you are again left with a naked second leg.
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The exchange halts withdrawals or trading — one leg gets stuck. Lessons 2 and 8.
The first one is covered here; the other four are covered in the practical track, each on its own.
Exercise
Five minutes, not a single dollar. Open the delta calculator (linked on this lesson’s page, it also works in Telegram). Pick spot and perp for the same coin on any exchange, enter both prices and the same number of coins. Move the price around: the price moves — the total stays put. Then change the number of coins in one leg and see what happens to the total.
Terms
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Coin — Here, any asset you work with; technically most of them are tokens.
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Delta — How much a position’s result changes when the price moves by one unit. Long 1 coin: +1, short 1 coin: −1.
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Delta neutrality — The combined delta of the positions is zero — price direction does not affect the result.
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Leg — One of the positions in a pair. A spot-perp pair has two legs: long spot and short perp.
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Directional risk — Dependence of the result on where the price goes. A single position has it; a delta-neutral pair does not.
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Funding — Periodic payments between the two sides of a perp. One of the two sources of profit in delta-neutral arbitrage.
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Insurance fund — An exchange reserve used to cover the loss when a liquidated position could not be closed at the bankruptcy price. When it runs short, ADL kicks in.
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ADL (auto-deleveraging) — The exchange forcibly closing profitable positions on the opposite side to cover the loss from someone else’s liquidation when the insurance fund is not enough.
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Leg divergence — The gap between the two legs’ prices growing after entry. It doesn’t affect the outcome when both are closed together, but puts pressure on margin along the way.
Check yourself
Why is spot-spot with a transfer arbitrage with directional risk?
While the coin is moving between exchanges, you are holding it — you are long, and a price drop eats the spread. The second leg only appears after the transfer.
Long spot for $1,000 and short perp for $1,000. Is delta zero?
No. With different spot and perp prices, that is a different number of coins — 100 and 99.8. Legs are matched in number of coins, not in dollars.
If price direction doesn’t matter — where does the profit come from?
From funding (the perp pays one of the sides) and from the gap between the legs at entry and exit. Neutrality removes the risk, and profit is collected from these two sources.
Next lesson: spot-spot with a hedge — buy on the first exchange, immediately remove directional risk with a short on the perp, transfer, sell on the second, close the short. Two exchanges, a perp, and the full calculation from start to finish.
This material is for educational purposes only and is not investment advice. You make all trading decisions on your own and at your own risk.