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Bitcoin Power Law Global Liqudity Model by G. Santostasi
Atualizado
In recent studies, we've observed a notable correlation between Bitcoin's price and global liquidity metrics. This relationship reveals significant insights into Bitcoin's price movements and offers a new perspective on using macroeconomic indicators to understand and predict Bitcoin's market trends.
Our analysis shows that Bitcoin's price exhibits periodic bubbles, which seem closely associated with oscillations in global liquidity. Notably, the overall price path of Bitcoin appears to be a complex function of global liquidity. This relationship is not as simple as the Bitcoin Power Law in time that can be described with a simple equation, Price ∼ time⁶.
Instead, we have developed a polynomial model to describe this complex relationship between liquidity and Bitcoin price. With a 4-degree polynomial (with 5 different parameters needed to fit the data), we can get a decent fit to the data.
The fit is obtained using 500 data points by polynomial regression. The vector coefficients of the polynomial are obtained such that the sum of squared error between the observations and theoretical polynomial model is minimized.
This model needs to be taken with a grain of salt given the warning by famous mathematician Von Neumann: "With four parameters I can fit an elephant, and with five I can make him wiggle his trunk." discussing a model created by Italian Physicist Fermi. By this he meant that the Fermi simulations relied on too many input parameters, presupposing an overfitting phenomenon.
We can still gain some insights into the relationship between Global Liquidity and the price evolution of Bitcoin using this complex model.
When the price of Bitcoin is plotted against our global liquidity index, we observe a polynomial relationship. This model allows us to see when Bitcoin's price deviates significantly from the predicted value based on global liquidity:
Above the Model: When Bitcoin's price is above the polynomial fit, it indicates a potential lack of sufficient liquidity to support the current price level, suggesting a likely correction.
Below the Model: Conversely, when the price is below the fit, it implies that liquidity might be higher than what is reflected in the price, indicating potential upward movement.
Our global liquidity index comprises several key macroeconomic metrics from major financial institutions worldwide. Here are some of the major components:
RRP (Reverse Repurchase Agreements): This metric indicates the level of liquidity in the financial system through temporary sales of securities with an agreement to repurchase them.
FED (Federal Reserve System): Represents the balance sheet of the US central bank, reflecting its monetary policy actions.
TGA (Treasury General Account): Reflects the US Treasury’s cash balance, impacting the liquidity in the banking system.
PBC (People's Bank of China): Shows the monetary policy actions and liquidity management by China’s central bank.
ECB (European Central Bank): Represents the balance sheet and liquidity management actions of the Eurozone's central bank.
BOJ (Bank of Japan): Reflects Japan's central bank's monetary policy and liquidity measures.
Other Central Banks: Includes metrics from various other central banks like the Bank of England, Bank of Canada, Reserve Bank of Australia, etc.
M2 Money Supply: This includes money supply metrics from various countries like the USA, Europe, China, Japan, and other significant economies.
These components collectively provide a comprehensive view of global liquidity, which is crucial for understanding its impact on Bitcoin's price.
Using the polynomial model and the author's Bitcoin power law model we can create 2 oscillators, one that shows deviations from the trend (normalized to the price to make the peaks more uniform) and the other showing deviations of the polynomial liquidity model from the power law trend.
The oscillators show the difference between the price and the power law model relative to the price, Orange Line. The Blue Line is instead the difference between the Global Liquidity Model of the price and the power law model relative to the model itself. The two oscillators can be overlayed to show their differences and similarities.
Analysis: In addition to similar observations from the discussion above we can see that most Bitcoin bottoms are not directly associated with bottoms in the liquidity model indicating a different mechanism at play that determines Bitcoin bottoms (probably due to miners' capitulation).
Using the new force_overlay function we plot the polynomial liquidity model directly over the Bitcoin price chart while we display the 2 oscillators in a separate panel.
Our analysis shows that Bitcoin's price exhibits periodic bubbles, which seem closely associated with oscillations in global liquidity. Notably, the overall price path of Bitcoin appears to be a complex function of global liquidity. This relationship is not as simple as the Bitcoin Power Law in time that can be described with a simple equation, Price ∼ time⁶.
Instead, we have developed a polynomial model to describe this complex relationship between liquidity and Bitcoin price. With a 4-degree polynomial (with 5 different parameters needed to fit the data), we can get a decent fit to the data.
The fit is obtained using 500 data points by polynomial regression. The vector coefficients of the polynomial are obtained such that the sum of squared error between the observations and theoretical polynomial model is minimized.
This model needs to be taken with a grain of salt given the warning by famous mathematician Von Neumann: "With four parameters I can fit an elephant, and with five I can make him wiggle his trunk." discussing a model created by Italian Physicist Fermi. By this he meant that the Fermi simulations relied on too many input parameters, presupposing an overfitting phenomenon.
We can still gain some insights into the relationship between Global Liquidity and the price evolution of Bitcoin using this complex model.
When the price of Bitcoin is plotted against our global liquidity index, we observe a polynomial relationship. This model allows us to see when Bitcoin's price deviates significantly from the predicted value based on global liquidity:
Above the Model: When Bitcoin's price is above the polynomial fit, it indicates a potential lack of sufficient liquidity to support the current price level, suggesting a likely correction.
Below the Model: Conversely, when the price is below the fit, it implies that liquidity might be higher than what is reflected in the price, indicating potential upward movement.
Our global liquidity index comprises several key macroeconomic metrics from major financial institutions worldwide. Here are some of the major components:
RRP (Reverse Repurchase Agreements): This metric indicates the level of liquidity in the financial system through temporary sales of securities with an agreement to repurchase them.
FED (Federal Reserve System): Represents the balance sheet of the US central bank, reflecting its monetary policy actions.
TGA (Treasury General Account): Reflects the US Treasury’s cash balance, impacting the liquidity in the banking system.
PBC (People's Bank of China): Shows the monetary policy actions and liquidity management by China’s central bank.
ECB (European Central Bank): Represents the balance sheet and liquidity management actions of the Eurozone's central bank.
BOJ (Bank of Japan): Reflects Japan's central bank's monetary policy and liquidity measures.
Other Central Banks: Includes metrics from various other central banks like the Bank of England, Bank of Canada, Reserve Bank of Australia, etc.
M2 Money Supply: This includes money supply metrics from various countries like the USA, Europe, China, Japan, and other significant economies.
These components collectively provide a comprehensive view of global liquidity, which is crucial for understanding its impact on Bitcoin's price.
Using the polynomial model and the author's Bitcoin power law model we can create 2 oscillators, one that shows deviations from the trend (normalized to the price to make the peaks more uniform) and the other showing deviations of the polynomial liquidity model from the power law trend.
The oscillators show the difference between the price and the power law model relative to the price, Orange Line. The Blue Line is instead the difference between the Global Liquidity Model of the price and the power law model relative to the model itself. The two oscillators can be overlayed to show their differences and similarities.
Analysis: In addition to similar observations from the discussion above we can see that most Bitcoin bottoms are not directly associated with bottoms in the liquidity model indicating a different mechanism at play that determines Bitcoin bottoms (probably due to miners' capitulation).
Using the new force_overlay function we plot the polynomial liquidity model directly over the Bitcoin price chart while we display the 2 oscillators in a separate panel.
Notas de Lançamento
Added a shading indicating areas where the price is above the liquidity price model or vice-versa. 
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