Quantitative Update: Bitcoin vs. The Rest of the World

This post is meant to be an addition to what I said earlier this year. Here we compare, in the same historical period of existence of bitcoin, Bitcoin vs other assets: us stock market indexes, US stocks of different sectors and Gold.

Let’s start with this summary table, who follow me regularly should already know the meaning of Shannon’s probability, RMS, G yield and compounded annual G yield; for all the others I refer you to the end of the article.
The data have been sorted in descending order according to Compounded Yearly Gain  G.

Comparison Bitcoin vs. The rest of the world
July 17, 2010 – Dec 31, 2019

Asset RMS or Volatility Shannon Probability P Daily Gain G Compounded Yearly Gain  G Optimal Fraction of your capital to wage
Bitcoin               0.0567                       0.5219        1.00087 38% 4.4%
MasterCard               0.0155                       0.5265          1.0007 19% 5.3%
Visa               0.0144                       0.5241          1.0006 16% 4.8%
Amazon               0.0193                       0.5196        1.00057 15% 3.9%
Apple               0.0161                       0.5172        1.00042 11% 3.4%
Google               0.0148                       0.5167        1.00038 10% 3.3%
Microsoft               0.0143                       0.5169        1.00038 10% 3.4%
Nasdaq Composite Index               0.0106                       0.5179        1.00032 8% 3.6%
Standard & Poor’s 500 Index               0.0091                       0.5160        1.00025 6% 3.2%
McDonald               0.0098                       0.5119        1.00019 5% 2.4%
Berkshire Hathaway Inc. (W.Buffett)               0.0105                       0.5112        1.00018 5% 2.2%
Pfizer               0.0115                       0.5078        1.00011 3% 1.6%
Facebook               0.0226                       0.5080        1.00010 3% 1.6%
Tesla               0.0318                       0.5096        1.00010 3% 1.9%
JPMorgan               0.0155                       0.5070        1.00010 2% 1.4%
Intel               0.0153                       0.5040        1.00001 0% 0.8%
**Gold (XAUUSD)               0.0094                       0.4951        0.99986 -3% 0%
*Ethereum               0.0634                       0.5138        0.99974 -6% 0%
General Motors               0.0178                       0.4903        0.99950 -12% 0%
General Electric               0.0164                       0.4868        0.99943 -13% 0%

*Ethereum Data since Aug 7, 2015, source coinmarketcap.
**Gold since 1970 has been a bit better with +3% yearly compounded gain.

The first comparison to make is with the main competitors of bitcoin, credit cards. I’m surprised to see how good are quantitative parameters of Mastercard and Visa, on the other hand they are monopolies, perhaps that’s why the CEO of mastercard hates so much Bitcoin, he sees it as a strong threat. Even Amazon has worse parameters compared to Visa and MC.

I included only Ethereum  in the comparison because in terms of market cap is second to Bitcoin, its yearly yield G is negative and i’m not surprised because I remind you that volatility reduces by far the yield G and in the case of all altcoins, not only Ethereum, the volatility reaches very high levels and therefore as an investment vehicle altcoins in general are absolutely not recommended, can eventually be considered as purely speculative assets for short-term trading.

Unfortunately for Mr.P.Schiff, in the last ten years Gold performed badly, for your curiosity i computed Gold parameters using available daily data since January 1970 and its yearly gain G or yield has been +3%, nothing exceptional, basically Gold protected you against inflation in the last fifty years but nothing more then this.

As i said 20 days ago Bitcoin volatility is dropping but it remains very high compared to other assets, despite this Bitcoin yearly compounded gain G is an astonishing +38% and it’s the best investment vehicle of the world.
Compared to other bitcoin price models this value is not much, ten years from now compounding 38% yearly bitcoin should be at around 200k usd while, for example, the stock to flow model has a forecast of 10 millions usd after 2028 halving, this is the equivalent of 144% yearly compounded gain instead of 38%.
Let me know what you think, does the stock to flow model price return appear realistic to you or not? Personally i prefer to rely on numbers and they say a clear “no” to me. This is why i’m a bit skeptic about also the bitcoin price model i developed on tradingview but i’m curious to see how it’ll end in a couple of years.

Tech Addendum

The concept of entropic analysis of equity prices is old and it was first proposed by Louis Bachelier in his “theory of speculation”, this thesis anticipated many of the mathematical discoveries made later by Wiener and Markov underlying the importance of these ideas in today’s financial markets. Then in the mid 1940’s we have had the information theory developed by Claude Shannon , theory that is applicable to the analysis and optimization of speculative endeavors and it is exactly what i’ve done just applied to bitcoin and the other assets considered in the above table, especially using the Shannon Probability or entropy that in terms of information theory, entropy is considered to be a measure of the uncertainty in a message.
To put it intuitively, suppose p=0, at this probability, the event is certain never to occur, and so there is no uncertainty at all, leading to an entropy of 0; at the same time if p=1 the result is again certain, so the entropy is 0 here as well. When p=1/2 or 0.50 the uncertainty is at a maximum or basically there is no information and only noise.

Applying this entropy concept to an equity like a stock or a commodity or even bitcoin itself common values for P are 0.52 that can be interpreted as a slightly persistence or tendency to go up, this means that for example stock markets aren’t totally random and up to some extend they are exploitable, same for btc.
Knowing the entropy level of bitcoin/usd is crucial if we want to compute its main quantitative characteristics, as i explained in the technical background of my blog this process is quickly doable once you have all the formulas, the process is as follows:

To compute the Shannon Probability P you should follow these steps:

  1. compute natural logarithm of data increments (today price / yesterday price)
  2. compute the mean for all data increment computed in step 1
  3. compute RMS (root mean square) of all data increments, squaring each data increment and sum all togheter
  4. Compute price momentum probability with the formula P = (((avg / rms) – (1 / sqrt (n))) + 1) / 2
    where avg = data computed in step 2, rms = data computed in step 3, n = total samples of your dataset. If the resulting probability is above 0.5 then there is positive momentum, otherwise under 0.5 negative momentum

To compute the Gain Factor use the following formula:

G = ((1+RMS)^P*((1-RMS)^(1-P))

To compute the yearly gain G or growth just raise daily gain G to the 365th power for Bitcon or 252 for stocks (252 trading days in a year).

Long Term Update: 2018 Outlook with entropic methods

Every beginning of a new year i post an outlook using entropic methods explained in the technical section of this blog. Here you can find the 2015, 2016 and 2017 forecast update, where you can find more information about this approach.

Updated values for bitcoin (in brackets values of last year) using daily data since August 2010 (average of 4 exchanges when possible).

 BTC/USD
Growth Factor G 1.0028 (1.0007)
Shannon Probability P 0.5384 (0.519)
Root mean square RMS (see this as volatility) 0.059 (0.045 )

Bitcoin’s entropic values versus the Usd strongly improved in 2017 but volatility increased a bit, despite this the Growth Factor (G) increased up to 1.0028% (remember that volatility is detrimental to the Growth Factor) compounded daily or 280% yearly up from 30% of 1y ago. Also the optimal fraction of your capital to invest in bitcoin improved in 2017 with a 7.7% instead of 6.4% of 1y ago.

 2018 Price forecast  Full volatility  Half volatility
Forecast using only G* ~38700$ ~38700$
Upper bound adding volatility ~121000$ ~68000$
Lower bound subtracting volatility ~12300$ ~21800$

*38700 is obtained with today price (around 13800$) times (1.0028^365)=~2.77
13800*2.77=38740, just change 365 with the number of days you prefer for a different forecast.

It’s interesting to notice that with reduced volatility the support level is above the actual quote of XBTUSD (13800$ at the moment i’m writing) because the growth factor (G) is very high and is skewing everything to the upside. If volatility stays low the uptrend should push bitcoin above 22k USD during the year without too much effort, it’s a scenario i prefer instead of wild price swings.

What went wrong in 2017?

A year ago, I forecasted a top of $2900, reached in July 2017 with an intermediate Top well ahead of the end of the year. I tried to double the volatility factor (rms) to see the next level after a reader asked me about the possibility that bitcoin was in a bubble above 2900$. The next level was around 6000$, again this new level has been broken at the end of October.
The last 2 months have been crazy and the explanation is a huge change in shift in this market happened in March 2017 (with altcoins literally exploding) that basically erased the reliability of the January 2017 forecast. I think that this year forecast should be more accurate compared to last year.

Conclusions

For this year i think that i’ll consider the support/resistance levels obtained with a full volatility value with the result to have for the whole 2018 a good probability to stay inside the 12300$-121000$ price zone.
At the same time i think that at the end of a strong buying climax period, if any, it will be wise to reduce your bitcoin investment if the price goes above 60k-70k USD.

I’m at your disposal for any questions; see you at the next update and Happy New Year!