Estimating Bitcoin’s Adoption Curve and Maximum Price (December 2020)

Estimating Bitcoin’s Adoption Curve and Maximum Price 15 December 2020

RESEARCH NOTE 15 December 2020

Estimating Bitcoin’s Adoption Curve and Maximum Price Executive Summary 

Bitcoin’s maximum price probably lies in the range of $1 million to $10 million USD. This maximum price would likely be reached in the next 15 to 30 years.

 Bitcoin’s adoption curve follows a path very similar to that of internet adoption. Both adoption functions can be modeled with a Gompertz curve.

 The theoretical maximum price does not incorporate the possibility of negative events, which would further reduce the value of the bitcoin network. These obstacles include internet access, government intervention, competition, and obsolescence.

Source: Our World In Data

FIGURE 1

Diffusion of Innovations Diffusion of innovations is a theory that explains the rate at which new ideas and technology spread and are eventually adopted. The distinction between adoption and diffusion is subtle: adoption is an individual process describing the stages one undergoes from first hearing about a product to finally adopting it, whereas diffusion is a group phenomenon which suggests how an innovation spreads. Diffusion happens in an ecosystem and individual adoption is the result.

The categories of adopters are innovators, early adopters, early majority, late majority, and laggards.

Within this adoption schema, there is a point at which an innovation reaches critical mass.

Diffusion Models The most common model for diffusion is a logistic curve [Figure 1]. The blue line indicates the periodic uptake of the technology, and the yellow line is the cumulative total uptake over time.

Source: Wikipedia

Another function is the Gompertz trend curve [Figure 2]. It is a similar sigmoid function which describes growth as being slowest at the start and end of a given time period. However, the right-hand or future value asymptote of the function is approached much more gradually by the curve than the left-hand or lower valued asymptote. This means the majority do not adopt until after peak exposure; there are more laggards than leaders.

15 December 2020 FIGURE 2

data for bitcoin and the internet. Presented are various “goodness of fit” statistics for each.

INTERNET ADOPTION CURVE t

p

R2

RMSE

Gompertz

-7.39

0.00

0.77

101.94

Logistic

1.78

0.09

0.73

2121.76

BITCOIN ADOPTION CURVE

and regressing

φ ≡ ln [ln(Δ𝑥𝑥𝑡𝑡 )] φ = 𝜕𝜕 + 𝛾𝛾𝛾𝛾 + 𝜏𝜏𝑡𝑡 2

and selecting based on the t-statistics for τ and γ, where τ significance would indicate a logistic function and γ significance would indicate a Gompertz 2 2 function. Alternatively, one could evaluate R or Χ for φ ∶ τ and φ ∶ γ.

Bitcoin and the Internet

Frances’ method was applied to Bitcoin in Peterson [2019]. Using updated data, it is applied here using

Estimating Bitcoin’s Adoption Curve and Maximum Price

RMSE

Gompertz

1.03

0.34

0.15

16.50

Logistic

-.70

0.51

0.06

123.15

However, the overall trend of bitcoin adoption is comparable to that of the internet [Figure 3]. The values for bitcoin shown in Figure 3 are based on user growth; data for internet users is obtained from www.internetworldstats.com/emarketing.htm.

FIGURE 3 100,000,000

Bitcoin and Internet Growth

10,000

10,000,000 1,000

1,000,000 100,000

100 10,000 1,000 100

10 Bitcoin Users

Internet Users (Billions)

Franses [1994] proposes a parametric selection method. This method involves defining

R2

Internet Users

10

1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Curve Selection

p

Every statistic favors Gompertz as the diffusion function for both the internet and bitcoin. Bitcoin’s statistics are less impressive because there are fewer data points (n = 9) versus the internet (n = 29).

Bitcoin Adjusted Active Addresses

The Gompertz and logistic trend curves are often applied in forecasting market development. One of the most important differences is that the Gompertz process is asymmetric, whereas the logistic curve is a symmetric process. To the naked eye, and early in the diffusion process, Gompertz and logistic functions appear similar.

However, the selection of the appropriate curve is important, because using an inappropriate growth curve can have a substantial impact on forecasting.

t

Years Since Inception (Internet = 1995)

Example: Internet Adoption Rates and Value of the Internet Given a set of data known to follow a Gompertz curve, Stata will estimate the curve parameters of the function

2

15 December 2020 −𝑏𝑏(𝑡𝑡 − 𝑐𝑐)

FIGURE 6 Internet Value and DJ Internet Composite

DJ Internet Composite

where a is the asymptote, or saturation value. Once a, b, and c, are estimated, the curve can be extrapolated to future periods (Figure 4).

FIGURE 4 Estimated Actual and Forecast Internet Users 12,000

Internet Users (Millions)

10,000

60,000,000

3000

50,000,000

2500

40,000,000

2000

30,000,000

1500 1000 500 0

20,000,000 10,000,000 0

8,000

The fit is exceptional. The goodness of fit statistics for 2 2 Figure 6 are R = 0.97 (97% fit) and Χ = 0.00 (0% probability of sampling error). The conclusion is there is compelling evidence that the internet, as a network, follows Metcalfe’s Law and that the long-term value follows a Gompertz function.

6,000 4,000 2,000 0

The relationship between network value and users is 2 not 1-for-1. Value grows proportional to n according to Metcalfe’s Law (Figure 5). Note: the value shown at right is not dollars, it is merely an index value.

FIGURE 5 Network Users vs. Network Value

We can surmise from the above that the DJ Internet Composite is currently overvalued relative to longterm trends, an assertion that is supported with other metrics such as Price/Earnings and Price/Sales. Also consider that the forecasted values are estimates based on several assumptions; the actual growth pattern and associated price levels may be higher or lower than this estimate.

7 20

6 5

15

4 10

3 2

5

1

Network Value (Billions of users2)

25

8 Internet Users (Billions)

3500

Internet Metcalfe Value (Users2)

𝑛𝑛 = 𝑎𝑎𝑒𝑒 −𝑒𝑒

0

Users

2049

2046

2043

2040

2037

2034

2031

2028

2025

2022

2019

2016

2013

2010

2007

2004

2001

1998

1995

0

Value

Network value is also a Gompertz curve, but one with a faster acceleration and higher terminal value. Using market data from the Dow Jones Internet Index, we can compare the expected value from Figure 5 to the observed value (Figure 6).

Estimating Bitcoin’s Adoption Curve and Maximum Price

Bitcoin Adoption Rates and the Value of Bitcoin Using the same approach just demonstrated, determining Bitcoin’s adoption curve, and therefore it’s estimated saturation value, is relatively straightforward. Saturation value is the terminal value at which the technology has been fully adopted. At the saturation point, demand has stabilized. The technology is used by a constant, rather than growing, portion of the population.

Long-term price appreciation then only occurs through inflation or supply decreases. With bitcoin, only the latter would be applicable.

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15 December 2020

FIGURE 7 Bitcoin Historical Price and Forecast Saturation Price

FIGURE 8 140 120 Trillions of US Dollars

User growth is estimated through on-chain metrics of network use such as active addresses and non-zero balance addresses. The resulting user estimate is used to determine an estimate for Metcalfe Value and hence Bitcoin Price in Figure 7 [Peterson, 2018; Peterson 2019].

Forecast Bitcoin Reserves (Blue) vs. Forecast Gold Reserves (Red) and Forecast US Equity (Green)

100 80 60 40 20

10,000,000

0

1,000,000 100,000 10,000

On the assumption that bitcoin’s value is determined independent of global economic cycles, it may be the case that bitcoin never overtakes gold as a reserve asset [Desjardins 2020]. Then again, gold has a 6,000year head start on bitcoin.

1,000 100 10 1 2050

2048

2046

2044

2042

2040

2038

2036

2034

2032

2030

2028

2026

2024

2022

2020

2018

2016

2014

2012

2010

0

Relative Value A terminal value for bitcoin of between 1 and 10 million dollars would equate to a total reserve value of $14 – $140 trillion by 2050. In calculating this figure, an available coin supply of 14 million bitcoin is used, rather than the often cited 19 or 21 million supply used to calculated “market capitalization.” The latter does not account for irretrievably lost bitcoins and overstates the total value [Cane Island 2020].

“Reserves” is also a better suited nomenclature. Since reserves are associated with stores of value and market capitalization is associated with equity and debt. Since bitcoin is not issued to “capitalize” any venture, it does not make sense to refer to it in this manner.

Gold prices follow long-term economic cycles, and the average annual return fluctuates between -1% in good economies to +13% in bad economies. Average US equity returns range from +12% in good economies to -2% in bad economies [Peterson, 2018b]. These cycles are represented in Figure 8, along with a forecasted bitcoin reserve value.

Estimating Bitcoin’s Adoption Curve and Maximum Price

More importantly, the asset class size for gold and equity serve as a reasonableness check on bitcoin’s reserve value. Bitcoin’s limitations make it unlikely that it will ever become a global currency in the traditional sense. It’s most likely use case is as a digital but spendable store of value for developed countries, and a “currency of crisis” for at-risk and failing economies. Accordingly, it seems there are no reasonable scenarios where bitcoin permanently overtakes equities, debt, commodities, or real estate in terms of absolute value.

Constraints on Bitcoin’s Saturation Price Not every technology reaches saturation. Further, adoption rates associated with emerging technologies are not constant, and subject to several impediments.

For bitcoin, there are several considerations:

Barriers to adoption of underlying technology Bitcoin requires electricity and internet to function.

Over 40% of the worlds’ population is currently unable to access the internet (Figure 9). Bitcoin’s saturation is ultimately a function of those that can access it.

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15 December 2020 FIGURE 9

that prohibits evolution. There will come a time, perhaps well into the future, when bitcoin is as anachronistic as pocket watches and landlines.

Caveats and Conclusions

Source: Wikipedia

Barriers due to government intervention To the extent that bitcoin impinges on a sovereign’s ability to manage its economic policy, governments can be expected to limit bitcoin’s adoption directly.

This can be done by limiting access to the ancillary elements that facilitate adoption: for example, restrictions on exchanges or personal software that enable bitcoin transactions. This obstacle does not necessarily need to come in the form of direct legislation. Government pressure, as was the case 1 with Libra’s early supporters, may be sufficient.

Competition Holding gold or another digital asset (even speculatively) instead of bitcoin is definitionally a hindrance to adoption. A tenet of network economics is that a single network maximizes value, and Peterson [2019b] showed that competing coins detract significantly from bitcoin’s value.

Technology adoptions may substantially deviate from their diffusion function over the long term, as was the case with the telephone during the Great Depression.

However, such models provide some context and means to evaluate predictions for reasonableness.

The figures presented in this Research Note are rough estimates intended to illustrate the impact of network growth on value, and to illustrate and estimate the terminal saturation price of bitcoin. This information is not a price forecast and is unsuitable for investment decision-making.

Bitcoin’s current adoption rate indicates a future value of between $1 - $10 million, and likely between $3 $6 million, by 2050. This value is based on the assumption that bitcoin is a technology that follows a diffusion function; that the diffusion function is a Gompertz curve; and that bitcoin’s future adoption curve will closely follow the historical adoption curve of the internet. However, the actual price path that bitcoin may follow is inherently unpredictable in the short term and subject to several practical constraints.

Obsolescence Bitcoin is a technology, and technologies are eventually replaced. It seems unlikely that in an impending era of quantum computing and artificial intelligence that Nakamoto’s Blockchain could not be improved upon. The current mantra by some bitcoin proponents of “Code is Law” creates an intransigence 1

See “Signed Letters re Libra to Patrick Collison, Ajaypal Banga, and Alfred Kelly” where US Senator Schatz and Brown directly threatened Stripe, Inc., Mastercard Inc., and Visa Inc. https://www.schatz.senate.gov/imo/media/doc/Signed%20Letters

Estimating Bitcoin’s Adoption Curve and Maximum Price

%20re%20Libra%20to%20Patrick%20Collison,%20Ajaypal%2 0Banga,%20and%20Alfred%20Kelly.pdf

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15 December 2020 References 1.

Cane Island Digital Research. “There Will Never Be More than 14 Million Bitcoins.” 16 April 2020. www.caneisland.digital/research-notes.

2.

Desjardins, Jeff. “All of the World's Money and Markets in One Visualization.” Visual Capitalist, 28 May 2020, www.visualcapitalist.com/all-of-the-worlds-money-andmarkets-in-one-visualization-2020/.

3.

“Diffusion of Innovations.”

Wikipedia, Foundation, 11 Nov. en.wikipedia.org/wiki/Diffusion_of_innovations.

4.

Franses, Philip Hans. “A Method to Select between Gompertz and Logistic Trend Curves.” Technological Forecasting and Social Change, vol. 46, no. 1, 1994, pp. 45–49., doi:10.1016/0040-1625(94)90016-7.

5.

“Gompertz Function.” Wikipedia, Wikimedia Foundation, 14 Dec. 2020, en.wikipedia.org/wiki/Gompertz_function.

6.

“Internet Growth Statistics.” Internet Growth Statistics 1995 to 2019 - the Global Village Online, Miniwatts Marketing Group, Aug. 2020, www.internetworldstats.com/emarketing.htm

7.

Peterson, Timothy. “Metcalfe's Law as a Model for Bitcoin's Value.” Alternative Investment Analyst Review, Q2 2018, Vol. 7, No. 2, 9-18. http://dx.doi.org/10.2139/ssrn.3078248.

8.

Wikimedia 2020,

—, —. . “When to Own Stocks and When to Own Gold.”

Journal of Wealth Management, 2018, Vol. 21, No. 3, 26-36. http://dx.doi.org/10.3905/jwm.2018.21.3.026.

9.

—, —. “Bitcoin Spreads Like a Virus” (March 20, 2019).

Available at SSRN: https://ssrn.com/abstract=3356098 or http://dx.doi.org/10.2139/ssrn.3356098.

10. —, —. “Why Bitcoin Dominates.” http://dx.doi.org/10.2139/ssrn.3417334.

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Jul.

2019.

11. “Technology Adoption in US Households.” Our World in Data, Global Change Data Lab, 2020, ourworldindata.org/grapher/technology-adoption-byhouseholds-in-the-united-states.

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Estimating Bitcoin’s Adoption Curve and Maximum Price

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Estimating Bitcoin’s Adoption Curve and Maximum Price

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