As with Bitcoin, a PMR of 1.0 accurately predicted 4 of ETH’s major corrections while a PMR of -0.25 appears to identify strong buying opportunities.

Also of note is that PMR did not predict the most recent correction in early 2018 — in fact, according to PMR, ETH is currently in a strong buy zone. Does this mean that PMR failed? No. We believe the reason for ETH’s crash was Bitcoin’s over-inflated NVT and PMR — both of which indicated that Bitcoin was due for a major correction. And because Bitcoin is the dominant cryptoasset, when it corrects, the entire market tends to move with it.

Limitations of PMR

Despite the fact that PMR appears to offer some advantages vs. NVT, it’s not without its limitations.

We can’t explain why M2 works as well as it does or where it came from. Because PMR relies on transactions or unique active addresses, it cannot capture off-chain transactions. Off-chain solutions like Lightning Network, Raiden, other side chain or state channel scaling solutions that move transactions off the main chain may reduce the predictive power of M2 and its variants over time. Similarly, some proportion of transactions reflects exchanges moving money around (in terms of USD volume this may represent a decent chunk of total volume but in terms of raw numbers of transactions, it may be less an issue). In the case of Ethereum, ERC-20 transactions now represent upwards of one third of all on-chain transactions. Because ERC-20 transactions do not directly relate to trading of ETH, it’s possible that we’ll need to discount transactions in the future by some function to account for the rise in non-ETH transactions. Similarly, as dapps begin to launch and Ethereum sees increased non-speculative usage, further discounting may be needed. On the other hand, perhaps this increased usage will not affect M2’s correlative power. Time will tell.

Because of these limitations, we believe that both NVT and some variant of PMR will be useful metrics moving forward.

Conclusions

There is no single indicator that can accurately predict the price of a speculative asset like ETH or BTC as there are too many variables to consider; however, if we accept the premise that blockchain networks that are predominantly in the speculative stages of adoption behave like online telecommunications networks, then Metcalfe may help us to better understand where usage and price intersect and when one has significantly outpaced the other.

Whether this continues to hold true is difficult to predict, particularly as networks such as Ethereum begin to see usage beyond speculation. During these early speculative stages, however, the number of transactions or number of unique active addresses likely serves as a close proxy for demand.

Ken Alabi addresses this nicely in his paper:

Due to the fact that the assets we consider have very little actual use currently — they are not really used much as a transactional medium for payment systems, nor even significantly as a payment rail — it may be reasonable to interpret their adoption to be based on their perceived future potential. If that potential or value proposition is presented to a selected number of people, the expectation is that the same ratio in that set would convert into acquiring the assets. That group would then communicate that same value proposition to their own social network of friends and acquaintances, and on. Therefore, the basic adoption process might not be very dissimilar from that of a social network.

Indeed, when prices rise, demand rises and when prices drop, so too does demand. Price and usage therefore share a symbiotic relationship such that neither can be used to predict one without the other, but what PMR and NVT are likely telling us is that there is a threshold to the extent that one may outpace the other and that reversion to the mean will eventually take place.

Kalichkin refers to this concept as reflexivity.

Taken in context with other indicators and external factors, both NVT and some variation of PMR may serve as useful additions to the conscious investor’s toolkit. We caution however that thresholds should not serve as markers for immediate action. Instead, we would suggest a conservative approach: when an asset crosses above an upper threshold one could cease buying (as opposed to selling in hopes of timing the top and re-buying at a lower cost) and when an asset crosses a lower threshold one could start buying. The former suggestion is important because our charts show that a cryptoasset may continue rising in price after an upper threshold is breached and may even remain valued at a higher price even after a correction. In other words, it’s difficult to perfectly time the top.

Future Work

Ken Alabi’s paper suggests a new formula for valuing blockchain networks derived from Metcalfe. It is a more complex function that requires curve-fitting. Future work might involve fitting this function and comparing its performance to our variants tested here.

Ken Alabi’s revised model for network value

Mr. Alabi’s paper also details a model for predicting future growth of a network — the netoid function. As with Alabi’s value function, application of this growth function requires curve-fitting. Using the netoid function, Alabi predicted that Bitcoin would reach its maximum growth rate in October of 2017 and that Ethereum would reach its sometime in 2018. The netoid function for these networks should be re-fitted based on recent data.

If such a function is a useful predictor of future growth (in terms of transactions or active addresses) then it follows that it may be an accurate predictor of price given how well price correlates with network usage. This could make it a very powerful tool for speculation.

Of course, for this to be true, we need to make some assumptions and assert some precautions. For starters, this would require that Metcalfe and its variants continue to maintain their correlative power which might be problematic (see “Limitations of PMR” above). Second, no model of growth can account for external events. A black swan event or the rapid rise of a superior cryptoasset competitor could see network usage dramatically shift in ways that cannot be modeled.

As Alabi writes:

In as much as the value of the network correlates with the number of users actively participating in it, that value can also prove to be as fleeting as the ease with which those users can move to a different network or cease to participate. The idea behind some of the assets designated for use on the networks studied here is one of fungibility. That fungibility also means that users can create new addresses on different networks and move their assets there easily, or simply just pull their assets out. In short, the ease with which users can move from the blockchain networks of the types studied here exceeds that of networks such as social media, where the user may have cherished items including pictures, conversations, social contacts, and other historical items that may not be as easy to move.

We however disagree with Alabi’s assertion that users will readily move between different blockchain networks — at least more readily than between social media networks. As blockchain protocols grow and capture significant network effects, particularly through mainstream dapps built on top of their protocols, users will naturally become more vested within the network and its ecosystem making it harder to exit. Social circles are also generated both online and in meatspace which further constrains individuals to their respective blockchains.

Finally, future work is needed to formally test PMR, its thresholds, and its variants.

— Jacob Franek

Thanks to Kevin for insights and inspiration for this article.

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