Is Bitcoin’s exchange rate overvalued or undervalued? Stock market investors have developed a variety of metrics to spot a good deal. Can we do the same with Bitcoin?

Stock Valuation with P/E Ratio

The most commonly-applied stock valuation metric is the price to earnings ratio (P/E ratio). It is computed by dividing a company’s price per share by its earnings per share. Both forward (next year’s estimated earnings) and trailing (last year’s reported earnings) P/E ratios be considered.

Comparing the current P/E ratio of a stock with its historical average, or the average of similar stocks, can give insights into fair value. A P/E ratio that exceeds its historical value says that investors are willing to pay more today for the same unit of earnings than they were in the past. If P/E falls below its historical value, investors are paying less for the same unit of earnings. Likewise, two similar companies can be compared by P/E to spot potential over- or under-valuation.

Many factors, both internal and external, can influence a stock’s P/E ratio. If a company is expected to earn more in the next five years than it has in the previous five, then its P/E ratio might increase to reflect this optimism. Likewise, a company with gloomy prospects may be punished with a reduced P/E ratio. High interest rates tend to depress P/E ratios by making bonds more attractive than stocks, whereas overbought stock markets tend to inflate P/E ratios across-the-board.

Bitcoin Valuation with NVT

Willy Woo recently proposed a Bitcoin valuation metric he calls the Network Value to Transactions Ratio (NVT). This is an interesting first step toward a fair market BTC/USD exchange rate analogous to a P/E ratio. NVT can potentially be applied to any cryptocurrency for which a block chain records publicly-viewable transaction values. As Woo explains:

What would be the equivalent [of P/E ratio] in Bitcoin-land? We have a price per token, but it’s not a company so there are no earnings to do a ratio. However since Bitcoin at its essence is a payments and store of value network, we can look to the money flowing through its network as a proxy to “company earnings”.

Bitcoin’s NVT is computed by dividing its network value (n, in dollars) by the daily value of all spent outputs (t, in dollars).

NVT = n/t.

Network value n is in turn defined as Bitcoin’s money stock (s) multiplied by the dollar exchange rate (e). In other words, network value equals n×e. This value is often referred to as “market capitalization,” but doing so confuses the very different purposes of a for-profit company and the Bitcoin network. Output value (t) is defined as the 24-hour on-chain value in bitcoin of all spent outputs (b) multiplied by the exchange rate e.

Combining these relationships yields an equation for NVT in terms of money stock (s), exchange rate (e), and daily spent output value (t).

NVT = (s×e)/(t×e)

Woo goes on to observe that a high NVT ratio (above about 50) coincides with corrections in the BTC/USD exchange rate. When NVT extends beyond 50 it eventually reverts, with a simultaneous exchange rate bear market. Woo’s site hosts an interactive NVT chart extending from 2011 to the present.

NVT vs. Exchange Rate An overextension of NVT Ratio is associated with exchange rate declines. However, the NVT Ratio peaks lag these declines.

One aspect of NVT that Woo doesn’t discuss is that that exchange rate (e) can be cancelled from the NVT equation because it appears in both the numerator and denominator. In other words, NVT can be obtained by simply dividing money stock (s) by the 24-hour on-chain transaction value in bitcoin (t):

NVT = s/t

An observant Twitter user noted this possibility when Woo first mentioned the NVT:

Cap = supply price. VT = output volume price. Price cancels. Cap / VT => supply / output volume = inverse of daily velocity — Clark Moody (@clarkmoody) September 19, 2017

It seems odd that a metric designed to reflect the fair market BTC/USD exchange rate should have no dependence on the value of the US dollar, or any other currency for that matter.

Velocity of Money

Economists have developed many quantitative relationship for money, one of the best known of which is the equation of exchange. One of its expressions takes the form:

M×V = P×Q

where M is the money stock, V is the velocity of money, P is the price level, and Q is a measure of spending on goods and services.

Changes in money velocity are closely linked to the economic cycle. In the US, for example, M1 money velocity tends to decrease prior to a recession. Conversely, growth in money velocity coincides with expansion.

M1 Money Velocity. Velocity decreases during recessions and increases during expansions. Source: St. Louis Fed.

Parallels between NVT and the equation of exchange can be drawn. The quantity P×Q can be thought of as the annual total of all transactions occurring in an economy. As such, this product bears a close resemblance to the variable t, defined above as the one-day on-chain transaction value although this simplification doesn’t account for exchange rate changes. Likewise, the quantity M bears close resemblance to its counterpart from the NVT discussion (s, the money stock).

If the velocity of money were expressed using the NVT variables, we’d end up with the following relationship:

V = t/s

In other words, the monetary concept of “velocity” for a national economy roughly corresponds to the reciprocal of Woo’s NVT (s/t) for Bitcoin.

Rather than discovering an exchange rate valuation metric, Woo appears to have rediscovered a concept for gauging the internal health of an economy.

Bitcoin Days Destroyed

On-chain transaction value may contain information about economic activity, but this information is buried in noise. Consider:

Bitcoin’s cash properties ensure that the value of a transaction will always exceed the value tendered;

Bitcoin’s privacy model makes it very difficult or impossible to distinguish self-payments from payments to other users;

unlike the participants of a national economy, Bitcoin users are equipped and sometimes incentivized to send money to themselves (e.g., CoinJoin).

It should be parenthetically noted that on-chain transactions capture only a fraction of Bitcoin economic activity. The block chain doesn’t record exchange-settled transactions. Nor does it record off-chain activity by payment processors such a BitPay that settle privately. As Lightning Network begins to take shape, even less Bitcoin economic activity will be visible on the block chain.

The limitations of on-chain data have prompted some to seek an alternative gauge of economic activity. In 2011, the first reference to such a metric appeared: Bitcoin Days Destroyed (BDD). The number of bitcoin days destroyed (d) for a single output is computed as:

d = b×a

where b is the value of the output being spent in bitcoin and a is the age of the output in days. The units of this metric are bitcoin×days, giving the metric its odd name. The longer a coin remains unspent, the more days accumulate. Spending a coin destroys these days. BDD can be summed over any desired interval to give an aggregate measure.

Consider a coin valued at ฿1. It was last spent exactly 10 days ago. The owner decides to spend this coin today. The transaction yields 10 bitcoin days destroyed (฿1×10 days). To determine the number of days destroyed for a block, we’d sum the contributions from each spent output. And so on.

By weighting coin age, BDD has the potential to filter out activity resulting from rapid self-payments such as wallet reorganization and coin mixing. However, BDD does nothing to address the more serious problem that spending an output is an all-or-nothing proposition. In terms of days destroyed, buying a pack of Alpaca Socks is indistinguishable from buying a Tesla. Interesting discussions of BDD can be found here and here. John Ratcliffe has analyzed BDD’s limitations here.

The raw data to compute BDD are available from the block chain, but few sources of precompiled data sets are available. Although Blockchain.info used to make this data set available, it was removed in 2016. OXT offers a graph labeled “BDD”, but it’s unclear what method is being used to compile the data, nor is a raw data set available.

Nevertheless, we can get a glimpse into the relationship between BDD and the exchange rate. In January of 2017 Nikita Zhavoronkov‏ tweeted a graph that overlaid the two data sets.

Bitcoin Days Destroyed vs Exchange Rate. Spikes in BDD appear to precede major corrections in the USD/BTC exchange rate.

Zhavoronkov‏ points to the graph as evidence that increasing USD/BTC exchange rate induces “hodlers” (savers) to sell. To the extent that this activity represents a major component of the total, then BDD could serve as an important contrarian indicator. Notably, spikes in BDD appears to occur prior to major corrections. NVT, in contrast, appears to be a lagging indicator.

One problem with using BDD to value bitcoin or measure activity is that it fails to account for exchange rate fluctuations. This is not hard to fix: we simply multiply BDD by the corresponding USD/BTC exchange rate. We could call this metric Dollar Days Destroy (DDD, or d d ):

d d = d×e

where d is Bitcoin Days Destroyed and e is the USD/BTC exchange rate. As such, DDD represents the dollar value of time-weighted transactions on the Bitcoin block chain.

Conclusions

Valuing Bitcoin isn’t easy, mainly due to lack of good metrics. Network Value to Transaction Ratio is a good first step, but it merely recapitulates velocity of money. Although velocity may serve economists well in modeling the behavior of national economies, Bitcoin’s idiosyncrasies make velocity a misleading metric at best. Bitcoin Days Destroyed can fix some, but not all of these problems.

What’s needed is a valuation metric that does at least two things: (1) incorporates the USD/BTC exchange rate; and (2) captures some aspect of real Bitcoin economic activity.