Valuing Cryptoassets from the Ground Up

  1. The Equation of Exchange, which offers an underlying framework.
  2. Velocity, which shows how the timing of everything makes all the difference.
  3. Holding, which digs into the quantities people use versus keep.
  4. Total Value, which gets to the nature of competition and what drives the value.

First, a Disclaimer

This is not investment advice. This is solely intended for informational purposes.

Existing Works

Many of the ideas here can be attributed to or were inspired by prior works, in particular these, which I recommend reading further:

The Equation of Exchange

The Formula

Most current approaches to cryptoasset valuation start with the Equation of Exchange. It’s a short formula, MV = PQ, that describes how the amount of money in circulation relates to how that money gets used. Here is what each variable means:

Example with Dollars

To show the equation in practice, let’s use an example with dollars.

Example with “Things”

The formal definition of this equation refers to money. However, it describes a rule about the use and reuse of things that can apply more broadly. With a few tweaks we can abstract it to explain any supply of “Things”:

Example with Stamps

With a more general version of this equation, we can apply it to something besides money. For example, stamps.

Example with “StampCoins”

Now let’s get interesting and create our own currency. Let’s say we call it “StampCoin” and we create 1,000 coins. We tell everyone that they can only pay for deliveries in StampCoins, so they need to first buy the coins. But here’s the catch: we’re not going to set a price per StampCoin, nor a fixed price (in StampCoins) per delivery. Instead, we’re going to let market forces determine those prices.

Velocity

Changing When People Arrive

There’s an important detail I glossed over in the last example: the fact that 5 people show up each week. This timing is critical.

Velocity as a Function of Timing

What we’re seeing is the timing of demand determines the velocity. Smaller, more frequent groups of people speed up the velocity, whereas larger, less frequent groups slow it down. Intuitively this is because when there are more groups of people that don’t overlap with each other, we can reuse the StampCoins more often.

Applying Queuing Theory

These relationships introduce the idea of the time between activities. If we can estimate that interval, then we can estimate the velocity. Fortunately, there’s a whole field of study from operations management that can help: queuing theory.

Idle Time

The last step is estimating the percent idle time. Another way of phrasing this is the probability that zero people are in the system. Conveniently, queuing theory derives this value, π(n), which is defined as the probability that there are n people in the system once reaching a steady state. The mathematical proofs get complex (here’s a good resource), but we can skip to the final M/M/∞ equation:

Back to StampCoins

To see our new equation in practice, let’s go back to our StampCoin example. We still have 260 total deliveries, but this time let’s say the timing is random over the course of the year (which the above equation assumes). Let’s also assume we now have infinite delivery drivers — meaning no one ever waits in line — and that on average each delivery takes 3 hours.

Holding

Effects of Holding

Throughout these examples, we’ve assumed everyone uses all of their StampCoins once they get them. It’s possible, though, that they’ll hold on to some of them. When they do, that affects the results because it decreases the available supply.

Reasons to Hold

To dig into the holding percent, it helps to think about a real life example like regular postal stamps. Generally, we don’t stockpile stamps. We can’t do much with them besides mail letters, so it doesn’t make sense to buy too many extras.

Optimal Order Amount

The field of inventory management has a term for this optimal amount. It’s called the economic order quantity (EOQ), and it generally applies to physical items with holding costs like warehousing. In the case of coins and cryptoassets, we don’t really have physical holding costs, but we do have the opportunity cost of keeping that money somewhere else where it can earn interest. So we need a refined version of EOQ that uses the interest rate as the holding cost. This is called the Baumol-Tobin model.

Optimal Holding Percent

Given an optimal amount, we need to translate this into a holding percent. In general terms, the holding percent is the average amount we hold at a time, H, divided by the total of both what we hold and the average amount we spend per activity, y. That gives us the following equation:

Total Value

Competition

In all of our StampCoin examples so far, we’ve worked with the assumption that the “going rate” per delivery is $4. This is, of course, a pretty important detail. Ultimately many market forces balance out to determine this rate. With cryptoassets, however, the primary driving force is supplier competition. So we can focus on that.

  • All of the software is public. To offer an identical alternative, you can literally copy and paste the code.
  • All of the data is public (albeit, encrypted). If the fees are too high, the protocol can be forked into a new version where the same users can still use their same addresses and passwords, but pay lower fees.
  • There are minimal capital costs to get started. Cryptoassets have built-in financial incentives for other people to run the network, so you don’t need to pay for the computing or hardware costs yourself.
  • The friction between options is low. Since cryptoassets are based in code, it’s possible to programmatically interact between them. The process of switching from one to another can therefore be scaled and automated with software, minimizing friction.
  • Trust is built into the system. There’s less of a need to develop a new, trusted reputation because the code and network are transparent.

Total Cost

Without any barriers to competition, the competition is essentially infinite. A cryptoasset will face downward pressure on the value until it basically equals the cost of running that cryptoasset.

Store of Value

This cost-based value is often described as the “utility” value. The utility of a cryptoasset means the services it can perform, like storing data, verifying information, and executing network requests. In other words, doing activities. So our discussion so far has all focused on the value a cryptoasset has because of its utility.

Bringing It All Together

We now have all the pieces. Taking our above equation for total cost, we can solve for the value of a cryptoasset, A, to get A = C / (MV). We can then plug in our equations for M and V from the prior sections to produce one big equation:

  • C: Total annual cost (in $) of operating the cryptoasset
  • i: Risk-free interest rate
  • k: Transfer cost (in $) to buy the cryptoasset
  • N: Total number of cryptoasset coins or tokens
  • Q: Total annual quantity of cryptoasset transactions
  • Y: Average total cost (in $) of the annual cryptoasset transactions per user
  • μ: Single server rate (which equals the total time divided by the average time per transaction)

Example Calculations

Let’s try some calculations for potential real-life utilities. We’ll use Ethereum since it’s currently the largest smart contract platform, and we’ll start with these general inputs:

  • N — The total supply of Ether (ETH) is about to reach 100M.
  • i — We’ll assume 2%.
  • μ — We’ll assume transactions take 15 seconds, which means μ = (365*24*60*60) / 15 = 2,102,400. I realize this is slower than current transactions, but practically speaking it’s about the maximum acceptable time for real-life utilities like a payment system. Either Ethereum would need to achieve this speed, or another faster cryptoasset would probably end up providing these utility services.
  • k — Many exchanges charge fees on a percentage basis, which don’t affect the holding percent. But some do have minimums. We’ll assume a fixed (minimum) cost of $1.00 for exchanging USD for ETH. And for exchanging ETH for other cryptoassets, the costs are often lower, so we’ll assume $0.10.

Example: Ethereum executes all VISA payments

According to the annual report, VISA executed 111.2B transactions in 2017, so this is our Q. Those payments were worth $7.3T, our C. (We need to add in operating expenses too, but at only ~$6B, they’re less than a rounding error of the $7.3T.) With 3.2B cards, the average annual spend is 7.3T / 3.2B = ~$3,200 per card, our Y. Let’s also assume people buy their ETH with US dollars and use the higher $1.00 transfer cost.

Example: Ethereum delivers all global emails

A study from 2015 estimates that 246B daily emails will be sent globally by 2019. That equals roughly 90T annually, our Q. Amazon’s email service charges $0.09 to $0.12 per 1000 emails, plus a fee of $0.12 per total GB. If we assume a net $0.15 cost per 1000 emails, the total cost is 90T * (0.15/1000) = $13.5B, our C. The study also estimates those emails will be sent by 2.9B users, so the average annual spend per user is 13.5 / 2.9B = $4.66, our Y. We’ll also assume ETH is being exchanged with other cryptoassets and use the lower $0.10 transfer cost.

Example: Ethereum handles all Dropbox storage

The recent Dropbox IPO filing states that 2017 cost of revenue excluding stock compensation was $356.7M, our C. Since files can take longer to upload and download, we’ll say transactions average 30 seconds. That means μ = (365*24*60*60) / 30 = 1,051,200. With over 400B pieces of content, let’s assume annual transactions is 10% of that, 40B, our Q. And with 500M registered users, the average annual spend per user is 356.7M / 500M = $0.71, our Y. We’ll again assume ETH is exchanged with other cryptoassets and use the $0.10 transfer cost.

What It All Means

The first thing that’s clear is this equation produces low valuations. Across the different examples of potential utility services, the values are all under a dollar, a small fraction of current prices. You might expect cryptoassets to gain value with adoption, but this equation suggests the opposite. At scale, cryptoassets will likely achieve hyper efficiency that reduces the price.

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Mike Sall

Mike Sall

5.7K Followers

Cofounder at @Goldfinch_fi. Previously Head of Product Analytics at @Coinbase, Head of Data Science at @Medium.