Quantifying Price Fragmentation Across Bitcoin's Biggest Exchanges

One feature of bitcoin that clearly demarcates it from other major currencies in circulation today is the dramatic variation in its price across exchanges.

But why is bitcoin so unlike the major national currencies in this regard? Additionally, is this price fragmentation a characteristic of all decentralized alternative currencies, or just a temporary phenomenon?

The law of one price

The US dollar and other major national currencies effectively trade at the same price, regardless of whether they are exchanged in Tokyo, London, New York, or any other major foreign exchange market.

Small discrepancies in price may be observed periodically, but they are quickly pounced on and erased by algorithmic arbitrageurs seeking to profit from such asymmetries.

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In short, the price for US dollars across the world’s major exchanges trades in lockstep.

The reason for the near-perfect price synchronization we see in major currencies like the US dollar relates to an economic concept known as the ‘law of one price’.

Put simply, this concept means that prices for fungible, freely-traded items like currency should be equal across all open markets.

If we were to observe any material, persistent price variation between US dollars exchanged in Tokyo versus those exchanged in London, then this would be due to the existence of some cost or barrier – like variations in transaction fees, the speed at which information can travel, transportation expenses, or restrictions to the flow of funds.

However, we do not observe any such variance, due to the very low frictions across the major forex markets.

Measuring Bitcoin price differences across exchanges

In contrast to the forex markets for major currencies like the US Dollar, at any given moment the bitcoin exchange rate can vary by tens or hundreds of dollars from one exchange to the next.

For example, approximately a week before bitcoin first crossed the $1,000 mark on Mt. Gox, the price of bitcoin had already reached the renminbi equivalent of $1,000 on China’s largest exchange, BTC China.

Following the recent announcement by Chinese authorities that banks would no longer be able to transact with bitcoin (which, in turn, triggered Baidu’s decision to suspend its acceptance of bitcoin), the price on 5th December as of 08:30 GMT had plummeted in China by a renminbi equivalent of approximately $177 more than prices on exchanges located outside of China (see Chart 1).

Large price variances triggered by sudden shocks in a relatively thinly-traded currency like bitcoin are not altogether surprising.

However, significant price variances across different exchange are also observed during longer periods of time which feature lower overall levels of price volatility, as can be observed in Table 1.

Looking at data sourced from CoinDesk's Bitcoin Price Index (BPI) for just over a three-month period from late August through to early December, we can confirm significant price differences across the three index component exchanges (Mt. Gox, Bitstamp, and BTC-e) in both average and median price.*

The significantly higher average price, compared to the median, shows us there is evidence of outliers – meaning more extreme price variations across exchanges over relatively shorter periods of time.

However, Mt. Gox has still maintained double-digit median price variances with Bitstamp and BTC-e over the past three months, meaning price fragmentation is a persistent feature across exchanges, even during periods of relatively lower volatility.

Quantifying the Mt. Gox premium

A common refrain heard across the bitcoin community is that the price of bitcoins traded on Mt. Gox is typically higher than other exchanges.

It has been suggested that bitcoins trade at a premium on Mt. Gox due to the restrictions on some national currency withdrawals, meaning some Mt. Gox customers are having to purchase bitcoins to transfer account assets out of the exchange.

Due to the ‘Mt. Gox premium’ those eager to see the maximum current value of their digital wallets have, prior to China's bitcoin boom and BTC China's high prices, traditionally turned to Gox.

But, on average, just how much higher is the Mt. Gox price than other bitcoin exchanges?

Looking at the same three-month dataset, we can confirm that the average price on Mt. Gox is significantly higher than Bitstamp and BTC-e, at $21 and $34, respectively.

Furthermore, we can see that during the sample period Mt. Gox achieved an all-time price high which was greater than Bitstamp and BTC-e by $77 and $160, respectively.

Looking ahead

Should the bitcoin market continue to grow in the months and years ahead, it would be reasonable to expect a decline in price fragmentation across the various exchanges as trading volume and liquidity increase.

For the time being, however, relatively illiquid markets alongside the barriers which have been erected around and between the various bitcoin exchanges will continue to drive price fragmentation.

In other words, the law of one price may one day apply to bitcoin but not for the foreseeable future.

* The CoinDesk Price Index uses minute-by-minute data sourced directly from the exchanges. While bitcoin prices can often vary significantly over smaller units of time (seconds) it is unlikely that the observed variance would be significantly impacted or eliminated with higher frequency data.

Stock Chart photo via Shutterstock