Metcalfe’s Law and the Value of Cryptoassets

Metcalfe’s Law and the Value of Cryptoassets

The substantial volatility of Bitcoin and cryptoassets more generally has sparked an intense debate among investors, policy makers and regulators. Two questions are typically at the centre of this discussion: what type of assets are cryptoassets? And what is their fundamental value, if any? Of course, opinions diverge greatly on whether we should treat Bitcoin and alternative coins as currencies, commodities or securities. The conventional wisdom outside market participants and crypto enthusiasts is that indeed Bitcoin and similar cryptoassets do not really have fundamental value and/or their fundamental value cannot be determined.

Unlike traditional asset classes, understanding the fundamental value of cryptoassets is indeed particularly complicated. The reason is threefold. First, most cryptoassets by default do not pay regular dividends and so one cannot use standard cash-flow based valuation analysis. This leads to the predominant idea that cryptoassets have value simply because adopters and investors simply believe they have one. Put it differently, the entire cryptoasset market is a system in which non-dividend-paying assets are bought and sold primarily based on the expectation that they will increase or reduce in price (or market capitalisation). The second reason has to deal with the extreme heterogeneity within the ecosystem of cryptoassets. In fact, one could argue that indeed there are some types of cryptoassets which pay some sort of dividends. For instance, some of the decentralised exchanges or borrowing/lending platforms reward investors simply for staking their assets, acting therefore as liquidity providers. Nevertheless, there is no “one-size fits all” valuation scheme, let alone common conventional framework akin to the discount cash flow analysis in Equity markets. The third, and perhaps more visible complication in cryptoasset markets is the absence of widespread and self-contained regulatory framework. It is often complicated even to agree on the terminology across different classes of cryptoassets, let alone on some sort of accounting standard. The valuation task is therefore quite challenging.

Metcalfe’s “Law”

Reaching a consensus on valuations is often challenged by the lack of sufficient understanding of the interaction of supply and demand for cryptoassets. However, if the main goal of any project underneath a given cryptoasset is to succeed and be broadly adopted, it is fair to assume that one simple way to ascertain a valuation is to observe how many participants a given project is actually able to attract. This is often referred to as Metcalfe’s “Law”, the heuristic argument attributed to Robert Metcalfe that a telecommunication network’s value will be proportional to the square of the number of connected users of the system. Within the context of cryptoassets, adoption is typically measured as the number of wallet/addresses which are active over time (see, e.g., Pagnotta and Buraschi 2018). This hypothesis has often been criticised based on the assumption that cryptoassets, unlike communication networks, do not necessarily have real uses and, as such, if demand expressed via new and/or active wallet addresses is not always clear.

Overall, it is fairly intuitive that an increasing network size positively contribute to the value of the network itself. Although the proportionality between the network size and value might be unknown and quite heterogeneous across projects, one should expect some sort of positive correlation between the two. Figure 1 reports the correlation between the market capitalization as of March 2022 (in log scale) of the top 300 cryptoassets sorted by market capitalization and the sum of the new addresses (left panel) and active addresses (right panel), both in log scale, as of the same period, March 2022. There is some positive correlation, both between the market value of cryptoassets and the number of new addresses or active addresses. In fact, the fit for both is somewhat similar. The positive correlation is affected by the largest cryptoassets (the dots in the scatter plots in the top-right corners). This is shown by the regression line of a cubic-spline regression (red curve) vis-à-vis a simple linear regression model (yellow line). However, the positive correlation is far from perfect. The adjusted R^2 from both regressions is 0.41 and 0.43, when considering the new and active addresses, respectively. 

Figure 1: Blockchain addresses and market capitalization 

                                  Source: Aaro Capital Research
Notes: The figures show the market capitalization (in log scale) of the top 300 cryptoassets sorted by market capitalization and the sum of the blockchain new addresses (left panel) and active addresses (right panel). The market cap and the addresses are as of March 2022. The original data are from 

Figure 1 looks at the cross section of addresses and market values, that is, it represents a snapshot across different assets of the relationship between the size of the network, proxied by Blockchain addresses, and market valuations. Figure 2 gives a more dynamic perspective by showing the aggregate number of new addresses (left panel) or active addresses (right panel) in a given day, against the total market capitalization. We consider the same panel of cryptoassets in Figure 1, that is the top 300 sorted by market capitalization. Both the addresses and the market capitalization are simply the cross-sectional sums of the corresponding individual values in a given day. The sample size is from October 2017 to March 2022.

Figure 2: Aggregate blockchain addresses and total market capitalization 


                                                                                                               Source: Aaro Capital Research

Notes: The figures show the total market capitalization (in log scale) of the top 300 cryptoassets sorted by market capitalisation and aggregate sum of the blockchain new addresses (left panel) and active addresses (right panel). The market cap and the addresses are from October 2017 to March 2022. The original data are from 

Again, there seem to be quite a positive correlation between the growth of the network, proxied by the blockchain addresses, and the market value at the aggregate level. The aggregate time series relationship is slightly more non-linear than the cross-sectional one. This is shown by the fitted value of a cubic-spline regression (red line) compared to the fitted value of the linear regression (yellow line). Nevertheless, the correlation between addresses and market value is positive and quite significant with an R^2 in the range of 0.42-0.63.

A few interesting results arise from Figures 1 and 2. For starters, there seems to be a positive and somewhat significant correlation between the size of the network, or the level of adoption, and the market value of cryptoassets. Although a direct comparison is outside the scope of this report, such positive relationship echoes the logic underlying the Metcalfe’s “Law”: a network value is proportional to the number of connected users. Second, and perhaps more importantly, such correlation materialises both in the cross section, meaning across assets, and in the time series, meaning at the aggregate market level. This confirms a rather tight link between network activity and market values.

Nevertheless, some word of caution is still in order. First, the number of addresses is sometimes not necessarily representative of the full extent of a network growth. For instance, Bitcoin users could use multiple addresses, therefore overstating the network size. On the opposite, multiple assets that coexists on the Ethereum blockchain could understate the extent of adoption and diffusion of a given cryptoassets. Second, the correlation between the network size and the market value is positive but far from perfect. That is, there is a great deal of variation both in the cross section and in the time series of market values which do not correlate with the number of addresses. 


In this article we discuss the role of on-chain network activity and the market value of different cryptoassets. We build upon the so-called Metcalfe’s “Law”, which states that the value of a network should be proportional to the number of users and look at the correlation between the number of addresses both in the time series and in the cross section for the top 300 cryptoassets sorted by market capitalization as of March 2022. A series of correlation plots suggest three main results:

1. There is a positive correlation between the number of (active) addresses and the market value across different cryptoassets. 

2. The above positive relationship holds both in the cross section (among different assets as of March 2022) and the time series (market-level aggregation of addresses and values from October 2017 to March 2022). 

3. The often ambiguous calculation of the blockchain addresses, e.g., multiple addresses for single users, cross-chain uses, means one should take caution in interpreting the results.

To summarise, the results point towards some moderate optimism in linking the market value of different cryptoassets with their network growth, proxied by the number of (active) addresses. This evidence suggests that on-chain measures of network activity could be useful to assess the growth prospects of both Bitcoin and the whole cross-section of alternative coins.  


Pagnotta, Emiliano, and Andrea Buraschi. "An equilibrium valuation of bitcoin and decentralized network assets." Woking Paper (2018).

Erb, C., 2021. “Bitcoin is Exactly Like Gold Except When it Isn’t.” Working Paper (2021).


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