by Luisa Eguren, Bryan Fondufe, Caleb Hogan and Claire Matthews

**Introduction**

As four first year MBA students at the MIT Sloan School of Management, we worked with the Fidelity Center for Applied Technology to determine the nexus of price discovery between the bitcoin spot and derivatives markets as part of Blockchain Lab, an action-learning lab offered by MIT. To answer this question, we performed field research with individuals both in traditional financial markets and in crypto markets, as well as studied tick-by-tick data from unregulated exchanges for the period of one year. The overarching opinion of our interviewees is that derivatives lead pricing during periods of high optimism, but that the relationship does not hold true during downturns. Derivatives offer the opportunity to take a view on the asset class in a capital-efficient manner (high leverage), thereby inviting mostly retail investors to speculate on the price of Bitcoin and generating greater liquidity for the spot markets. On the data analysis side, we obtained tick level trading data from Kaiko for 25 spot exchanges and 10 derivative exchanges, 2 of which are futures exchanges and 8 of which are perpetual swaps. We performed several analyses on this data including summary statistics, lead-lag analysis, a deep dive into May 17, 2019, arbitrage index within markets, arbitrage profits within markets, and arbitrage profits across markets.

**Key Takeaways**

- According to our lead-lag analysis, the derivative market leads price discovery of Bitcoin more frequently than the spot markets.
- The spot market is more likely to indicate the direction of the price movement while the derivatives market is more likely to lead the magnitude of the price movement.
- Arbitrage opportunities exist both within and across the spot and derivative markets.

**Lead-Lag Analysis**

For context, from the summary statistics, we found that within our dataset, BeQuant, Huobi, and Quoine have the largest value traded in the spot markets. On the derivatives side, OKEx and BitMEX dominate the futures and perpetual swaps markets respectively.

The lead lag study we performed is an examination into the price behavior of the universe of data we analyzed. Between the dates of March 1st, 2019 to March 1st, 2020, for every pair on every exchange, we looked at every 5-minute window that resulted in a price change of over $100. To further reduce the set of these windows, we exclude all events with low trading volume, which we define to be 30 trades within the 5-minute window. The total number of events we analyzed is 59,718. See below for the breakdown on the events, through the months.

We then created another subset of the data, limiting events to have at least 5 exchanges that fit the criteria aforementioned. From these events, we found the price at the start, price five minutes later, and the price movements in between. In each event, we ranked the exchanges based on their correlations within the event window, the biggest price move up or down, and the best price at a given time (each having equal weighting on the rank). We then gave, for each rank, a score; the first rank scored 1 point, the 2nd rank scored 0.5 points, the 3rd rank scored 0.33 points and the 4th rank scored 0.25 points. We then added the scores for each exchange and added them together to create a lead/lag score. Below are the overall results.

The results are a bit surprising for the study. They suggest that the unregulated derivatives market leads in price discovery, for the majority of the part. There are a few things to note. Namely, we expected to see Binance, Huobi and BeQuant much higher on the list of exchanges which lead in price discovery. As a follow-up to our analysis, we would like to consult with Kaiko on getting even more tick-by-tick data from Binance. We also want to highlight that this scoring method was based on a medium blog post, titled “An Analysis of Price Discovery in Bitcoin Spot Markets”(www.medium.com/digitalassetresearch/an-analysis-of-price-discovery-in-bitcoin-spot-markets-7563fbf1c890). While we think this scoring method is really robust, it does not control for exchanges that have fake volume. The authors of the article had a vetting methodology that points out exchanges that likely have fake volume, but we would like to develop a methodology that integrates more into the process of scoring the exchanges.

**May 17, 2019 Deep Dive**

We decided to do a deep dive into May 17, 2019 and study the Bitcoin flash crash that dropped almost $2000 in the matter of minutes, from $8000 down to $6100 and back to $7800. We chose this date because traders and researchers in the cryptocurrency derivatives space heavily cited and referenced this as clear evidence of manipulation. The resounding opinion we heard is that there were a series of large sell orders at low prices on Bitstamp, which caused BitMEX to crash and liquidate over $250 million in positions. It is important to note that Bitstamp comprises 25% of the price composition of the BitMEX price index:

In order to study this, we took a general look at the BitMEX and Bitstamp prices across May 16th to May 18th to see the trends in price and then isolate the time frame we would look into. After doing this, we realized that the majority of the activity occurred between 2:59 AM to 3:10 AM on May 17th.

We looked at every trade that occurred, across BitMEX, Bitstamp, and the general spot market (composed mostly of the Coinbase price). When analyzing the Bitstamp price, it was important for us to get a sense of how big the trades were, and how they compared to the average trade size of Bitstamp in the trade data of $1,722 (see table below). We saw very interesting results. We see a series of large block trades, from a sell order of over 30 Bitcoin priced at around $6,300 (more than 100x the average trade size) to sell orders of over 100 Bitcoin priced at around $6,200 (more than 350x the average trade size), that push the BitMEX price down.

More specifically, we saw the BitMEX-Bitstamp price difference increase to 8.6% as the block trades occur at 3:08.52 AM. Not even a second afterwards, the price of BitMEX quickly follows to reduce the difference in price to 6.7%. As we trace the Bitstamp price, on its decline from $6,365 to $6,211, we see the price of BitMEX fall incredibly fast (in the span of 1 minute) to $6,426 at a price difference of 3.5%. This is clearly evidence that Bitstamp significantly impacted the price of BitMEX. Furthermore, we can see that the price of the general Bitcoin to USD price pairing did not follow Bitstamp directly. In fact, the price of the general spot market followed BitMEX instead. Once BitMEX begins its cascade down, we see the difference in price, from BitMEX to the general spot market, increase as wide as 3%. Then, within just a few milliseconds, the price decreased from $6715 to $6495 and the difference in price decreased to 1.1%. See the table below for the detailed, millisecond-by-millisecond activity that highlights the price movement across BitMEX, Bitstamp and the general market.

**Arbitrage Studies**

In an effort to expand upon the initial question and study the relationships between the spot and derivatives markets, we computed the arbitrage index within markets, arbitrage profits within markets, and arbitrage profits across markets. To be clear, this study does not take into account the collateral required to put on the trade or the fees on each exchange.

In order to calculate an arbitrage index within markets, we first calculated the volume weighted average price for each exchange at the minute level. Then, we divided the maximum price by the minimum price to get an arbitrage index for each minute. Finally, we aggregated the arbitrage index up to the daily level in order to reduce intra-day volatility (Source: Trading and Arbitrage in Cryptocurrency Markets). Starting by looking at the arbitrage index across all three markets, we see that most arbitrage opportunities exist in the spot market, with the largest spike occurring in early April of 2019.

The index in the derivatives market is much closer to 1, which suggests a small price spread within these markets.

Next, we wanted to quantify the magnitude of the opportunity by calculating arbitrage profits. In order to calculate arbitrage profits, we first calculated the volume weighted average price for each exchange at the minute level. Next, we determined the maximum and minimum price within each minute along with their corresponding volumes. From here, we calculated arbitrage profits for each minute using the formula below:

*Arbitrage profits = (Max Price — Min Price) * MIN(Max Volume, Min Volume)*

We used the minimum volume in order to ensure that there was adequate demand for the trade to occur. We also only looked at minutes where the difference between the minimum and maximum price was larger than 2%. Finally, we aggregated the arbitrage profits up to the daily level by summing profits over each minute (Source: Trading and Arbitrage in Cryptocurrency Markets).

Looking at all three markets, we see that arbitrage profit opportunities are most frequent in the spot market, which makes sense based on the arbitrage index calculated in the previous section. However, we also see that while arbitrage profits are infrequent across the derivative markets, they do allow for much larger profits when they occur, particularly in the perpetual swaps market.

Finally, we wanted to see what sort of potential arbitrage profits exist across spot and derivative markets. In order to calculate this, we first calculated the volume weighted average price for each exchange at the minute level. Then we determined the maximum and minimum price within each minute along with their corresponding volumes for both the spot and derivatives markets. From here, we calculated arbitrage profits for each minute using the formula below:

*Arbitrage profits =*

*MAX(Spot Max Price, Der Max Price) — Min Price) * MIN(Max Volume, Min Volume)*

Note, the minimum price used is the price of the market not chosen for the maximum price. For example, if the spot market has the maximum price, then the minimum price is the minimum price in the derivatives market. Again, we used the minimum volume in order to ensure the trade would be feasible. Finally, we aggregated the arbitrage profits up to the daily level by summing profits over each minute.

From the results, we can see there are arbitrage opportunities across both markets. Recently however, more profits are recognized from the spot market to the perpetual futures market. In both cases, the spike of profits occured in late June of 2019.

Apart from profits, we looked at how the arbitrage opportunity was most often implemented. In the graphs below, the red dots represent the minutes per day where the spot price was the maximum price, and the blue dots represent the minutes per day where the derivative price was the maximum price. As you can see, across both markets, it is more common to short the spot and long the derivative in order to recognize the arbitrage opportunity.

**Limitations**

While this is a comprehensive study of tick-by-tick data for twelve months it just begins to scratch the surface of what goes on in crypto markets and hence might not necessarily be fully representative of the market or the players within the market. The asset class is extremely new and volatile, with bitcoin derivatives first coming into existence in 2017. Additionally, this asset class has become more popular during a period of unprecedented distortion in markets given fiscal stimulus and black swan events (ie COVID19). As such, we must be clear in vocalizing the limitations of the study given the time and computational constraints.

The first limitation is regarding the scope — in order to take the study one step further, we would have liked to extend the time period of the study to include data from 2017 to today. This would have included trades since the inception of the derivative space, and might have either confirmed our findings or proved that the lead lag relationship between spot and derivative markets oscillates. One exchange where we lacked data was Binance — a key market player, but unfortunately one that we did not have full access to. Furthermore, we have decided to group stablecoins, such as Tether and USDC, as fiat for the purposes of this analysis. This does not, clearly, take into consideration the credit risk that stablecoins pose. Furthermore, a concern we have with the data is volume manipulation; while this is extremely hard to point out in the data set, we examined over 30 unregulated exchanges that could have significantly altered our results given fake volumes. The next step would be to work with Kaiko and traders to perhaps create a sample set of exchanges with more trustworthy figures, and to re-run the study.

A second limitation of the study are the thresholds and the dates evaluated. While we stuck to thresholds and dates that were suggested in our conversation with traders, there were other thresholds and dates that we could have evaluated to substantiate our results. For example, there was a specific date in July when volatility and arbitrage profits from spot to perpetual futures spiked dramatically. Online research pointed to increased concerns over regulation of Facebook’s Libra, however a deeper analysis of the data could have perhaps pointed to a different cause. Doing deep dives on dates other than May 17th would perhaps also have helped clarify the consistency of the relationship between spot and derivatives; it would have been interesting and enlightening to find a period of a rapid increase (rather than decline) in the price of bitcoin to analyze what happened in the spot and derivatives market. This would have helped ascertain whether what was mentioned in our trader interviews holds true — that derivatives lead in bullish markets, and that spot markets lead in downturns.

Lastly, our study did not take into account trading fees or any structural barriers across markets when calculating arbitrage profits. The calculations are contingent on one market player capturing all the profits by making use of the whole minimum volume; while this is a useful calculation to understand the opportunities within the market, it is not a practical calculation. In addition, the trade opportunities discussed did not consider the real collateral that traders would need to put up, along with further mechanisms such as the funding rate for opportunities in the derivatives market, for those orders to be executable.

**Acknowledgements**

We would like to acknowledge and thank the following people who supported us throughout the project.

First, we would like to thank Brian Wright and Juri Bulovic from the Fidelity Center for Applied Technology. FCAT partnered with us throughout the project, and we appreciate their support.

Next, we would like to thank our Blockchain Lab professors from the MIT Sloan School of Management, Gary Gensler and Simon Johnson as well as Neha Narula from the MIT Media Lab. They mentored us throughout the semester, and we appreciate their guidance.

Finally, we would like to thank Sacha Ghebali from Kaiko for not only helping us to acquire the data but also for helping us analyze the data and for providing feedback on our results.

### References

- Makarov, Igor and Schoar, Antoinette, Trading and Arbitrage in Cryptocurrency Markets (April 30, 2018). Available at SSRN: https://ssrn.com/abstract=3171204 or http://dx.doi.org/10.2139/ssrn.3171204
- Cipolaro, G., 2020. An Analysis Of Price Discovery In Bitcoin Spot Markets. [online] Medium. Available at: <https://medium.com/digitalassetresearch/an-analysis-of-price-discovery-in-bitcoin-spot-markets-7563fbf1c890>.

Price Discovery in the Bitcoin Spot & Derivatives Markets was originally published in Kaiko Data on Medium, where people are continuing the conversation by highlighting and responding to this story.