A new working paper from Canada's central bank has found little evidence that arbitrage opportunities in cryptocurrency markets exist.

The paper, Competition in the Cryptocurrency Market, analyses 10 months of publicly available data from exchanges like BTC-e and Cryptsy, from May 2013 to February 2014.

Examining how 'network effects' (the phenomenon of new users augmenting the value of a technology) affect competition in the cryptocurrency economy, the paper looks at competition between both cryptocurrencies and cryptocurrency exchanges. The authors write:

The paper was written by Hanna Halaburda, a senior analyst in the bank's currency department, and Neil Gandal, chair of the Eitan Berglas School of Economics at Tel Aviv University.

For data, the authors have used 'closing rates' of bitcoin, litecoin and other digital currencies from exchanges BTC-e, Cryptsy, Bitstamp and Bitfinex for the period between 2nd May 2013 and 28th February this year.

This data was obtained from Cryptocoinscharts.info and the closing rate is the given digital currency's price at midnight GMT, according to the paper.

In analysing competition between exchanges, the authors looked at 'two-sided network effects'. This is a phenomenon that arises when buyers and sellers in a given market both compete for a larger number of counterparties: buyers of bitcoin prefer markets with more sellers, while the opposite is true of sellers.

The aggregate effect of this phenomenon is the creation of "thicker, more liquid" markets. A large exchange possesses more liquidity, and over time, it will dominate the exchange market. In this scenario, network effects would give rise to a convergance in digital currency trading to a single exchange over time.

But other network effects are also simultaneously at work. The 'negative same-side effect' suggests that sellers, while seeking markets with more buyers, also wish to avoid competition, or markets with large numbers of sellers. The opposite holds true for buyers.

To determine the aggregate network effects at work between exchanges, the authors looked at prices for three currency pairs, BTC/USD, LTC/USD and LTC/BTC, on three exchanges: BTC-e, Bitstamp and Bitfinex. It ran two tests, correlation and regression analysis, on the data.

The paper's correlation analysis found that the BTC/USD currency pair prices were highly correlated between BTC-e and Bitstamp. It found the same for the LTC/BTC pair across BTC-e and Bitfinex.

Regression analysis yielded similar results, with the paper concluding that arbitrage opportunities were unlikely to have existed across the exchanges in trading any of the currency pairs.

However, two traders who were alerted to the paper dispute its conclusions and methodology. Arthur Hayes is a former equity derivatives trader at Citi and the chief executive of BitMEX, a bitcoin derivatives exchange. He makes money as an arbitrageur, trading between various exchanges. He observed:

In other words, Hayes is an arbitrageur who profits from a market phenomenon that the Bank of Canada’s working paper says does not exist.

Hayes even offered a historic example of a profitable arbitrage strategy:

"For almost a week, there was 20-40% arbitrage [opportunity] between European and Chinese exchanges trading at considerable premiums. The reverse, where China traded cheaper than Europe, was also witnessed [this spring] when [China's central bank] made announcements relating to banks dealing with bitcoin exchanges."

In Hayes' view, the authors couldn't pick up on arbitrage opportunities for two reasons: comparing prices between too few exchanges and using regression analysis instead of a simple time series of price data.

Hayes pointed out that paper only compared prices between European exchanges. For a better insight the authors should have compared prices across continents, he added.

Another trader, Joseph Lee, created arbitrage bots that managed his trading for a year, netting him hundreds of thousands of dollars. He has since retired the bots to focus on derivatives exchange BTC.sx. Lee also disagrees with the conclusions of Halaburda and Gandal's working paper.

"Without a doubt, arbitrage opportunities have existed in [the period of study] and will always exist in the market. They even exist in the current financial market which has trillions of dollars of liquidity," he said.

Lee points out a flaw in the paper's methodology: the authors relied on 'closing rates' for price data, which Lee says would never show an opening for arbitrage.

Closing rates are a snapshot of prices at a given time (in this case midnight GMT) and they are used to represent the currency's price for a 24-hour period. However, because arbitrage opportunities are fleeting – they disappear in seconds as arbitrageurs see them and pile in – closing rates aren't sensitive enough to reveal these moments.

Lee added:

The paper briefly acknowledges that its use of daily price data may have problems. It notes that arbitrage opportunities may be found if price differences between exchanges are compared at different times during a day.

"We leave this more detailed analysis to further research," the authors noted towards the end of their paper.

Halaburda and Gandal also came to a number of other conclusions about network effects and cryptocurrencies. The pair found that bitcoin enjoyed positive network effects, but that other currencies, like litecoin, were gaining ground. Bitcoin may not be able to maintain its dominant position in the long run, it concluded.

The Bank of Canada's working papers are intended for publication in peer-reviewed academic journals, but are works in progress. They are published with the intention of soliciting feedback from a technical audience. In the case of Halaburda and Gandal's paper, bitcoin's arbitrageurs have made their opinions known.

Featured image via epsos / Flickr