Zipfian Distribution of Cryptocurrency Market Capitalizations
TLDR: There appears to be a relationship between the various cryptocurrency market capitalizations that adheres to a Zipfian distribution with exponent s = 1.618, the Golden Ratio. If so, it could be a tool for trading cryptocurrency pairs. The distribution also appears to be signaling future coins to be available for trading/investment.
Background: I’ve been following bitcoin and cryptocurrencies in general since September 2013 (before the run up to +$1000). I first heard of bitcoin on a Planet Money podcast in 2011:
I listen to Planet Money a lot. I’m interested in things like money, technology, futurology, and the like, so this episode stuck with me. And it reminded me of another Planet Money podcast that described a small Pacific island called Yap where the population used limestone as money:
So I thought bitcoin was an interesting idea that dove tailed nicely with this other concept — that money is simply what everyone agrees is money. Regardless, I quickly forgot about it until it showed up in the news in early 2013 during the Cyprus bank crisis. At that time the price of bitcoin went from approximately $13 in January 2013 and topped out at over $250 in April.
That’s when I decided to read into it some more. I found myself beginning to believe that this was something akin to the early days of the Internet. More importantly, unlike the Internet, making an investment in this new thing was simple — just buy some bitcoin. Even if you had been certain in the early to mid 90’s that “this Internet” thing was going to be big, investing in it was a whole other endeavor.
In September of 2013 I bought some bitcoin as a speculative investment. I am not a trader, but a hodler (before “hodler” was a meme). I’ve been watching bitcoin and cryptocurrency prices ever since to keep my eye on how my investment is doing. Over time, I saw many other cryptocurrencies being created, but bitcoin was clearly the king. Generally, it consisted of anywhere from 80% to 90% of the total cryptocurrency market cap.
Observation: While bitcoin’s market share had been declining gradually over the last few years, this past March it dropped precipitously:
The long debated scaling solution for bitcoin was coming (it ultimately culminated in two different approaches; the Bitcoin Cash hard fork on August 1st followed by the activation of SegWit on Bitcoin Core). Presumably because of the uncertainty in the whole cryptocurrency space, many alternative coins began to rise in price. There was talk on reddit of the “flippening” meaning that Ethereum’s ether token would overcome bitcoin and become the dominant coin. And it came close. In mid-June they were very briefly within 10% of each other, but bitcoin rebounded and ether pulled back.
Since then the market caps of all of the coins has settled into a pattern that reminds me of a Zipfian distribution or Zipf’s law.
Zipf’s law pertains to the word frequency in any large body of work, but it applies to other social and physical systems as well. It states that the frequency of a word is inversely proportional to its rank among all other words. For instance, in the Satoshi Nakamoto white paper, the most frequent word is “the”. It shows up 237 times. Zipf’s law predicts that that the 2nd most frequent word should show up 118 times (237 / 2 = 118.5). It just so happens that the 2nd most frequent word is “to” and it appears 117 times.
I recommend watching Vsauce’s YouTube video if you want a much better explanation on this topic.
I have been watching the top 100 coins on https://coinmarketcap.com since August and I’ve noticed that they follow a Zipfian distribution. As an illustration, here are the top four coins by market capitalization that I captured on October 5th, 2017:
1 Bitcoin ………$71,558,821,502
2 Ethereum ….. $27,982,107,990
3 Ripple ……….. $8,901,522,893
4 Bitcoin Cash…..$5,902,349,246
And here are the top 100 coins on a log-log chart below. In it I have placed a “Fit” line in red that shows the predicted market capitalizations based on rank and the actual market capitalizations from coinmarketcap.com.
What I found most interesting was that the best fit was found with the exponent s = 1.618, or the Golden Ratio.
The fit line above predicts a market capitalization for the nth most valuable coin to be a fraction of the most valuable coin, with that fraction defined as:
1 / n ^ 1.618
As an example, the 2nd most valuable coin is predicted to be 1 / 2 ^ 1.618 = 32.579% of $71,558,821,502 (the market capitalization of bitcoin). This equates to 0.32579 x $71,558,821,502 = $23,312,369,336. The 2nd ranked cryptocurrency is ether with an actual capitalization of $27,982,107,990.
The 45th most valuable coin is predicted to be 1 / 45 ^ 1.618 = 0.2114% of 0.002114 x $71,558,821,502 = $151,254,792. The 45th ranked cryptocurrency is GameCredits with an actual capitalization of $150,081,829.
Analysis: If this relationship continues, it could be a useful tool in trading cryptocurrency pairs. Comparing the actual market capitalization to the predicted value from the distribution (and assuming it maintains its ranking), can identify discounted coins to buy up or overvalued coins to sell.
I found something interesting as I played with the numbers in my spreadsheet. I noticed that the coins ranked 3rd–40th were consistently lower or undervalued. They seemed to have a ranking that was one or two ranks too high. When I changed the ranking to reflect a “missing” 3rd ranked coin (SegWit2X perhaps?) and a 6th ranked coin (?), shifting the remaining coins by one each time, the data look like this:
I think it’s reasonable to assume that the market is pricing in a future SegWit2X coin due to the impending hard fork in November and possibly a 2nd coin.
Conclusions:
- It appears that cryptocurrency market capitalizations follow a Zipfian distribution with exponent s = 1.618.
- This distribution provides an opportunity to identify undervalued and overvalued coins relative to the overall market.
- This distribution may predict the value of future forked coins.
Time will tell if this relationship holds. I will certainly be keeping my eye on it.