Bitcoin Power Law

Source: williamgorfein.com


Support Line and Years Ahead Channels

Introduction

This website provides insights into Bitcoin's price behavior using advanced analysis focused on applying a power law to Bitcoin's historical prices. By examining historical price data, trendlines, and deviations from this power law, the goal is to explain long-term trends and identify relatively better or worse entry and exit times for Bitcoin. This work builds upon the contributions of @giovann35084111, @apsk32, and @moneyordebt, whose analyses have inspired this project.

The above chart uses a logarithmic scale for the Y-axis to display Bitcoin prices, ranging from 1 to 100,000, and a time scale for the X-axis, spanning from Bitcoin’s genesis block to present. The chart features several trendlines: the Support Trendline, calculated using the power law formula \(10^{−17.35} × (days)^{5.836}\), and additional trendlines showing 1 to 6 years ahead of the support trendline.

A power law is a mathematical relationship where one quantity varies as a power of another. In the context of Bitcoin, following a power law means that its growth can be modeled predictably over time, showing exponential increases. This behavior indicates that Bitcoin's price history can be understood and anticipated through its long-term trends and patterns.

By analyzing these deviations, investors can identify potential buying or selling opportunities based on historical trends. The support trendline offers a baseline for Bitcoin's price, while the "years ahead" lines highlight the extent to which Bitcoin's price deviates from this baseline.

As of December 22, 2024, the current price of Bitcoin is $96,430, which is 2.4 years ahead of its Support Trendline.

Calculation of Lead/Lag in Time

To calculate the lead/lag in time, we determine the ratio of the actual price to the model price and use this ratio to find the temporal deviation in years ahead or behind. The formula used is \(R = \frac{P_a}{P_m} = (\frac{T}{t})^k \), and \(\triangle{T} = t (R^{1/k} - 1) \) where \({P_a}\) is the actual price, \({P_m}\) is the model price, \({t}\) is the current time, \({T}\) is the theoretical time when the actual price matches the model price, and \({k}\) is the power law index.

A deviation below 1 year ahead is generally a good buying opportunity, while a deviation of about 4 years ahead often imminently precedes cyclical market tops in a bull cycle. Bitcoin follows a strong power law with an \(R^2\) greater than 0.95 relative to its trendline, indicating a high correlation between Bitcoin's historical price data and the power law model.

Years Ahead Deviations

Historical Years Ahead Deviations

The chart above shows the number of years ahead of the support line that Bitcoin's price was at any given historical date, including the most recent date. The X-axis represents the date, while the Y-axis shows the years ahead of the support trendline. This chart highlights extreme deviations and their implications, providing insights into potential buying or selling opportunities. Understanding these visualizations can help investors make more informed decisions about Bitcoin investments by emphasizing long-term trends and potential future price projections.

Bitcoin Price Projection with Years Ahead Metric

The Bitcoin Price Projection visual allows for an interactive exploration of Bitcoin's projected prices based on a specified number of years ahead. This tool is designed to provide a practical way to understand how Bitcoin's price could evolve over time, using the established power law trendline as a foundation.

To use this visual, you can adjust the "Years Ahead" slider to project Bitcoin's price a certain number of years ahead of the trendline. The interactive chart updates to show the projected prices for the selected period, alongside the historical prices and the Support Trendline.

The chart includes three key elements:

By analyzing these elements together, investors can gain insights into potential future price movements and identify periods of relative overvaluation or undervaluation. For instance, a significant deviation above the Support Trendline (e.g., 4 years ahead deviations or greater) might indicate a period of speculative excess, while a price closer to or below the trendline could suggest a buying opportunity.


Created By

William Gorfein © All rights reserved

williamgorfein.com