# Bitcoin Bubbles and e-folding

### Are we near a cycle top?

*This is not investment advice. Bitcoin is highly volatile. Past performance of back-tested models is no assurance of future performance. Only invest what you can afford to lose. You must decide how much of your investment capital you are willing to risk with Bitcoin. No warranties are expressed or implied. *

**Four Year Cycle**

Bitcoin has a clear four year cycle driven by the shock-to-flow of the block reward subsidy that is cut in half each cycle. The three halvings to date occurred in November 2012, July 2016, and May 2020, after 4, 8, and 12 Block years had elapsed from Bitcoin’s first block in January 2009.

In this analysis we use Block monthly data, with each month representing 4375 blocks, and each Block year having a duration of 52,500 blocks. The halving cycles for Bitcoin are separated by exactly 4 Block Years or by 210,000 blocks.

This is the natural calendar to evaluate Bitcoin price and market cap behavior given the strong influence of the halvings on price behavior. In practice, Block years are typically only a few percent shorter than Gregorian calendar years, reflecting average block times slightly shorter than the nominal 10 minutes. Difficulty adjustments every two weeks continually push the block time up or down toward the 10 minute nominal duration.

**Has Bubbles**

Bitcoin has high volatility, with standard deviations from a range of models (such as the Lindy power law, stock-to-flow, Weibull S-curve and Future Supply models) exceeding a factor of 2, approaching a factor of e (2.71828). Most models other than stock-to-flow show strong positive skew from their regression ‘fair value’ curves.

Bitcoin exhibits bubble-like behavior with large peaks each cycle occurring about one year or a year and a half after the halvings. The first peak occurred about 1.33 Block years after the prior halving and the second 1.5 Block years after its halving.

Can we realize that a bubble is about to burst? Wheatley et al. in a 2019 paper “Are Bitcoin bubbles predictable?” say yes. Their model is based on Didier Sornette’s Log-Periodic Power Law Singularity model which has found application to other financial markets, stress fractures, and earthquakes. They also assume a generalized Metcalfe Law for Bitcoin’s secular growth trend.

Sornette’s work across financial asset bubbles and examination of Bitcoin’s long-term price chart indicates that the price rise steepens as one heads into a blowoff top and a bear market phase back toward long-term support.

To be clear, we are not talking about tulips here; the price does not go to zero within a year or two. We are looking at a long term upward price trend that has bursts of irrational exuberance each cycle, fueled by the late entry of unsophisticated traders chasing price (FOMO). When a Bitcoin bubble burst in the past it always found support at the 200-week moving average (which is basically the four Block year cycle average). I cover this in the article Bitcoin’s Four Block Year Price Floor.

Sornette’s LPPLS model is complex, with four parameters and the need to identify a starting time for the local rise toward a bubble. It is “decorated with accelerating periodic volatility fluctuations” on top of a power law trend model. The question we want to address here is, given the limited number of long-term bubbles observed in Bitcoin to date can we identify something that works in practice and that is a much simpler mathematical calculation.

**e-Folds**

I propose that we simply look at how many e-folds in price increase have occurred in the past year. If the price rises by e (2.71828) in a year that is one e-fold, if it rises by a factor of e*e , that is, two e-folds. It is the natural log of the relative price ratio over a Block year timespan.

One can estimate the current e-fold value by taking the ratio of today’s price with that of a year ago. The ratio of the current (as of September 15th, 2021) price of $47,124 to $10,797 a year prior is 4.36 and its natural log is 1.47. The price has thus gone up by almost one and a half e-folds in the past year.

When the e-fold number peaks we could be close to the inevitable end of a bubble. Figure 1 below is a plot of both the long-term Bitcoin price and the number of e-folds of price increase in the prior year.

What we see in the graph is that the e-fold number (green line) rises and falls and itself exhibits peaks spaced roughly four years apart and about a year or so after the halvings (indicated by arrows). Although the price series and e-fold number series are uncorrelated overall (R^2 = 0.00) they have nearly coincident cycle peaks.

In the case of the third peak, we don’t know whether it has occurred or not. If we have seen the peak already when the price reached $64,000, it was just about a Block year after the third halving. Or the peak may be yet to come. Based on the prior two cycles it should occur before the current Block year elapses, probably by next May.

Prior peaks occurred at 3.64 and 2.80 e-foldings, whereas to date for this cycle the largest e-fold number achieved is 2.34. Bitcoin’s high volatility is gradually decreasing so this may reflect that.

**Near Next Peak?**

Table 1 below summarizes the peak times, and the lead time of the e-fold peak relative to the price peak. It also summarizes the peak price and the minimum price within the next two years afterward. Both minima occurred fourteen Block months after the price peak.

Following the 2013 peak in price of $873, the following Block monthly low was at $217, a factor of 4 lower price. Following the 2017 peak in price of $16,700 the following low was at $3582, a factor of 4.7 lower in price.

If we have not yet seen the peak for this Block era, then we should expect the green e-folding curve to continue rising in concert with the price of Bitcoin. If there is a divergence between the two curves then we may have seen a top for this cycle.

See my previous article on the advantages of dollar cost averaging:

Bitcoin, although volatile, is a premier savings asset, treat it as such.

## Create your profile

## Only paid subscribers can comment on this post

Sign in## Check your email

For your security, we need to re-authenticate you.

Click the link we sent to , or click here to sign in.