How to Calculate Arbitrage Profit
Arbitrage profit equals the price gap between two markets times the quantity traded, minus transaction costs, and it is locked in because both trades happen at the same moment.
The Arbitrage Profit formula
Calculator
Enter the two quotes, the size of the trade and the costs to get the profit and the quantity it takes to cover them.
The price you can actually buy at, not the midpoint of the quote.
The price you can sell the same asset at, at the same moment.
Both legs have to be the same size, or part of the position is left exposed.
Fees, borrowing costs and the price impact of your own orders on both venues.
Costs come out of the gross figure and leave $2,400, locked in the moment both legs are placed.
- Price gap per unit
- $0.75
- Gross profit before costs
- $6,000
- Quantity needed to cover costs
- 4,800
- Return on the capital committed
- 0.32%
- Verdict
- Profitable after costs
The two venues are $0.75 apart on every unit, and that gap is the whole source of the profit.
The gap times the size of the trade is $6,000 before anything is paid out.
Anything under 4,800 units loses money, since the costs do not shrink with the size of the trade the way the gap grows with it.
Buying the position tied up real money, so the profit works out to 0.32% of it, which is why this trade is run at size and at speed.
The gap survives the costs, so the trade pays whichever way prices move next.
How to calculate Arbitrage Profit, step by step
- 1Check it is the same asset in both markets. Arbitrage needs one asset, or two bundles that are economically identical, quoted at two prices at the same instant. Two similar but different assets at different prices is a bet on the gap closing, not an arbitrage.
- 2Take the gap between the two quotes. Selling price minus buying price is the gross gap per unit. Use the prices you can actually deal at, since the quote you see and the quote you get are rarely identical.
- 3Multiply by the size of the trade. Gross profit = gap × quantity. Both legs have to be the same size and go on at the same time, otherwise part of the position is exposed to the price moving.
- 4Subtract every cost of getting it done. Fees on both venues, borrowing costs on the short leg, and the price impact of your own orders all come out. Costs are what usually turns a visible gap into nothing.
- 5Find the break-even quantity. Divide the costs by the gap per unit. Below that size the trade loses money, which is why small gaps are only worth taking in large amounts.
Worked example: Arbitrage Profit
The same share is quoted at $92.40 on one exchange and $93.15 on another at the same instant, a gap of $0.75 a share. A trader buys 8,000 shares on the cheap venue and sells 8,000 on the dear one at the same moment, for a gross profit of 0.75 × 8,000 = $6,000. Fees, borrowing and the price impact of the orders come to $3,600, leaving an arbitrage profit of $2,400. The trade needed at least 3,600 ÷ 0.75 = 4,800 shares to cover its costs, so half that size would have lost money. The capital committed was 92.40 × 8,000 = $739,200, so the profit is a return of 0.32 percent on it.
Arbitrage Profit questions
What is the difference between arbitrage and speculation?
An arbitrage buys and sells the same asset at the same time, so the position closes immediately and the profit does not depend on where prices go next. A speculator holds a position and is paid only if the price moves the right way. Buying a share you expect to rise is speculation however confident you are, because the payoff is still unknown when the trade is placed.
Why do arbitrage opportunities disappear so fast?
Because taking one destroys it. Buying in the cheap market pushes that price up and selling in the dear market pushes that price down, so the gap closes as the trade goes on. With many fast automated traders watching the same quotes, gaps that survive are usually either too small to cover costs or a sign that the two assets are not actually identical.
What counts as a transaction cost in this formula?
Exchange and broker fees on both legs, the cost of borrowing the asset if one leg is a short sale, any currency conversion, and the price impact of your own orders. The last one grows with the size of the trade, which puts a ceiling on how far you can scale a small gap. Taxes and settlement charges belong in the same bucket.
Does a positive gap always mean a profit?
No, the gap has to clear the costs, and the break-even quantity is the quickest way to check. Divide total costs by the gap per unit, and if the trade you can actually place is smaller than that number, the gap is not worth taking. This is why price differences between markets can sit there in plain sight without anyone closing them.
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