To an algorithmic trader, Bitcoin is just another foreign currency. It is freely convertible to most major currencies, it can be traded 24×7, and it can even pay interest[1]. Furthermore, one can ask for historical data for backtesting, including level 2 quotes, from most of the exchanges. These exchanges offer application programming interfaces (API) to algorithmic traders for connection to their own automated trading programs. So the only question left is: what sort of systematic strategies can work on Bitcoin?

It turns out that we can also take the cue from currency trading in the search for Bitcoin systematic strategies. Let’s examine some of these in turn:

### DIRECTIONAL TRADING

Using traditional time series analysis[2] such as ARIMA, we can try to predict the future return of Bitcoins traded on one exchange using linear models. This prediction can be made over various time frames: from one-second bars to one-day bars. I have found that the simpler the ARIMA model, the better it works in a walk-forward test (parsimony rules!) For example, here is the equity curve of a trading model on BTCCNY using an AR(3) model with one-minute bars. (The data was provided by BTC China.) I have displayed only the last 5,000 bars’ cumulative returns, since the first part of the data was used for training the model using the customary maximum likelihood parameter estimation.

The strategy is simple: just buy BTCCNY whenever AR(3) predicts a positive return for the next bar, and vice versa. The holding period is just 1-minute. One note of caution: this backtest was done using trade prices, and without incorporating transaction costs. However, the shorter the bar duration, the more important it is to use bid-ask quotes data, not trades data, for backtesting. Otherwise one will be earning phantom profits from simple bid-ask bounces. I wasn’t able to obtain quotes data for this test, but if you plan to trade this live, it is crucial to do so.

### MEAN REVERSION STRATEGY

Using the previously mentioned ARIMA model, one can ascertain that many Bitcoin price series are mean-reverting. This suggests that we don’t really need to predict the next period’s return: we can just assume mean-reversion of prices and trade this with a Bollinger Band model. I display below a pictorial summary of a typical Bollinger Band strategy, where MA stands for “Moving Average of prices”, and MSTD stands for “Moving Standard Deviation of prices”. The lookback period for both is one minute in our backtest. k is the entry threshold for both long and short trades, and it is set to 2.

We have backtested this with the same data used in the AR(3) model, and without transaction cost, the daily return is as high as 61%. Obviously, much of this is just bid-ask bounce and unattainable. But there is an important difference from the AR(3) strategy: since this is a mean-reverting model, one can use limit orders for executions. So we do not have to pay the bid-ask spread (which at 20bps for Bitcoin is quite considerable). Instead, we just need to pay the opportunity cost of our limit order not getting filled. It is hard to estimate opportunity cost though, unless one actually trades live.

### MOMENTUM STRATEGY

One favorite momentum indicator of mine, especially for short-term use, is order flow. Order flow is signed transaction volume, and its ability to predict exchange rates has been well-known[3][4]. Order flow is particularly easy and accurate to compute for some Bitcoin markets, because many exchanges’ data feed come with an “aggressor flag” that unambiguously tells us the sign of the transaction. As a potential trading strategy, we can aggregate order flow over some lookback period, and simply send a buy market order whenever the aggregate flow is greater than some threshold ( and vice versa for sell market order). We backtested one such model using data from Bitstamp, and the result (again without transaction cost) is sterling. The usual caveat applies: since this is a momentum strategy using market orders, one cannot avoid paying the bid-ask spread, which is likely to destroy any high frequency strategy. And high frequency strategy this certainly is – it trades hundreds of times a day.

### CROSS-EXCHANGE ARBITRAGE

Just like the currencies, Bitcoin is traded in multiple unconnected exchanges. But to a much greater extent than currencies, the prices of Bitcoin at any moment on these exchanges are very different. This may appear to be fertile ground for cross-exchange arbitrage. For example, at Feb 2, 2015, 7pm EST, BTCUSD has bid-ask

Bitfinex 239.19-239.48

BitStamp 237.8-237.96

btc-e 233.232-233.546

The substantial differences in prices result from the different credit-worthiness of the exchanges. (A startling statistic: 45% of bitcoin exchanges fail due to thefts and hacks[5].) Besides the bankruptcy risk of a Bitcoin exchange, the cross-exchange arbitrageur must also contend with three market frictions: 20 bps commissions, 1% coin withdrawal fees, and the delay of at least an hour before one can transfer a coin from one exchange to another. Of course, without these frictions, there won’t be such lucrative arbitrage opportunities. Even taking all these costs and difficulties into account (except for credit risks), one can realize a profit of about 4% a day from this type of trading.

### CONCLUSION

Because of the credit risks of some Bitcoin exchanges, and the illiquidity of the market compared to traditional currencies, Bitcoin trading is not (yet) for large institutions. But for a smaller account, these precise features present inefficiencies that can be exploited by an adept algorithmic trader. As I have demonstrated, the tools to exploit them can easily be borrowed from existing techniques that are well-studied in other financial markets. No doubt experienced Bitcoin traders can discover for themselves unique properties of this market that are amenable to novel techniques as well.

*REFERENCES*

*[1] “How to Earn Interest on Bitcoin 5 Different Ways” http://cryptorials.io/how-to-earn-interest-on-bitcoin-5-different-ways/.*

*[2] Ruppert, David, and Matteson, David S. 2015. “Statistics and Data Analysis for Financial Engineering”, 2nd edition, Springer.*

*[3] Lyons, Richard. 2001. “The Microstructure Approach to Exchange Rates”. MIT Press.*

*[4] Menkhoff, Lukas, et al. 2013. “Information Flows in Dark Markets” BIS working paper #405.*

*[5] Johansson, Nathalie Stråle, and Tjernström, Malin. 2014. “The Price Volatility of Bitcoin”. www.diva-portal.org/smash/get/diva2:782588/FULLTEXT01.pdf*