The Fundamental Valuation Framework for Cryptoassets — Part 1.5 ($LUNA)
In our last article, we introduced few valuation metrics based on cryptoassets’ fundamentals with $ETH as the primary example. We also dropped on $LUNA and $FTM along the way as these two chains offer much more statistics on their respective explorers than their competitors. This time, we will run a similar analysis again on $LUNA, but with a much deeper look into the valuation models.
Why $LUNA? We thought $LUNA was a much better example to play with as it dynamically adjusts its supply through the $LUNA-$UST burn mechanism, as opposed to $FTM which has a fixed supply cap. Other L1 chains does not offer easily accessible on-chain statistics, so they are off the table.
We searched the Web2 last week and slightly expanded our boundaries of knowledge — we brought two more models here.
Now the model we examined(=we looked at the abstracts and discarded) are:
- Blais (2021) : transactional benefits as a medium of exchange
- Cong (2020) : dynamic asset pricing model as a medium of exchange
- Hayes (2016) : COP(Cost of Production) approach
- Woo (2017) : NVT(Network Value to Ttransaction) model
- PlanB (2019) : S2F(Stock-to-Flow) model
- Mahmudov (2018) : MVRV(Market Value to Realized Value) model
- Sockin (2020) : valuation as a membership in a platform
- Liu (2021) : valuation according to technological sophistication
- Liu (2022) : PU(Price-to-Utility) ratio
Most of the above valuation models were discarded as they were overly complex, with lots of parameters to estimate, as they try to explain behaviors of each economic agents. And some were discarded as they were only applicable to PoW(Proof-of-Work) cryptocurrencies. If you are interested in economics and math, maybe you could check them out.
We cherry-picked a few of them for our $LUNA analysis:
- Alabi (2017, 2020) : network value (MetCalfe’s Law)
- Burniske (2017) : QTM (Quantitative Theory of Money)
- Viswanath et al. (2021) : valuation for Proof-of-Stake tokens
The first two we already introduced in our last article, the latter one not yet. We will look over the model’s assumptions and intuitions, and we will value $LUNA accordingly.
For the basic idea of Alabi (2017, 2020) and Burniske (2017), please refer to this link. However, there was one thing we intentionally left out in our last write: Alabi (2017, 2020) used a different form of MetCalfe’s Law, not V(N) = C*N².
We will run the Alabi’s version for the pricing function, and compare it to the MetCalfe’s one.
Viswanath et al. (2021) — PoS Valuation
Viswanath el al. (2021) provided us with a framework to value PoS tokens. Their logic is quite simple — since PoS tokens can be staked, investors needs to make a decision on whether to HODL the token for transaction purposes, or to stake them to generate cash flows. This PoS attribute renders PoS tokens into a risk-return profile similar to TradFi assets.
We will not go over the all derivations as it is beyond our scope, but the basic flow goes:
- Every transaction is taxed, and taxes are accrued to stakers(all tax rewards are converted to USD).
- Consumers need the token to consume goods and services(or to make transactions).
- So there should be an equilibrium proportion of staked tokens to held tokens.
- Higher velocity for a PoS token means more staked tokens as less tokens are required to transact the same output. If a PoS token has INFINITE velocity, no one holds the token and everyone stake all their bags(in this case inflationary tokenomics yields no economic benefit as all stakeholders are equally diluted).
- Higher taxes(transaction fees) might increase the yield to stakers until a certain inflection point, and the yield actually decreases as too high taxes imply less transactions(Laffer Curve).
For a stationary case with constant growth rate, tax rate, etc., the above process abbreviates to:
Model parameters
Pt : token value (in USD)
Yt : total tx (measured in USD)
k : consumer holdings, inverse of velocity
c : tax rate
gs : inflationary staking reward rate
rf : risk-free rate
gyQ : transaction growth (risk-neutral tx growth rate)
So more transactions = higher token value.
More HODL behavior = higher token value.
Higher staking rewards = higher token value (iff there are enough HODLers).
Higher transaction growth = higher token value.
We will illustrate the model with $LUNA soon.
$LUNA Valuation
Before we carry out any valuation, we need to determine the velocity of $LUNA. The velocity of a token shows how many times a token changes wallet during a period of time. Since the blockchains contain all the transactions unlike in TradFi, we can directly calculate velocity from the transaction volume and the circulating supply.
We will drastically simplify the Terra ecosystem as having a sole product: $LUNA. The effect of its stablecoin adoptions would be taken into account in the supply side.
More people use $LUNA = Higher demand for $LUNA.
More people use $UST = Lower Supply for $LUNA.
In our simplified model of $LUNA, only $LUNA transactions affect the demand for $LUNA, and the $UST adoption only burns $LUNA. This simplification has an additional advantage outside of being easy to calculate — it could tone down self-churn problem.
Self-churn problem refers to activities such as burning & minting tokens, self-sending tokens, moving to CEXes, etc. that are not used as transactions of value. A study by Zochowski showed that removing self-churn problems would bring the cryptocurrency velocity from double-digits to single-digits.
As we are taking out a huge transaction volume — $UST — from our calculation, we are automatically adjusting our velocity of self-churn problems.
We can find the transaction volume of $LUNA on Terra Station, but that sudden spike of the transaction volume is a bit disturbing. So we will take the last 14 days of $LUNA transaction volume and annualize them.
$LUNA annual transaction volume = 58.58M $LUNA/14*365
If we divide the annual transaction volume with the circulating $LUNA supply which is at ~400M right now, we have velocity of 3.8.
Depending on which period we take, we end up with velocity between 3 — 6. It is also coherent with the $ETH velocity, which was around ~4, so we will take it as a fair value.
PoS Valuation Model
So our model parameters for Viswanath et al. (2021) would be
k = 1/6 = 1/velocity
c = 0.002% = annualized 30d average tax rate (available on Terra Station again)
gs = 5% = inflationary staking rewards (in the LR)
rf = 17.8% = Anchor deposit yield
gy = 5% = transaction volume growth rate
Now k, c, gs are easy to get, but rf and gy are tricky ones. Remember we have stated that the Viswanath model intended to compare $LUNA to TradFi assets?
Naturally we thought we should use the US Treasury rate, but then getting the “risk-neutral transaction volume growth rate” would be another hard task. So instead we chose the most used risk-free metrics for the Terra ecosystem, the Anchor rate.
For gy, please look at the graph below.
If you look at the transaction count on the Terra network, it seems to be quite growing linearly with t. If you run a linear regression on Tx to t, you would get a t-value of >100 with the beta coefficient of 937, translating to the current annual growth rate of 70%. Since we are looking at the “long term” growth rate, we will greatly tone down the growth rate to 4.5% — if the network continually grew at the rate of 937 transactions per a day, after 20 years it would be growing at ~4.5% annually.
Plug in those parameters and divide by the circulating LUNA supply, and we have the graph below.
At first glance the model seems quite off, but the beauty of this model is that we have not used any market price data(except maybe for the transaction volume) to value LUNA, we arrived at the model price solely with the fundamental numbers.
Now we will use the model to project the future price of LUNA from its projected transaction volume. We will use tx(t) = 937*t regression equation for this year.
Thus we can have our price projection with respect to the transaction volume:
With our parameters, LUNA would reach $92 by year end. The circulating supply is set to decrease towards 362M throughout the year.
Network Model
We have done the same work last time, so this time we will 1) run sensitivity tests on LUNA price and 2) graph the Alabi version as well alongside with the MetCalfe’s version.
First, we need a representation of the active addresses on Terra network. As we did last time, we can fit the netoid function parameters with the actual values grabbed from FlipsideCrypto and get our Network Function.
The model parameters are
p = 38,988
v = 0.012
tm = 347
which means, the maximum daily active addresses Terra network would have is capped at 38,988, it grows at 1.2%, and its maximum growth period was at t = 347, which was around Nov 2021.
Another function we need to estimate is Price Function, and we will go for the MetCalfe’s Law first. If we fit the active addresses (30D MA) to $LUNA MC, we have the following graph:
For MetCalfe’s Law, we have C = 39.14. We combine our Network Function and Price Function, and divide by the circulating supply to have LUNA price estimate.
We have many great write ups regarding $UST MC ~ $LUNA Supply relationship, and for convenience, we will divide the circulating supply into two cases: Bear case, with the supply rising to the max supply LUNA historically had, and base case, with the supply dropping to the min supply LUNA ever had.
If we look at the supply data from SmartStake, we can observe the supply of LUNA skyrocketed recently with the MIM-UST unwinding. For our analysis, we set the UST adoption with MIM-UST as our base case.
As aforementioned, the blue line represents the daily active addresses of ~38,700 by the EOY, with the circulating supply at 362M. The red line represents the same daily active addresses, but with the circulating supply at 485M. The green line represents the daily active addresses of ~31,000 by the EOY, with the circulating supply at 362M.
With our base case, LUNA should reach $162 by EOY, and each of our bear cases also points at >$100 LUNA by EOY.
Network — Alabi Model
The only difference between the above one and this one is that the value of network becomes:
Not V(N) = CN².
If we use statistical programs to estimate the parameters, we have the following graph.
Two models are nearly identical in terms of the trend, but the Alabi’s version catches up with the upward trend a bit quicker.
Alabi’s model points at $131 per LUNA by EOY.
QTM Model
The QTM model has a relatively simple structure, so we don’t really need any statistical tools to estimate paramters.
We already have our model parameters from our previous calculations, so we can straight head to the actual valuation.
Tx Count simply means the daily transaction by the EOY, and we used it for the PoS Valuation, and multiply it by Avg Tx price to get the transaction volume measured in USD. Velocity, we also established that it should be in the range 3 ~ 6, the rest are quite self explanatory.
As the actual data shows the Avg Tx price of ~610, and we calculated the velocity to be 3.8 above, this serves as our base case. To be a bit more conservative, we could use the velocity of 6.
According to the QTM model, LUNA should be $123 by EOY.
Personally I prefer the Network Model to other valuation models, because it requires much less assumptions compared to other models. Nonetheless, although all models come with drawbacks, the Network Model has one serious limitation: The maximum active address count is hard capped at a number.
LUNA MC would reach $60B by 2023 year-end, and it would not grow from there. Of course, still the LUNA burn mechanism could lead to the appreciation in price, but capping the network growth at a certain number is a huge drawback. Maybe the Terra network is still in its nascent stage, so all our parameters might be wrong due to the short time span.
The Ethereum network, if we only used the data until Jan 2018, would have been modelled to attain its maximum MC about early 2020. Did it grow from there? Certainly.
The bottom line is, believe it or not, the network fundamentals we all know about — transaction counts, transaction volume, active addresses — are actually important factors in pricing the network tokens. Although there wouldn’t be the magic number of “Transaction Volme/Price Multiple”, as we have none of that even in the 400 years old stock market, but at least we can now confidently say “the Network A has growing transaction volume and active users, so it’s gotta be more expensive.”
