Dec 12, 2018

**Bitcoin & the Logarithmic Growth Curve by **dave the wave

*DISCLAIMER; This post and its contents should in no way be considered investment advice.*

**SUMMARY**

This is the first piece to come out of our contributor series which represents market analysis by individuals independent of the MAX Exchange, helping to write quality content on our platform in a freelance capacity. In this first article, @davthewave looks at the model of logarithmic growth in so far as it may help investors identify not only the long term trend of prices for Bitcoin, but also identify a possible end of the corrective phase of the present cycle**. **Looking forward @davthewave speculates the next parabolic spike may come in 2022.

**Bitcoin and the Logarithmic Growth Curve**

Many things in life follow growth curves, logarithmic or exponential. Exponential growth is seen in things such as compounding interest in a bank account, or a ballooning amount of followers on a social media site — the gains come slowly at the start, and only later really begin to take off. Logarithmic growth on the other hand is seen where the gains come quickly at the start and then begin to taper off toward a plateau. Bitcoin is an example of the latter.

Growth comes in cycles [with cycles culminating in exponential spikes and corrections]. During an earlier cycle in Bitcoin, the model of the log growth curve had been applied by various analysts. Here we have the example of an early chart by Trololo posted to Reddit in 2014.

What is of significance here is the use of the curve as a mean of prices. Prices are thought to oscillate around that mean both to the upside and downside, thereby enabling both future price prediction and optimal entry points. Quite remarkable with Trololo’s example is his prediction of price at a mean of 10,000 at the end of 2017, and this at a time when the price was well below 1,000 during the previous correction in 2014. Though BTC is currently well down from the 10,000 range to the 3,000 range, this is still roughly in keeping with Trololo’s model as the following chart illustrates.

Though the 10,000 target was indeed met, that came near the top of the parabolic spike up. Given we are now in another corrective phase that is looking as deep as the former, it seems clear ,with the benefit of hindsight, that the log growth curve should be drawn lower.

Even before the very recent capitulation of price from the 6,000 range to the 3,000 range, it made sense, with the long term investor’s perspective in mind, to start focusing on the log growth curve. For multi-year trend-lines, extending in straight lines, always have to be problematic on the logarithmic scale — a straight line stretching upward represents a continuous rate of appreciation [acceleration], which is clearly impossible as the following chart portrays. Even before the recent market capitulation, it was apparent that the long term trend line would not hold due both to the nature of the log scale and the evidence of a developing growth curve. Also notice that the curve as a mean of prices is drawn lower here.

As investors are most interested in long term trends, the growth curve on the log scale starts to become more compelling given the nature of explosive logarithmic growth, the cyclic volatility of Bitcoin, and the redundancy of long term trend-lines [better suited for shorter term charts].

Also, with the recent capitulation of price, it begins to make sense to use the log growth curve, previously used as a mean, as support in a more technical manner. For long term linear trend-lines, always prone to be eclipsed, due to the nature of the log scale, have indeed become redundant with recent price developments. And here a few chartists had already been using the curve to inform their predictions of a future range or channel. Here is an interesting example published in early 2018 on Twitter by @KunalDaSen

Insightful though it is, with the growth curve transitioning into TA [and one that focuses primarily on the phenomenon of halving], my point of criticism with it is the widening channel. The channel lines in this chart appear to be almost diverging, whereas I think any channel created by the logarithmic growth curve is better portrayed as converging. The reason why this channel should converge [and so far is] is that a maturing market will tend to lead to increasing price stability. As Bitcoin becomes more liquid, it becomes less volatile. Given the principle of the growth curve, this increasing price stability should incrementally come into fruition, with subsequent cycles, as the real volatility of those cycles diminish. These subsequent cycles also see the law of diminishing returns coming into effect though at this relatively early stage of the curve, future returns are projected to remain on quite a different scale to that of traditional asset classes.

And this is in fact what is observable in the long term chart of Bitcoin. The following chart looks to modify the previous chart in order to incorporate this principle of decreasing volatility. Besides depicting lessening volatility in the macro sense, the trend of the channel shows current support and future price direction.

In this chart, the growth curve is drawn to accommodate as many of the previous points of price as possible on the long term chart. Note that the channel lines are converging, signalling a reduction in real cyclical volatility. This is confirmed with the measurements of each subsequent cyclical peak — the rise in percentage terms, as measured from the base, is decreasing. Also useful here is the MACD, a major momentum indicator, that further confirms this reducing volatility — the trend lines connecting peaks and troughs are converging. It is of interest to note that presently, after this recent capitulation event in the market, price is sitting right in the lower band of the channel. From a purely charting perspective, it’s arguable that this lower band currently provides support.

Finally, one last chart focusing on a comparison of the cycles, of which three are identified. As opposed to the standard fib, which can only measure nominal prices, I use the channel fib here. In measuring the ‘y’ axis, the axis that gives you the rate of appreciation, the channel fib enables a comparison of cycles in real terms on the logarithmic scale.

Notable in this chart is the correction of the previous cycles to the 0.382 level of the Fibonacci retracement. Whereas many are presently waiting for a ‘fuller’ correction, based on an equal correction in nominal terms from peak price compared to the previous cycle [85%], the above chart actually measures this cycle having already further corrected than the previous, suggesting that the bottom may well be in.

In conclusion, I’ve hoped to illustrate the nature of the growth curve as it relates to both the long term trajectory of Bitcoin, and the medium term price direction at this juncture. Bitcoin may be at, or very nearly at, the end of the corrective and final phase of this current cycle. Going forward, I expect to see price stabilize along the log growth curve [traced here as support] for a year or so, an extended period of accumulation before the next move up through the channel, where price will reclaim its previous all time high. Given the nature of the time extension of each subsequent cycle, the next parabolic spike may come in 2022, but that would be the topic for another article.

DISCLAIMER; This post and its contents should in no way be considered investment advice. We may individually hold positions in some of the assets we discuss. Any projections, conclusions, analysis, views are to be considered hypothetical & for informational purposes only & not meant as recommendations for investment. Anyone considering an investment in crypto should only invest what they can afford to lose. You alone are responsible for evaluating the risks & merits of our content.