• Bitcoin could be the great pick for the next 10 years, compounding significant returns for investors who are ‘ready’ to stomach an elevated volatility.
  • We expect Bitcoin to capture 3 to 5 percent of the gold market share in the medium to long term.
  • Bitcoin is significantly undervalued relative to its fair value (Metcalfe’s law).
  • We expect Bitcoin to settle around $25,000 in the long term.


Picking the right asset in a big theme could generate astonishing returns for investors over time. Figure 1 shows us the 5 greatest picks in each of the past 5 decades: we first had gold in the 1970s due to the unexpected sudden rise in inflation coming from the oil shocks, then came the Japanese stocks in the 1980s with Japan’s economic miracle, then the US boom in the 1990s led to a titanic performance in US growth stocks, then the double-digit growth in China led to an outperformance of consumer staples in the 2000s, and then the prominent growth of new Internet companies led to a strong performance in Tech stocks in the past decade. If we look at the cumulative returns of each asset in the past 50 years, a person who invested $100 would have accumulated over USD 1.3 million of wealth, averaging 22.2% in annual return for a volatility of 25.3% (Sharpe ratio of 0.88).

Even though this chart looks very appealing, we cannot extract anything from the past except the fact that it is important to choose the right asset in the right narrative. What is the big theme of the next decade?

We think that cryptos (especially Bitcoin (BTC-USD)) could be the right pick for the next 10 years, compounding significant returns for investors who are ‘ready’ to stomach an elevated volatility.

Source: Eikon Reuters, RR calculations

Bitcoin: an asset with no fundamental value

Asset prices should all equal expected discounted cash flows. According to the Fundamental Theorem of Asset Pricing (FTAP), the value of any asset should be equal to the sum of the fundamental value and the terminal value (both discounted), which could be written as the following (in discrete terms):

Where Pt represents the price of the asset at time t, C(t+i) are the expected cash flows, r is the discount rate and T is the Terminal value.

As opposed to equities or bonds, Bitcoin carries no fundamental value such as a variety of alternative investments (gold, paintings or wine) and therefore violates the classical Financial Theory. Hence, investors have been skeptical about the outlook of cryptos and Bitcoin in particular: is it a Tulip or is it the start of something bigger?

Since it reached its high of $20,000 in the end of December 2017, Bitcoin has failed to rebound significantly in the past two years, struggled to break through some resistances and trade back above the psychological $10,000 level. Opinions are currently very divided, with some analysts expecting the price of a unit to reach $100K and others simply stating that it is a bubble that is about to burst. Bearish investors have used a popular chart that overlays the dynamics of Bitcoin prices with the previous historical bubbles (figure 2) and concluded that it is only a matter of time before the price of Bitcoin collapses to zero.

Source: BoA

We actually disagree with that statement and think that the crypto market can experience a significant growth in the next decade, with Bitcoin gaining the status of the ‘currency of the last resort’.

Bitcoin: to capture a little share of the gold market

Many investors have been surprised by the little impact that the titanic growth of central banks’ total assets has had on inflation in the past decade. In early 2010, a lot of smart money managers were convinced that the US was going to experience a double-digit inflation, which was going to lead to a significant appreciation in gold prices (up to $5,000 an ounce). One thing we can learn from this experience is that ‘it is never that obvious’, and it is crucial in finance to constantly challenge your views and reassess the probabilities that you attribute to each scenario.

However, we think that this time is different, and that the combination of both monetary and fiscal stimuli will be inflationary in the medium term. We saw that gold has already been trending higher against all currencies, and we do expect the trend to start in the crypto market as well. In fact, we think that Bitcoin will eventually capture 3 to 5 percent of the gold market share in the medium to long term. With approximately 190K tons of gold available above ground, the total market cap of gold is USD 10.5 trillion (for a spot price of $1,730 per ounce). Hence, with the total number of mined bitcoins at 18.3 million, a 3 to 5 percent of the total gold market cap would price a unit of Bitcoin between $17,240 and $28,740. This may not impress a lot of investors as Bitcoin was trading at $20,000 in the end of December 2017, but it is 2.5 to 4 times higher than the current price. We think it is a very valuable investment in the medium to long term if individuals are ready to stomach high volatility.

In addition, there is a high probability that gold surges to higher levels in the coming 12 to 18 months amid elevated political uncertainty and rising inflationary pressures. If we look at Bitcoin as a leverage play on gold, the ‘fair’ value could actually be significantly higher.

Figure 3 shows the dynamics of gold price with Bitcoin in the past few years and the results of a simple OLS regression of daily changes in Bitcoin prices on changes in gold prices. Even though the coefficient on gold is significant but lower than 1, we would expect it to become greater than 1 in the coming two years, implying that Bitcoin will become a ‘high-beta gold stock’.

Source: Eikon Reuters

Metcalfe’s law: one popular Bitcoin model

Based on the mathematical tautology, Metcalfe’s law states that the value of a network is proportional to the square of the number of connected users: M = A * n (n-1)/2 where A is the proportionality factor relevant to the network under review. In recent years, we saw that a significant number of practitioners have used Metcalfe’s law to value the price of Bitcoin, particularly since 2018.

In this part, we extend the work of Peterson (2019) who uses the Gompertz sigmoid as a decay factor to compute the value of a unit of Bitcoin (the Gompertz function has been used for decades to model viral infection, bacterial growth, and mobile phone proliferation). The Gompertz growth model is expressed as the following:

Where bt represents the number of bitcoins mined at time and B is the total number of bitcoins that will be mined (21 million). Peterson proposes the following model:

Where n is determined by the number of wallets and A is a constant, expressed in terms of dollars per transaction (we chose A=1).

Looking at quarterly data since 2012, we calculate all the variables and the value of Bitcoin for each period. Results are shown in figure 4 and 5.

Prior to the first half of 2018, empirical research has found that Bitcoin price was following Metcalfe’s law with an R_square above 80 percent. However, the two times series have significantly diverged in the past 20 months, with Bitcoin currently being 32% undervalued relative to its fundamental value. Even though the use of Metcalfe’s law to estimate the fair value of Bitcoin is still questionable, and we have learned from the FX market that a currency could remain significantly undervalued for a while, this model is also pricing in further appreciation in the cryptocurrency in the medium term.

Source: Eikon Reuters, RR calculations, Peterson (2019)
Source: Eikon Reuters, RR calculations, Peterson (2019)

Main risks coming ahead

The main risk in the long run is that unlike other alternative assets such as gold, Bitcoin has not experienced a dramatic 50% plunge in equities and therefore investors are questioning the robustness of cryptocurrencies in the coming 12 to 18 months. While we saw previously that gold has historically performed well in periods of market selloff, we do not have enough data to see if Bitcoin tends to perform well in periods of elevated price volatility. Figure 6 shows the resilience of gold during periods of market stress; gold is also defined as a zero-beta asset and has remained strong during the Q4 2018 and Q1 2020 selloffs.

Source: Eikon Reuters, RR Calculations

If we look at recent daily data, we can notice a strong co-movement between BTC and one of our favorite assets, the Japanese yen (FXY). Figure 7 (left frame) shows that positive trends in Bitcoin prices have been associated with a stronger FXY since January 2017. Even though we find this chart interesting, we would expect the relationship to break in the long run as our main LT scenario favors higher equities, cheaper yen and stronger Bitcoin.

We can also overlay prices of Bitcoin with US equities in the past two years and notice that there are periods of significant co-movement between the two time series. Figure 7 (right frame) shows that Bitcoin was also sold aggressively this year during the equity rout in March. Should we expect bigger downside correlations between equities and cryptocurrencies in the future?

Source: Eikon Reuters

BTC outlook

Although we cannot look at the historical behavior of Bitcoin in periods of market stress and in periods of accelerating and decelerating prices, we do think that cryptos will generally trend higher if inflation starts to rise suddenly in the next 12 to 18 months. Investors who are bullish on gold in the long run should also consider allocating some of their wealth in Bitcoin, as we believe that it will trade as a high beta ‘gold stock’ in the future and capture 3 to 5 percent of the gold market cap.

Figure 8 shows a strong support line at 3,088, which corresponds to the December 2018 lows, and there is also an upward trending support line that shows that Bitcoin should receive significant bids at around $5,000 if we see a sudden selloff in the short run. We think that $5,000 represents a great entry level on the asset for long-term investors; this would imply that LT investors will quadruple or quintuple their money if the price of Bitcoin settles between $20K and $25K in the long run.

Source: Eikon Reuters