The Same Bitcoin, Different Prices: Arbitrage in Crypto Markets

The law of one price is close to a religious doctrine in finance. The same asset cannot trade at two different prices at the same time, because if it did, someone would buy it cheap, sell it dear, and pocket the difference until the gap closed. Textbook arbitrage. It is supposed to happen in milliseconds.

Then Bitcoin arrived, and Bitcoin is the most fungible asset ever created. A bitcoin on one exchange is byte for byte identical to a bitcoin on another. There is no delivery, no quality difference, no counterparty variation in the asset itself. If the law of one price holds anywhere, it should hold here.

Igor Makarov and Antoinette Schoar looked at what prices Bitcoin actually traded at across the world's exchanges, and found gaps so large and so persistent that they made a mockery of the doctrine.

The problem: enormous gaps that refused to close

Gather the order books from dozens of crypto exchanges across many countries, and line up the prices at the same moment.

They do not match. Not by a basis point or two, which you could shrug off as a bid-ask artefact. Bitcoin traded at prices that differed across exchanges by large margins, and the gaps stayed open for days and weeks. At various points, buying Bitcoin in one country and selling it in another was a spread you could see with the naked eye.

This is bizarre. This is not an illiquid corporate bond that has not traded in a month. This is the single most talked-about, most speculated-on, most electronically-traded asset of the era, and it was trading at meaningfully different prices in different places, in plain sight, for weeks.

Something must be stopping the arbitrage. The question is what.

The key idea via analogy: the money cannot get there

Here is the shape of the answer, and it is quietly profound.

Imagine the price of apples is higher in one country than another. Normally, traders ship apples until the prices converge. Now imagine that shipping apples is trivially easy, but getting your money in and out of the country is the hard part. Customs will not let you repatriate the proceeds. Your bank blocks the wire. The paperwork takes three weeks.

Now the price gap can persist indefinitely, and it has nothing to do with the apples.

That is exactly what Makarov and Schoar found. The critical finding is the geography of the gaps:

Price deviations were much larger across countries than within them. Two exchanges in the same country tracked each other tightly. Two exchanges in different countries could diverge dramatically. If the friction were about crypto plumbing, blockchain confirmation times, exchange technology, that pattern would make no sense, because moving Bitcoin from one exchange to another is the same operation whether they are in the same city or different continents.

The gaps between cryptocurrencies were small. The relative prices of different coins on the same exchange were consistent. So the internal pricing was not broken.

Put those together and you get the diagnosis. The barrier to arbitrage is not the crypto. It is the fiat. To capture the spread you must buy Bitcoin cheap in one place and sell it expensive in another, but that means you have to get dollars (or won, or yen, or rupees) into the cheap exchange and get the proceeds out of the expensive one. That means bank transfers, currency conversion, capital controls, anti-money-laundering checks, and the willingness of a bank to touch a crypto exchange at all. Those frictions are slow, expensive, sometimes legally impossible, and they are precisely what varies by country.

Two further findings sharpen the picture.

The gaps moved together. Price deviations across countries co-moved. When one country's premium widened, others tended to move with it. That points to a common driver rather than a set of local accidents.

The gaps opened up when Bitcoin was rising. Arbitrage deviations widened during periods of large Bitcoin appreciation, and countries that habitually traded at a premium to the US price saw their premium widen precisely when Bitcoin was surging. This has a natural interpretation: enthusiasm is local. When retail investors in a particular country pile into Bitcoin, they buy on their local exchange, and the buying pressure pushes the local price up. Arbitrageurs cannot get capital in fast enough to flatten it, so the premium sits there, visible to everyone and capturable by almost nobody.

There is one more implication the authors draw out that traders should sit with. The arbitrage in the direction that requires buying Bitcoin in the cheap country and moving fiat out of it is exactly the direction blocked by capital controls. So the gaps are not symmetric. They persist in the direction the plumbing forbids.

Why it mattered

• It gave a clean natural experiment on capital controls. Economists have argued for decades about how binding capital controls really are, and the evidence is always contaminated by differences between countries. Here the asset is identical across borders, so any price gap is a pure measurement of the friction in moving money. This paper turned Bitcoin into an instrument for measuring capital mobility, which is a genuinely creative use of a speculative asset.
• It explained the crypto arbitrage business. For a stretch of 2017 and 2018, cross-exchange arbitrage in crypto was one of the most profitable trades in the world, and everyone wondered why it was not competed away. The answer is that the constraint is banking relationships, not trading skill. The firms that made the money were the ones with fiat rails in multiple jurisdictions.
• It showed the law of one price needs plumbing. Arbitrage does not enforce itself by magic. It requires someone to be able to move capital. Where they cannot, prices diverge, and they will stay diverged for as long as the pipes stay blocked. That is a lesson well beyond crypto: it applies to closed-end funds, to onshore versus offshore currency markets, to any asset trading behind a wall.
• It is a rare empirical paper on crypto that is really about market microstructure. Most crypto research is about returns. This one is about how the market is wired, and the wiring turned out to explain more than the returns did.

The honest limitations

• The gaps were probably harder to capture than they look. A printed price is not an executable price. To actually harvest these spreads you would need capital pre-positioned on both exchanges (which means holding balances at venues with serious solvency and hacking risk), you would face withdrawal limits, and the exchanges themselves were not always trustworthy. Some fraction of these "arbitrage opportunities" was really a risk premium for the possibility that your money never came back.
• The data era is specific. The study covers the 2017 to 2018 boom, an extraordinary period of retail frenzy and immature infrastructure. Crypto market plumbing has professionalised considerably since. The gaps have narrowed, and a study of today's market would find much smaller numbers.
• Exchange data quality is a known problem. Reported volumes on some crypto exchanges have been credibly accused of being fabricated, and the reliability of quoted prices on smaller venues is uneven. The authors work hard around this, but the raw material is not audited exchange data in the way equity data is.
• "Capital controls" is a broad label. The friction bundle includes banking risk aversion, compliance checks, currency conversion cost, and outright legal prohibition. The paper convincingly shows the friction is in the fiat leg. Separating which specific friction binds where is harder.

The one-line takeaway

Makarov and Schoar found that the same Bitcoin traded at persistently different prices in different countries, and showed the reason had nothing to do with crypto and everything to do with money: the arbitrage was blocked not by the difficulty of moving coins, but by the difficulty of moving cash across borders, making Bitcoin an unusually clean measuring stick for how binding capital controls really are.