Many cryptocurrency projects serve as transaction platforms where buyers and sellers of goods and services come together to interact. Transfers of value, including payments to other users or to the platform, are to be executed by transferring the platform’s designated token, whose value comes from their use for this purpose.
In this post, I will apply models from finance and economics to come up with a back-of-the-envelope model for valuing such tokens that are not purported to derive their value from anything but the usefulness of their platforms. Ethereum is one example among many others, variously referred to as utility tokens, protocol tokens, or app tokens. I’m not touching Bitcoin to avoid a mess of arguments about intrinsic value and precious metals.
Security vs Currency
One of the issues that complicates valuation is the dual role that some tokens play. Besides serving as the designated transaction currency of the platform, some tokens also reward token holders in the form of token dividends or token burn. Token burn is analogous to a share buyback of stock for a public company, except the tokens to be removed from circulation are not purchased by the company on the open market, but by users paying the transaction fee. Incentives to own such tokens include both capital gains and platform usage. They serve a dual role as both security and currency, complicating their analysis because existing asset valuation models were developed for one or the other.
Even tokens that do not explicitly reward shareholders are thought to appreciate if the token supply remains fixed or expands slower than the rate of the platform economy’s growth. In that sense many more tokens have security-like attributes.
In this section, we formulate a separation of security and currency aspects of tokens so each can be analyzed separately using existing models.
We don’t have non-crypto examples of a platform with similar mechanics for comparison, but to get us closer, let’s consider a thought experiment. Suppose eBay started requiring all transactions to be done using EBAY stock. Sellers are to list prices in number of EBAY shares, while buyers are to purchase EBAY shares on the open stock market to transfer to seller. Seller pays the transaction fee in EBAY shares and is free to sell the remainder on the open market for cash.
Would this increase EBAY’s market cap? Seems plausible given the increased demand from users who need it to transact on the platform, but hey, if it were this easy, every company would be doing it. Netflix would require users to go buy a share of NFLX before subscribing. Some companies offer minor perks for shareholders, but no analyst is crediting these perks for bumping up their market cap.
Users want to use the system. Shareholders want to gain from capital investment. It’s inefficient to force users to also be shareholders. Even if there were no exchange fees, the price fluctuation of stocks, which is the very reason shareholders are rewarded a return for holding them, makes them undesirable to use for payments. Any user that wanted to be a shareholder could have done so before the requirement, so any extra demand comes from users who wouldn’t otherwise hold them. This is an extra cost burden to these users, which will diminish the amount in fees they would be willing to pay. A decrease in fee revenue causes a downward pressure on the stock price. Since the decrease in fees and the extra demand both stem from the same root cause of users having to hold the stock, we expect the downward pressure from diminished fees to correlate with the upward pressure from its use as platform currency. They may not cancel each other perfectly, but we can see that having users use stock as currency is not the free lunch it might first seem.
Creating a Pure Currency
Now consider a second scenario. Suppose that instead of stock, users will be required to use a newly created CUR token, which carries with it no rights or dividends but is guaranteed to be the sole accepted currency on eBay. The token can be traded on open markets with negligible exchange fees. Initially CUR is distributed to existing EBAY holders at a one to one ratio. To mimic inflationary fiat currencies (OECD 2.18% average), 2% more CUR will be created each year and distributed to EBAY holders as dividends.
Let M be EBAY’s original market cap, and let Ms (security) and Mc (currency) be the market cap of EBAY and CUR respectively right after CUR creation.
Since CUR is a resource that gates access to eBay, we expect Mc to be a significant chunk of M. If a single entity, say a hedge fund, were to own most or all of CUR, then it would be able to rent out CURs for a fee. Having a monopoly over eBay access would enable it to extract a significant fraction of eBay’s profits via rental fees.
In particular, if Ms + Mc were lower than M by enough to make up for overhead and acquisition premiums, even eBay itself would want to buy back all of CUR, revert to how things were before issuing CUR, and bump its market cap back to M. An efficient market would not value CUR too far from this lower bound. Give or take a small allowance, we have the inequality
M <= Ms + Mc
We cannot be sure of equality here. Even though we argued above that requiring users to use a designated currency should not create net value, we cannot rule out the possibility of CUR being valued for usage off the platform. Later we will estimate Mc based on CUR’s usage.
We define M, Ms, and Mc analogously for a crypto token platform. We calculate an upper bound on its (real) market cap M by estimating the (abstract) Ms and Mc that would result if it were to create a new CUR token for exclusive use on its platform. This makes our analysis much easier. The new token has only security-like properties so it can be valued as a security, while CUR has only currency-like properties and can be valued as a currency. We can analyze each of these separately using existing models.
Security Value
Security value Ms would be based on any dividends, token burn, and the annually created CUR awarded to shareholders. By analogy with stocks, we can value a security as a certain P/E ratio times profits, with the expectation that profits will eventually be used to pay dividends or repurchase shares. We model this as
Ms = P (F - C + i Mc)
where P is the P/E ratio, F is annual revenue (assumed for tokens to come from fees), C is costs taken out of F such as payment to miners, and i is the rate of inflation so (i Mc) is the value of the annually generated CUR. For a platform where no new tokens are ever instantiated, we set i = 2%. We use the S&P500’s average P/E ratio of P = 26.
For Ethereum, security value is not realizable without changes to the protocol. Fees go entirely to miners so C = F. Miners are also paid from newly generated block rewards, causing inflation of the token supply, an issue that we will discuss later. In any case, for the sake of illustration, let’s see what the best case scenario would be if we were able to change the protocol to reallocate transaction fees to benefit shareholders while reducing mining costs and block rewards to zero. On 2018–03–31 the average transaction fee was $0.202 with 588,725 transactions per day, for a rate of $43.4m per year. The Ms value is 26 * ($43.4m + 2% Mc) = $1.1b + 0.52 Mc. We estimate Mc in the next section.
The P/E ratio of 26 is for mature companies; companies expected to grow have higher P/E ratios. Potential growth is one of many factors affecting cryptocurrency prices today. I am not attempting to account for all of these factors, so I don’t expect results here to match the actual current market caps. The goal is long term, equilibrium valuation. Current data points are used for illustration only.
Currency Value
For Mc, we apply monetary theory from macroeconomics to estimate a currency value. We created the abstract CUR token exactly for this purpose. Security related issues of dividends, token burn, and block rewards are isolated into security value, while CUR offers no rewards and inflates at 2% like fiat currencies.
One of the tools to model valuation of currencies comes from the Quantity Theory of Money using the equation MV = PQ, for which a good overview of related work can be found in this article. This equation states that a country’s output PQ, which is equal to GDP, is paid for with its own money, so the greater the money supply (M), the less each unit of money needs to change hands (V) in a given time period. Expressed in terms of the value of the total money supply we have M = GDP / V where V is the income velocity of money, which the Federal Reserve tracks. By definition, only the part of monetary transactions that contribute to GDP are included, a small fraction of the total transaction volume.
The equation suggests that a currency’s value is derived from the output of its economy. In other words, money is valuable because of its acceptance for purchases. This purchasing power is the value that gets passed around when money is transferred, which is why M does not directly depend on transaction volume. However, it is difficult to estimate the GDP of a token in this expenditures based view that sums final goods and services, as many stages of production are likely to have occurred outside the cryptocurrency and cannot be tracked. Instead, we can think of GDP via the equivalent income approach, which for a token would be the total income earned by users in token transactions. The currency is valued because it allows producers to earn income and consumers to gain consumer surplus (untracked), which justifies their willingness to pay transaction fees.
For this equation to be a good model of currency value, V should be consistent across currencies, even if not across time. To check this, I computed V across countries using CIA World Factbook data for GDP and broad money supply M2 by country. For the 192 entries found in both tables, average V is 2.25 with standard deviation of 1.7. When limited to the 34 OECD countries, average V is 1.23 with standard deviation of 0.48. This seems consistent enough for our purposes, so we’ll use V = 1.23.
Let Y be the total income earned from token transactions by users. Miners’ income is included. They are users who provide service as part of every transaction. Currency value of the token is modeled as
Mc = Y / V
Unfortunately we do not have GDP data for tokens as we do for countries, so we do not have a measure of Y directly. We can look at the transaction fees users are willing to pay, but since tokens offer very different services for the fee (e.g. running applications vs transfer only), fee ratios vary across tokens. Later we will estimate Y for eBay where we do have data.
For tokens where we have transaction volume data, we can estimate the ratio of income to transaction volume by looking at fiat currencies to get comparable ratios. For USD, currency exchange ($5t/day) and Fedwire transfers ($3t/day) alone account for $3000t in annual transaction volume versus $20t in US GDP, so less than 0.67% of the transaction volume T of USD reflects economic output, or GDP < 0.0067T. For the euro, using analogous numbers (GDP, forex, wire), we get GDP < 0.010T. We’ll use the estimate
Y = 0.0084T
halfway between the two data points. One takeaway from this ratio is that a relatively small money supply supports the high volume of transactions required in productive activities.
For Ethereum, $685m was sent in 24 hours on 2018–03–31, which extrapolates to a currency value of Mc = 0.0084 * 365 * $685m / 1.23 = $1.7b. We have plugged in real world transaction volume data for the abstract CUR, which is fine for Ethereum because it has no security value and is essentially its own CUR, but this could be a source of inaccuracy for tokens that have security value.
We always apply the same value of model parameters, such as V = 1.23, for any token because it is applied to the abstract CUR token that has only currency properties. There are many properties that may influence currency valuation. Some, such as usage as store of value, are shared in common with fiat currencies and are factored in to an extent. Others are not, such as availability of financial services and size of the economy. Overall the comparison is far from perfect.
If we had chosen to compare with M1, a more narrow definition of money supply, V would be higher and the modeled market caps would be lower. M2 seems the better comparison to tokens until token based financial assets exist that can be transferred in their place.
Some have argued that low exchange fees would cause high V and therefore low currency value. However, there is more reason to hold the platform’s currency besides the exchange fee to release it. Given that a high transaction volume is required to earn Y, a user who gets in and out of the currency takes on a “foreign” currency risk, while paying a bid-ask spread each time. Producers and consumers have an interest in keeping inventory of resources they depend on to generate income or surplus. A resource that is critical to earning Y each year cannot be worth too little compared to Y, lest someone buys it up to extract rents.
This analysis has assumed an equilibrium state. If usage of the platform is expected to grow, currency value under this model is also expected to grow and should be accounted for. One approach would be to model the expected equilibrium state and then discount for time and risk.
Discussion
To summarize, we have Ms = P (F - C + i Mc) and Mc = Y / V. The final expression for the modeled market cap M can be written as
M <= P (F - C + i Y / V) + Y / V
assuming any excess fees (F - C) go toward rewarding shareholders. We can also rearrange terms to write M <= P (F - C) + (P i + 1) Y / V.
With P = 26, i = 2%, and V = 1.23, this formula implies that an extra dollar per year of user income Y adds 1.33 dollars to market cap, but a dollar extracted in fees F, if not consumed by marginal costs, adds 26 dollars. A security captures user income that a currency leaves to users, to reward the entity that enabled the income generation in the first place.
Sanity Check
As a sanity check, let’s see what the model would predict if eBay were to create a CUR token. For this example, let’s assume fees are directly proportional to user income, so F = f Y. eBay takes about 10% in fees while about the median seller profit margin is about 20%, so we’ll pick a rough estimate of f = 0.5, which implies user income is twice eBay’s revenues of $9.6b. Currency value would be Mc = 2 * $9.6b / 1.23 = $15.6b, or about 38% of eBay’s market cap, which seems consistent with the earlier prediction that CUR would be highly valuable.
The currency value comes at the expense of security value, as users would be less willing to pay fees after bearing the cost of holding CUR. Suppose eBay discounts fees by a fraction d to compensate users and keep the same level of usage. If we assume CUR creation did not cause total market cap to rise, we can equate before and after market caps to get
P (f Y - C) = P (f d Y - C + i Y / V) + Y / V
After some algebra, we have d = [ P f - (P i + 1) / V ] / (P f). Plugging in estimates for P, V, and f, we get d = 0.905, so fees would need to be shrunk by 9.5%. This seems a reasonable compensation.
Conversion of Value
A reverse shift from currency to security value can be enacted by charging higher fees and burning the excess. We start with a token that collects just enough fees to pay for costs, allowing the network to grow. Once the network has matured in size, fees can be raised to extract more income from users to raise security value. This comes at the cost of currency value because of the downward pressures on usage from deadweight losses and users migrating to a competing platform. Monopoly pricing power created by network effects may minimize the latter such that there is a net increase in market cap.
Block Rewards
Let us revisit the yearly inflation of Ethereum supply to pay block rewards to miners, a characteristic shared in common with many other tokens. Inflation is a cost to currency holders in terms of a lowered per unit value.
A standard amount of inflation is already factored into Ms as i = 2%, and factored into Mc because V is derived from 2% inflationary fiat currencies. To account for a token’s block rewards inflation of b% per year, we can set i = (2% - b%), changing Ms while leaving Mc the same.
For Ethereum’s block rewards, which are currently at 7.6%, i = 2% - 7.6% = -5.6% is negative, which is akin to saying shareholders are paying 5.6% per year to subsidize currency value. However, this model is only sensible if (F - C + i Mc) > 0 because the securities valuation model breaks down with negative profits. Unfortunately this is currently the case for Ethereum, so some discount should be made for not having fully accounted for inflation from block rewards.
The model does say that if only Ethereum were to earn sufficient fees net of costs, then it can increase its Ms from P (F - C - 5.6% Mc) to P (F - C + 2% Mc) by eliminating block rewards, a difference of 1.98Mc. That could mean close to a tripling of market cap.
Conclusion
We have developed a model for valuing cryptocurrencies by isolating security and currency aspects of tokens, and applying traditional valuation models on each separately. This has helped to untangle many intertwining issues that otherwise confuse the analysis.
The cryptocurrency space is in a state of flux, and with daily swings in such indicators as transaction volume, the modeled values vary day to day. There are many forces currently driving prices that are not captured here, so I don’t think these models can be too accurate at the moment. The goal of this post was only to come up with a grounded ballpark starting point.
