A huge $10-b Bitcoin reserve for UST was recently announced and purchases of BTC have already commenced: https://twitter.com/LFG_Reserve.
The plan currently includes an up-front purchase of $3-billion in Bitcoin to kickstart the reserve and then an ongoing purchase program for Bitcoin until $10-billion worth of Bitcoin is in hand.
Yesterday, Pomp hosted Do Kwon on his Pomp Podcast and Do mentioned that 40-50% of the growth in UST supply might be allocated to buying Bitcoin instead of burning LUNA.
This obviously has implications for the LUNA pricing model. If the value of the burn is split between Bitcoin and LUNA burning, the higher the proportion of Bitcoin purchases, the slower that price appreciation would be for LUNA.
However, having a huge Bitcoin reserve to protect UST from de-pegging (Agora proposal link) should have a strong impact on market demand for UST.
Investors who previously viewed UST as being too risky may now have a level of comfort knowing that UST can be used to purchase discounted Bitcoin should a de-pegging event occur.
In this LUNA price model update, I incorporate a parameter for specifying the relative split between BTC purchase and LUNA burn.
If you are a new visitor to my Substack LUNA pieces, you may find you need to dig around a little in prior articles to find some of the rationale and details for my particular modeling choices.
How the model changed this revision
As we are nearly through Q1 2022, I updated all model variables and assumptions, and am now using 01 April 2022 as the start date. Changes in the starting values include:
- $17-b UST market capitalization starting value;
- $90 LUNA price; and
- 350,000,000 LUNA circulating supply.
Changes in UST growth trajectory assumptions
Given the BTC reserve should make holding and using UST significantly less risky, I also bumped up the UST growth trajectory. In the last version, I had $47-b UST market cap after 12-months (31 Dec 2022).
Please note that in the charts immediately below I show UST growth out to 2027 but in the subsequent analyses I only show supply and price charts for three years out (see prior article for the rationale, which relates to the parameterization of the LUNA inverse demand function).
In this revised model, I changed the parameters slightly to give a more aggressive daily growth rate for UST early in the time horizon (Figure 1).
That revision to growth rate gives a UST market cap growth trajectory (Figure 2) and daily increment in UST supply that is substantially more aggressive than for UST growth in the prior models (see my prior Substack article link and tweet regarding an interim UST growth update).
The daily growth in UST supply (market cap), Figure 3, shows that daily growth starts at about $93-m per day and grows to $835-m per day after 3-years.
The UST growth rate assumption is the most important in the pricing model. While the current model takes a quite aggressive stance, it is easy to monitor UST and in the future adjust downward or upward as needed.
The increase [decrease] in daily UST supply is what defines how much LUNA must be burned [minted] on a daily basis.
Important note: the communications from Terraform Labs (TFL) so far has indicated that Bitcoin accumulation will total $10-billion. Of that, $3-b comes from a start-up donation from TFL (non-circulating supply) and $7-b comes from the daily change in UST supply. In this model I am going to assume that the allocation to Bitcoin continues beyond $10-b (which is actually achieved quite quickly - see below). By assuming Bitcoin will continue to be purchased over the next three years, the model’s price projections for LUNA should be ‘worst case.’
Changes in LUNA inverse demand function parameters
As in prior versions of the price model, I used the LUNA demand function to translate LUNA circulating supply into market price. Price is a function of available circulating supply and a demand shift parameter.
See my prior piece for the rationale for parameterization of the inverse demand function.
In order to calibrate the model and have a starting model price of $90 LUNA, I needed to do some minor tweaks to parameterization (see my Twitter thread for prior parameterization values). The current changes include:
- elasticity parameter (epsilon) - uniform distribution between 1.41 and 1.47;
- a - normal distribution with mean 42-million and standard deviation 5-million; and
- b - normal distribution with mean 17 and standard deviation 2.5
The new Bitcoin allocation parameter in this model (%BTC) is defined as a sequence starting at 0%, ending at 50%, and with an increment of 10% steps. The proportion of LUNA that is burned each day is simply calculated as (1-%BTC).
Model Results
Rather than presenting results for specific target dates, I decided to use UST market cap as the x-axis in all charts below. That gives a little more flexibility for making personal judgements about when the actual timing of those price and supply projections may actually occur (based on the UST growth module itself, which is defined using daily increments, the $400-b UST market cap in these charts would correspond to early-January, 2025)
LUNA burn
Figure 4 shows the projected daily LUNA burn as UST market cap increases (starting at $17-b on 01 April 2022). Each line represents a different level of parameter %BTC, which defines what proportion of the value of daily UST growth goes to purchase Bitcoin, and what proportion is left for the LUNA burn.
The initial burn levels are within the range of actual current burn rates, where the 21-day moving average of burn is around 650,000 LUNA per day. The bottom line (red) is the zero-BTC purchase level, and is the baseline for a non-BTC price model with the set of revised UST and LUNA parameters.
This level of burn stabilizes LUNA supply and prevents it from crashing to zero in this daily discrete time step model.
LUNA supply
Next, Figure 5 shows rapid deflation in LUNA circulating supply, which eventually leads to a consistently low burn rate and relatively steady supply of LUNA over time. This figure shows the mid-level (50% probability band) for LUNA supply under five different Bitcoin allocations, ranging from 0% to 50% of the increase in daily UST supply.
In this case, LUNA circulating supply stabilizes around 23-million if all of daily UST growth is allocated entirely to the LUNA burn and around 118-million if Bitcoin buying is maintained at 50% proportion all the way to a $400-b UST market cap (this results in a BTC reserve far above $10-b).
Alternatively, it is possible to look at confidence intervals for particular BTC allocations. Figure 6 shows the 90% confidence interval for an ongoing 40% allocation to Bitcoin (and 60% allocation to the LUNA burn). All confidence intervals reported in this piece are based on 500 model runs.
LUNA price
Given daily UST supply growth and an allocation for Bitcoin purchase, LUNA price projections for each level of %BTC are shown in Figure 7. These projection lines are all for the 50% probability band at each Bitcoin allocation level.
The upper line denotes 0% allocation to Bitcoin purchases, while the lowest line represents 50% purchases on an ongoing basis.
Key price levels include:
- $650 LUNA price at $100-b UST market cap, given Bitcoin purchase allocation rate is 50% over the duration of UST expansion to $400-b market cap;
- $1250 LUNA price at $100-b UST market cap if all UST supply growth resulted only in LUNA burn;
- $1000 LUNA price achieved by UST $89-b market cap (early-May 2023 with current UST growth trajectory) when there are no Bitcoin purchases; and
- $1000 LUNA price achieved by UST $127-b market cap (late-August 2023 with current UST growth trajectory) when there are 50% of UST supply growth is allocated to Bitcoin purchases.
At the far right of the x-axis, LUNA price ranges from $15,000 (%BTC=50%) to $49,000 (%BTC=0%) at $400-b UST market cap.
Yesterday (24 April), InvestAnswers ran a full YouTube segment on LUNA price, with a model that suggested LUNA price could theoretically reach $80,000 by the time UST market cap reached $348-b.
My results are lower at that $350-b UST market cap range, with a price of $32,000 if all UST growth was allocated to the LUNA burn and $10,000 if a 50% Bitcoin purchase allocation was kept up the entire duration to $350-b UST market cap.
Note that the models differ in how LUNA market cap is handled (fixed in the InvestAnswers video, variable in mine and calculated based on the LUNA inverse demand curve). At the end of the video, James had said he wanted to have me on to talk about the models, so fingers crossed we can combine our models with a combo of LUNA burn dynamics and Bitcoin pricing implications.
It is also possible to look at LUNA price in terms of confidence intervals for any particular %BTC allocation. Figure 8 shows the 90% confidence intervals for a 40% BTC allocation.
For example, at $100-b UST market cap, the results show that LUNA price will land in the $600 to $1000 range for 90% of all model runs. At $350-b UST market cap, the 90% confidence interval range is $8,400 to $21,200.
Again, just as a reminder, this assumes Bitcoin ac
cumulation through the entire period, not only to $10-b worth of spending for the BTC reserve (so these prices are very much on the conservative side compared with a model where BTC purchases were cut off when $10-b had been spent).
Bitcoin reserve
Next, let’s move to the Bitcoin reserve chart (Figure 9). This figure shows how much would have be spent on BTC if purchasing was maintained for the entire duration of the model’s time horizon.
The first thing to notice in this chart is how quickly the $10-b reserve level can be attained. At 50% allocation to Bitcoin purchases, the $10-b reserve is fully in place by the time UST reaches a $31-b market cap (end of July 2022 when translating to calendar time). At a 10% allocation level, the $10-b reserve level would be reached when UST market cap hit about $87-b (late-May 2023).
If the Bitcoin reserve were funded at 50% through to $400-b UST market cap, a total of almost $200-b would have been spent on Bitcoin reserve purchases.
I don’t have any special insights on how large the reserve fund could/should be. It’s quite apparent, however, that the reserve could be increased substantially beyond the $10-b spend level and really only modestly delay LUNA price appreciation. If Bitcoin spending was curtailed after reaching a $10-b spend level, it doesn’t really look like the LUNA supply shock timing would be impacted very much.
I thought it would be useful to look in more detail at the blank space in Figure 9, so ran the model again with 2% Bitcoin allocation increments between 0% and 10% (Figure 10).
Even a long-term Bitcoin purchase allocation of 6% (leaving 94% for LUNA burn) would result in a $10-b total Bitcoin allocation by $100-b UST market cap.
Some questions
This analysis, accounting for various levels of substituting Bitcoin reserve purchases for burning LUNA, leaves open some questions.
First, from a LUNA valuation perspective there is a question - if you are a LUNA maxi - as to whether you may be worse off because of the Bitcoin reserve purchases. That is, do you lose or create additional wealth because of the reserve?
The answer to that has at least two important parts.
First, the answer will rely on how must UST demand increases as a result of the extra level of risk mitigation Bitcoin provides. My own suspicion is that having the reserve in place is likely to increase UST demand to an extent that LUNA price appreciation will probably more that compensate for the loss of 100% burn. But only time will allow that part of the question to be answered.
Second, there is a question of how the Bitcoin reserve adds value to LUNA. Obviously increases in UST demand would be the primary pathway but it may also be possible that additional demand-side value is added. Conceptually, this could be because investors attribute some premium to LUNA price just because they know there is a large pool of Bitcoin securing the network. It is possible that investors who have no intention of using UST might still derive speculative value from LUNA. Trying to account for this in the model is far too sketchy to be defensible, so I just leave it as something to keep in mind.
Duration and magnitude of Bitcoin purchases
Another issue is also worth considering - that relates to how much of the current LUNA burn should be allocated to purchasing Bitcoin and how long that purchase program should last. Current information from TFL suggests the accumulation could stop once $10-b is spent.
The figures in this piece, however, were all created assuming Bitcoin purchasing continues unabated. This would result in a huge reserve (and the reserve calculations are based only on UST spent on Bitcoin, not any Bitcoin price appreciation that my occur later).
Figure 10 shows the ratio of LUNA to BTC market cap in this model (just ignore that top line - it is just LUNA market cap divided by the initial $3-b Bitcoin purchase that was funded from TFL holdings).
One thing that struck me looking at this is that the ratio declines early as UST growth picks up, stabilizing in the $75-b to $125-b UST market cap range. Even if the allocation rate was 10% to Bitcoin purchases, spending on the reserve would already have reached $8.8-b by the $75-b market cap.
I haven’t convinced myself yet, but it may make sense to the LFG to keep accumulating Bitcoin beyond $10-b. At $125-b UST market cap, Bitcoin reserve spending ranged from $14-b (10% allocation rate) to $57-b (50% allocation rate).
Much will probably hinge on how fast a large reserve should be built up. With a 50% Bitcoin allocation, a $10-b reserve could be fully funded by the time UST market cap hit $31-b (late-July 2022 given the model’s UST growth assumptions). For lower levels of allocation, the $10-b reserve could be filled when UST market cap reached about $34-b, $40-b, $52-b, and $87-b for allocation rates of 40%, 30%, 20%, and 10%, respectively.
Assuming BTC contributions cease at some time and all the UST growth goes back exclusively to the LUNA burn, all the supply and price projections in this piece are very much on the conservative side.
Conclusion
Some LUNA investors may be disappointed that LUNA price appreciation could be pushed back a little, as a portion of the LUNA burn is instead allocated to Bitcoin purchases.
Personally, I think that considering only price action is a little bit of a red herring.
The reason is that the expected value (EV) of LUNA will likely increase greatly once the Bitcoin reserve is in place.
Individuals with backgrounds in finance or economics will be familiar with EV, but I expect there may be people who read this piece that are retail investors and who didn’t receive formal math training. So a short explanation is warranted (please see my extended piece on EV if you want a more detailed explanation - there’s a downloadable Excel sheet for calculating EV too).
Let me first make the assertion that the price of LUNA is either going to go to zero or it is going to go to some astronomically high price. There’s probably not going to be much in the way of middle ground over the long-term.
EV attaches probabilities to possible price outcomes and tallies (probability x price) calculations across all possible price outcomes.
Say the odds of going to zero were 20% and going to $1000 were 80%. EV would be (0.2*$0)+(0.8*$1000) = $800.
You can expand the number of price points in the calculation but the process is the same. As an investor, you should be willing to buy an asset when it’s EV exceeds the actual market price you have to pay.
Now say for LUNA, that you believe (yes, EVs are subjective) there’s initially a 20% chance it goes to zero. If you believe that the Bitcoin reserve now reduces the probability that LUNA price falls to zero, that has a potentially very large impact on the LUNA EV calculation.
For example, imagine what would happen if LUNA either went to $0 or to $50,000, but that there was no middle ground. Every 1% swing in probability away from going to zero, in favor of going to $50,000, would add an extra $500 to EV.
Slowing the speed of LUNA price appreciation a little (if UST demand didn’t actually pick up enough to compensate) really doesn’t make any significant difference to the LUNA EV calculation in the medium- to long-term. What matters is reducing the likelihood of that zero outcome.
I personally think the Bitcoin reserve is a great move - my view is that it reduces the risk of downside price potential for LUNA, and thus has potentially huge impact on LUNA’s EV. But, do remember EV depends on personal beliefs about risks and potential price outcomes, so definitely my EV will not equal your EV.
That’s it for this post - I will be keeping an eye on UST growth rates and will provide another update when either the UST growth trajectory warrants, or if there are any major clarifications regarding the new Bitcoin reserve mechanics.
About the author
I am a Canadian applied micro-economist and policy researcher. My undergraduate and MSc degrees are in agricultural economics (UBC) and my PhD was in Environmental Sciences (economics of households and consumers / rural and agricultural policy) from Wageningen University, Netherlands. I have held faculty positions in environmental economics and policy at Memorial University (Assistant Professor and Tier II Canada Research Chair in Ecological Economics), University of York, UK (Senior Lecturer in environmental economics), Emory University (Associate Professor in environmental policy), and the UN’s World Maritime University (Professor and Nippon Foundation Chair in Sustainable Ocean Governance & Marine Management). My academic publications can be found on Google Scholar.
Disclosure
I am a LUNA investor. This piece should be viewed as investment opinion and education, not investment advice. Always do your own research and invest according to your own goals, objectives, and risk tolerance.