# Arbitraging Inefficient Markets: Building a Trading Strategy on Correlations

By now everyone is aware just how correlated the Cryptoasset markets are. To borrow from an article by The Block, “if you own one cryptocurrency, you own them all.” This has become increasingly obvious during the bear market where all cryptoassets falling in unison. This correlation can be seen in the matrix bellow from Delphi Digital’s latest Entering the Ethereum report.

Overall unrelated assets (BTC digital gold vs ETH world computer) moving together is a sign of an immature market. Fundamental value and quality of the project becomes less important in highly correlated markets with prices being mostly a random walk of sentiment. Overall this leads to decreases in the diversification of portfolios and an increase in risk for cryptoasset investors and managers.

But this high correlation offers an opportunity to savvy investors. In this blog post, I introduce Pair Trading in cryptoasset investing as well as show a Case Study in Pair trading between Ethereum and Augur.

## What is Pair Trading?

Pair trading I a market-neutral trading strategy that takes two highly correlated assets and implements a trading strategy when the two assets’ prices differ from statistical norms. Examples form traditional markets could be gold’s spot price versus publicly traded Gold mining companies, or Pepsi’s price verse Coke’s. Pair trading strategies profit when the two assets’ returns diverge from statistical norms, the pair trader would short sell the outperforming asset and buy underperforming asset under the assumption that the prices will converge to their statistical norms.

## Case Study: ETH vs REP

You can view my spreadsheet and analysis here

Ethereum and Augur are a prime candidate for Pair trading with how correlated their prices are. Ignoring the incredible correlations within crypto as a whole, it makes sense for ETH and REP to be especially correlated because Augur is built on top of Ethereum. This means much of Augur’s systematic risk comes from Ethereum, ultimately leading to REP’s price to follow ETH’s closely. This can be seen in the graph below comparing ETH vs REP’s prices.

Since Augur’s inception, ETH and REP prices have been correlated at a rate of 0.52. With 1 being perfectly correlated, 0 being completely uncorrelated, and -1 being perfectly negatively correlated. It is important to note that there are other projects on top of Ethereum that trade at much higher correlation than 0.52, but Augur is one of the oldest Ethereum based projects, and since this is only an example, I choose a larger data sample over a higher correlated pair. As we can see in the graph below from Coinmetrics ETH vs REP prices have been correlated much higher since the beginning of 2018 at an average rate of 0.68.

Like I said above, we are looking for a statistical divergence in the correlation of returns to find an opportunity to pair trade. Looking at the monthly returns of ETH and REP we can better see how prices have diverged in the past. The black line is ETH returns subtracted by REP returns find the difference in returns. When the returns difference line is greater than 0, Ethereum outperformed the pair. When the returns difference line is less than 0, Augur outperformed the pair. What I want to highlight here is a large spike in either direction shows a stray from statistical norms offering an opportunity for pair trading. It is also important to note that after the return difference line spiked in either direction it often spiked in the other direction to indicate a return to the statistical norm. This can be seen between January through May in 2016 where ETH outperformed, January through April 2018 and January through present 2019 where Augur outperformed.

## Price Ratio

To improve upon our analysis, we can look at the price ratio. The price ratio is ETH price divided by REP price. From there we were able to find an averaged out multiple of 8.49 of how many times greater ETH’s price is from REP’s price. This becomes our statistical norm. However, this takes into consideration data from REP’s inception and as stated above, ETH and REP became highly correlated at the start of the current bear market. Because of that for the rest of the analysis, we will only be using data from 2018 to present. Normally one would want to use data across a full market cycle, but since this asset class is so new, we must work with the data we are given and understand that there is some room for error with a smaller data sample.

Back to pair trading, using 2018 to present data we find the Price Ratio, this can be seen as the green lines in the graphs below or under the price ratio tab in the attached spreadsheet. The blue and yellow lines on the graph represent the Average Price ratio plus and minus 1 standard deviation. If the Price Ratio is trending upward, Ethereum is outperforming since the multiple of how many times larger Ethereum’s price is than Augurs is growing. If the Price Ratio is trending downward, REP’s price is outperforming. Looking for price movements that are statistically significant, any price ratio outside of the white and blue standard deviation lines represents a price movement outside of the statistical norms of the pair and is where an investor would want to consider a pair trade. From the graph below we can see that the beginning of the year 2018 ETH statistically significantly outperformed the trading pair, as well as almost the beginning of 2019 to present REP has been diverged by greater than 1 standard deviation.

For more risk-averse investors (do they even exist in this market, you are trading crypto) we can look for a divergence of two standard deviations from the pair. This can be seen in the graph below where REP outperformed the pair in January and February of 2019.

To complicate our analysis even further we can add moving averages to our Standard Deviation lines. This allows our analysis and pair trading to be on shorter time frames, rather than the couple month trades that we discussed above, as well as better take into account current levels of correlation between ETH and REP prices. In the graph below, the standard deviation lines take the price ratio of the previous 5 weeks plus minus the standard deviation over the past 5 weeks respectively.

As we can see in the 1 standard deviation moving average graph we can once again highlight the beginning months of 2019 as the best time to initiate a pair trade between the ETH and REP pair. Below is the 5 Week Moving Average price ratio graph using plus minus two standard deviations.

## Proof of Concept

To test Pair Trading in Crypto, I back-tested the trading strategy from the beginning of 2018, this can be seen on the back-testing section in the attached google sheet. The back-testing model used the +/- 1 standard deviation model outlined above, pair trading whenever the price ratio was above or below the standard deviation lines. Since the beginning of 2018, the model alerted to 6 trades, 5 completed and the 6th still open as of 3/3/19. To compare how pair trading performed, I created 3, $100-dollar portfolios. The first was a buy and hold ETH from the beginning of the data set, the second a buy and hold of REP and the third portfolio pair traded the two. As you can see from the graph below, the pair trading portfolio significantly out-performed the other two.

The buy and hold ETH portfolio would currently be worth $11.83 a decline of 88.17%. The buy and hold REP portfolio would currently be worth $16.47 a decline of 83.53% and the pair trading portfolio would currently be worth $279.41 an increase of 179.41%.

## Conclusion and Risks

To wrap this post up, pair trading is not without its risks. Though pair trading is a market neutral strategy used to hedge out volatile market swings, in incredibly illiquid markets such as crypto a positive tweet by a prominent member of one of the projects could theoretically break the correlation and make your trade go bad. It is also incredibly important to note that models are a tool in your analysis toolbox but shouldn't be the only thing dictating an investment decision. I like to point at Long Term Capital Management as an example of this. The LTCM team created the Black-Scholes Option pricing model and created incredible returns in highly leveraged volatility options. However, their models did not foresee the 1998 Russia financial crisis ultimately leading to the fund losing 4.6 billion dollars in 4 months.

Overall, I see the high levels of correlation as a sign of an immature market and believe a decoupling of Bitcoin and alternative coins with different goals and value propositions a necessary step for the cryptoasset markets to mature. However, even though a highly correlated market leads to more risk, doesn’t mean that a savvy investor can’t use it as an opportunity to achieve alpha. The goal of this post is to encourage more investors to think outside the box and consider using traditional investment strategies when investing in the crypto asset space.

*Note: A huge thank you to **Tanner Hoban** and **malexaffey** for review and providing feedback to this post! If you have any questions, thoughts, or concerns feel free to reach out over **Twitter**!*