Bitcoin’s Logarithmic Growth Curve — a Rationale for the Pragmatic Investor

11 min readMay 14, 2021

Bitcoin today must appear as something of a quandary to the more cautious investor. Out of nowhere it has exploded onto the scene, and in the course of a decade has gone from strength to strength. And yet it seems so volatile as to defy any standard of valuation with which investors might feel they better understand it — they’re more often than not left wondering if it’s just a super speculative bubble, ‘all noise and fury signifying nothing’. Though no doubt it has certainly appeared to be that at times, and especially on the lengthy corrections, this article will seek to outline a rational and real trend that underlies these appearances to the contrary. In doing so, it seeks to provide a rationale by which the more cautious investor might start gaining some exposure to this ‘asset class’.

The trend identified is the logarithmic growth curve [LGC]. It’s a phenomenon to be found elsewhere in nature — something first exhibits explosive growth, then sees that growth increasingly taper off until eventually achieving a plateau. If the developing market price of Bitcoin exhibits an LGC, then this suggests that Bitcoin, an incredibly intricate technology, is also [or more strictly, it’s market price] is something of a force of nature [this makes sense when you think of a market as a great mass of people that bid up and down prices]. The nature of this LGC has been previously discussed in an article two years ago, where not only was the LGC first analyzed, but also used in a more technical sense in order to predict price development. Those predictions made back then have largely been confirmed. This current article is something of a companion piece to that previous one.

Transitioning, as it has, from barely registering as an asset class to a quarter of a trillion dollar market cap in such a short time, Bitcoin’s extreme volatility should come as no surprise. At times, it has seemed to be quite literally ‘off the charts’, as something wild and incomprehensible, the very epitome of chaotic speculation. And so my aim here is to offer an interpretation that might make perfect sense out of Bitcoin’s erratic behavior. The aim is to bring Bitcoin pragmatically down to earth, without the hype on the one side, and the ‘aversion’ on the other, in order that any rational investor could begin to consider it as part of their portfolio. My twin focus here will be on the long-term actual trend of the chart, and then on a macro-economic explanation for that trend.

Whereas the LGC has been used as a support of prices, in a more technical manner [where previous to that, it had been used as a mean of prices], I’ll further look at how this phenomenon of an LGC [for a phenomenon it is] could be explained. The kinds of questions that interest me here are — why should price develop in this way? Could such a price development be undermined if deflationary forces in the wider economy get the upper hand? And is Bitcoin an unsustainable bubble? It’s these questions, of a macro-economic nature, that must also be of interest to those who may have so far observed Bitcoin’s rise at a distance from the sidelines.

Figure 1. The Logarithmic Growth Curve.

Figure 2. The LGC as zoomed in.

Where technical analysis seeks to predict future price, the logarithmic growth curve [LGC] provides an over-arching model for such predictions. Like any model, it should perform by having both predictive/ testable and explanatory aspects to it. In doing so, models serve to set out a rational case for a reasonable belief in something, which, in our case, amounts to whether longer term investment in Bitcoin might actually make sense at this particular point in time.

Given the background of an uncertain macro-economic landscape, the Bitcoin chart presents itself as something of a conundrum. On the one hand, with [hyper] inflationary concerns in mind, Bitcoin is considered to be the perfect response, where it functions as an inflation hedge, a sponge of sorts like any asset, to soak up all the excess liquidity perceived to be in abundance. We’re all familiar with the theory based as it is on money supply and central banks response to deflationary forces of one kind or another — the reflation of a deflating economy. On the other hand, those deflationary forces remain defiant [in spite of monetary theory], and hang like the sword of Damocles, over asset prices. You’d not have to go back many years to see central banks boasting that deflation was of zero concern given their ability to manage conventional currencies. With the benefit of hindsight [or with some scruples about a theory at that time], we can see it was not so. Once again, we’re all familiar with the countering theory of deflation.

When faced with the phenomenon that is Bitcoin, investors can find themselves stuck between a rock and a hard place, between two competing narratives calling for a decision. They may jump one way or the other, but may just as likely remain immobile and non-committal, like the proverbial mule of medieval times, unable to move [and eventually expiring from starvation] when confronted on either side with two equally attractive and equidistant piles of hay.

The way out of this dilemma, insofar as it involves investing in Bitcoin or not, is to re-think what Bitcoin actually is from a macro-economic perspective. If Bitcoin can be habilitated to both inflationary and deflationary narratives [arguably opposite sides of the same crisis coin], then investment in Bitcoin becomes a much less fraught decision.

What is common to both narratives here, as is typified in the ‘inflation/ deflation debate’, is an understanding of Bitcoin as an asset. It is due to this common understanding that one camp is willing to buy Bitcoin and the other is not — in inflation, asset prices go up; in deflation, asset prices go down. Yet the picture changes radically when instead of conceiving Bitcoin as an asset, we conceive of it rather as a currency. Now, for those also in the deflationary camp, or even for the undecided on the fence, Bitcoin becomes attractive. For in deflation, monetary value erodes out of assets and into [the strongest] currencies/ forms of liquidity, and Bitcoin, is just one such form of liquidity [though currently more of a ‘wildcard’ form]. And on the face of it, Bitcoin has always claimed to be a currency, a form of money, despite some re-conceiving it as only an asset. Indeed, it was in order to solve the perceived problems facing conventional currencies that it was created in the first place — a monetary response to a monetary problem. Of course, the obvious objection here is that Bitcoin is much too volatile to function as a currency, and is a point I’ll come to shortly.

Deflationary concerns also go some way to explaining the volatile swings in Bitcoin to the downside, which have always been proportional corrections to the previous exponential moves to the upside. As much of BTC investment ostensibly involves buying it as an asset/ inflation hedge, and then again on pure speculation, it’s no surprise that price should correct when uncertainty once again dominates the market, as to either the speculative price, or to the wider macro-economic landscape. Yet, once corrected, the price becomes more sustainable. This pattern of alternating explosive and corrective movements in the price [also seen as cycles] has led to the formation of a converging channel atop of the LGC [figures 1 and 2 above]. An extrapolation of this converging channel then gives you a picture of both eventual price discovery/ stabilization and reducing macro volatility [the convergence of the channel]. The volatility within the parameters of this converging channel are compatible with a market divided uncertainly between two narratives — the fear of missing out [FOMO] creates the spike, and then fear per se [of too high a speculative price] leads to the correction. But in the aggregate, you still see the macro trend of the LGC playing out, and it’s actually these existing deflationary concerns, the fear and uncertainty, that brings the volatile and speculative price back down to earth, or should I say, back to the LGC.

Which brings us back to the question as to how Bitcoin could be a currency if so volatile. As outlined above, a solid underlying trend is actually observable and distinguishable from the huge volatility that ranges back and forth from it. My explanation for this is that Bitcoin is a nascent currency in the process of capitalization, and hence the exponential moves, even while those moves are diminishing toward an eventual price discovery/ capitalization.

In keeping with this idea of Bitcoin as currency, the real and substantial parallel for Bitcoin, the newest form of money on the block, is not some asset class, but is rather gold, one of the oldest forms of money known to us. And indeed, Bitcoin has often been referred to as digital gold [for reasons most investors are no doubt aware of, and primarily involving the notion of scarcity]. Of course, if you don’t think of gold as a currency, you’ll struggle to think of Bitcoin as a currency [as they say, an ounce has always been able to purchase a fine suit and a decent pair of shoes]. Of course, Bitcoin is by many orders of magnitude more volatile against gold, just as it is against USD. Chart the two together, and one is near flat while the other is appreciating at a steep angle.

Figure 3. The relative appreciation of both BTC and gold as priced in USD.

Where gold has been fully capitalized over millennia, BTC has only had a decade to get going, and so is currently in that rapid process. It is this rapid process of capitalization that the LGC maps — first you see explosive growth, and then that growth, while remaining explosive, diminishes in relative terms. And of course, this is what you want from an alternative currency that is to function as a store of value — eventual price discovery and relative stability. With the capitalization of a nascent currency in mind, the more interesting chart that compares Bitcoin and gold is that which removes the third party of USD altogether — one that simply prices BTC in gold per se.

Figure 4. Bitcoin as priced in gold.

Here also you see a logarithmic growth curve [LGC] developing, and one predictive of price direction. It further supports the notion that Bitcoin is in the process of capitalization. It also serves to further confirm the LGC as seen developing in the BTC/ USD chart.

As Bitcoin matures in the marketplace, as it becomes increasingly capitalized, as liquidity increases, so too you’d expect to see a decreasing volatility in the macro cycles. And this is exactly what has been observed in the past. Extrapolate that trend, and price eventually plateaus, in relative terms, in the not too distant future. Looking at the LGC [figure 1], this may take a couple of decades. For the investor, this involves the notion of a diminishing ROI [return on investment]. Though the gains may no longer be astronomical, they are still projected to be stratospheric. And what is lost in the ‘wild west’ that was the early days of bitcoin, may be gained by seeing it mature into a more stable store of value.

Once the dual nature of Bitcoin is established, as both a currency and an asset, in much the way that gold is, any investor attracted to gold as part of their portfolio is likewise going to be attracted to Bitcoin… with the added benefit that this nascent currency has yet to be fully capitalized. Securing a position in both gold and Bitcoin offers that diversification which is always a fundamental consideration of any conservative portfolio.

Returning to the USD chart. As discussed, Bitcoin can clearly be seen to track a long-term trend, the LGC. For two years now [original article linked], price has tracked along a predicted narrow band at the base of the converging channel. This lower band I refer to as the ‘buy zone’. Currently, price is near the buy zone, and so an investment in a few tranches over a reasonable period of time would be appropriate insofar as one considered the LGC the long-term trend.

Figure 5. The buy zone.

As diversification has essentially been the rationale given for a pragmatic investment into Bitcoin, the investor might want to enquire of the alternative coins colloquially known as alts — if Crypto-currency is more than Bitcoin, why not buy alt coins also, or even instead of Bitcoin if their potential is greater?

The alt coins have certainly shown massive speculative gains in the past, and may do so again in the future, but their volatility equally outweighs Bitcoin’s to both sides. Of course, in being more speculative, they also offer a higher risk/ reward ratio. Their history, against USD, shows that they are best left to the shorter term/ cyclical position trader as opposed to the longer-term investor. That said, there would always be room for the more major ones [such as Ethereum for example] in a relatively conservative portfolio, but only if a position in Bitcoin was first established. This could involve something of a ‘layered approach’ [risk mitigation], where one’s core position in Crypto was Bitcoin, and subsequent exposure to other more speculative coins being acquired only after this central Bitcoin position was first established.

The following and final chart shows the relative appreciation of both Bitcoin and ETH as priced in USD.

Figure 6. BTC/ USD are relative to ETH/ USD.

After explosive growth [arguably two cycles in one as compared to BTC], ETH has managed to keep pace with BTC since the bottom put in near two years ago now. Along the lines of diversification, and the strategy discussed above, it certainly seems a reasonable [if more speculative] investment to layer in on top of BTC. The same could be said of other alternative coins such as NEO, ADA, and LINK, to name just a few. Depending on how speculative one wanted to get, they would rise like a great chain of speculation from the base that is Bitcoin. The cyclical history of Crypto essentially maps the rise and fall of this speculative excess, one that no doubt the more fleet-footed trader is more comfortable with than the investor.




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