Predicting the value of a bitcoin
It is surprising that bitcoin prices follow Metcalf’s Law but this is a possible indication of its bright future
Bitcoin has become high and dry over the past three months. The price of one bitcoin reached a new all-time high of $19,783 on 17 December 2017, an increase of about 1,824% since 1 January 2017 when a single bitcoin could be had for just under $1,000. Currently, bitcoin is trading at around $11,200, having witnessed the steepest decline at the end of January. Transactions also plunged from a seven-day average of almost 400,000 in mid-December to about 200,000 currently, indicating the possibility of a bubble.
The world is divided over the merit of bitcoin as an asset given its volatility. While the geeks are of the view that bitcoin is one of the disruptive technologies of the decade with its secure-proof, decentralized mechanism of functioning, financial sceptics warn against holding it due to its volatility and inadequate backing by regulators worldwide.
There have been attempts to predict the value of bitcoin earlier using various models and algorithms. Tom Lee, co-founder of FundStrat and an expert in predicting bitcoin prices, has suggested that the value of bitcoin could double or even treble by the end of 2018. Bitcoin network, consists of addresses (and hence, users) who are connected to each other to transact. Much like any other network such as telecom, bitcoin network has direct network effect that increases value both for the network owner as well as users connected to it, as the number of users in the network increases.
The billion-dollar question is: Is the value of the bitcoin network proportional to ‘n’ (the number of bitcoin users) or square/exponential in n. A number of researchers looked at this problem in detail: (i) Sarnoff’s Law (by David Sarnoff) is more conservative in estimating value that varies linearly with n and found to be true in case of Television and Cable broadcasting networks; (ii) Robert Metcalf, the inventor of Ethernet, is widely credited with Metcalf’s Law that states that value is proportional to square the number of users ; (iii) David P. Reed however proposed that in Group Forming Networks such as Facebook/Twitter, the value could be exponential as many sub-networks can be created; (iv) and finally a conservative but more pragmatic estimate in the form of Zipf’s law (by George Kingsley Zipf) that states that not all connections between users are equally important and hence the value is much less and can be approximated to nlog(n). In other words, increasing the number of users from 10 to 20, the value of the network only doubles (i.e. 10 to 20) as per Sarnoff; quadruples (i.e. 100 to 400) as per Metcalf; while it will be only slightly more than twice as much (i.e. 10 to 26) as per Zipf estimate.
We used the number of unique addresses used in bitcoin network as ‘n’ to predict ‘P’ (the average market price in dollars) of bitcoin across major bitcoin exchanges using various above models. The dataset had more than 3,000 values collected during 2009-2018. The model that best fits for bitcoin is Metcalf’s law that is indicative of quadratic increase in price as a function of network addresses. While there have been many arguments against Metcalf’s law, it is surprising that the price of bitcoin follows this law but this is a possible indication of its bright future.
We also fitted the above models for Ethereum—one of the most important alternatives to bitcoin as a crypto asset that was proposed in late 2013 by Vitalik Buterin. Ethereum also uses the blockchain technology of bitcoin. The more conservative Zipf’s law provides the best fit on the relationship between network addresses and price in case of Ethereum which is trading at about $835 currently.
However, unlike bitcoin where speculations are rife, Ethereum is mainly used by firms that build various solutions using the underlying blockchain technology. Unlike active trading of bitcoins, Ethereum was conceptualized as an Initial Coin Offering (ICO, similar to IPO) platform for investors to fund its development. This may be the reason for the difference in the fitting models of both these crypto-assets, with Ethereum having a more conservative fit than that of BTC.
A recent Communications of the ACMarticle points out that decentralized blockchain-based electronic market places alter the firm-controlled traditional market places by providing security, trust, privacy, lower transaction cost and transaction integrity. Such blockchain-based market places improve matching, transaction facilitation and open up new frontiers in financial engineering, smart-contract based systems and so on.
In the recent Union budget, it was mentioned that while all measures would be taken to eliminate crypto-assets in financing illegitimate activities, the government intends to explore the underlying blockchain technology for ushering in digital economy. This is a welcome step indeed given the potential of the underlying technology and associated crypto-assets in the digital economy of the country and hope that the crypto policy to be announced soon by the government nurtures the underlying technologies of crypto-assets and provide space for their legitimate use for the benefit of society at large.
V. Sridhar and Shashank Motepalli are, respectively, professor and student at International Institute of Information Technology in Bengaluru.