Unlock the Hidden Value of Bitcoin: Your Step-by-Step Guide to Understanding Its True Worth with Power Law
In this article, my objective is to explain the concept of the power law and how it can be utilized to predict the price of Bitcoin. I’ll avoid technical jargon as much as possible. Giovanni Santostasi, who has a background in physics, proposed the use of this model for predicting Bitcoin prices in 2018. The model appears to have stood the test of time and is quite robust.
The Power Law
The power law is a type of mathematical relationship where one quantity varies as a fixed power of another.
In the context of Bitcoin:
where,
To understand if this relationship holds, take the logarithm of both sides (any base will do, but I use base 10 like Santostasi, so “log” is actually log base 10):
This is a linear equation. If we plot log(BTCUSD) vs. log(tsGB):
We observe that the trend is indeed linear. A simple linear regression of log(BTCUSD) vs. log(tsGB) yields:
with an adjusted R_squared of 95%, which is a very good fit.
How Do We Predict the “Fair Price of Bitcoin?
The orange line in the chart below is the regression line:
Now, what does this mean?
It means that the Bitcoin price (actually the logarithm of the Bitcoin price) fluctuates around this orange trend line, which can be deemed as the fair price of Bitcoin for the sake of simplicity.
Visually, as of May 19, 2024 (the date when this graph ends), it seems that the price of Bitcoin is very close to its fair value. Indeed, for May 19, 2024:
which implies that the fair price of Bitcoin is:
Where Are We Currently At?
On May 19, 2024 BTCUSD was 66,950 which is 2% below the fair price.
In all of these calculations, I used the maximum number of significant figures, but I only show two decimals for the sake of readability.
I guess this is simple enough.
Is This Model Robust?
Can we rely on this model?
Up until now, it seems to hold pretty well.
The following chart depicts the evolution of the slope of the regression line (the power “n” in the log-log equation) right from the start:
The power “n” seems to be in a steady state (fluctuating very little) since 2016. Hence, the model is pretty robust.
What Next?
The extent of deviations from the fair price can be used for trading Bitcoin.
This will be the topic of the next article.
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