# The BTC equilibriumating and the ETH one-eightening

*Epistemic status: may or may not make you a bajillion dollars. Tots not investment advice.*

These are my summary notes on John Pfeffer's [An Investor's Take on Cryptoassets](https://s3.eu-west-2.amazonaws.com/john-pfeffer/An+Investor's+Take+on+Cryptoassets+v6.pdf) [December, 2017] and
 and one "[SquishChaos](https://squish.substack.com/)"'s [aka Nikhil Shamapant] [Etherium, The Triple Halving](https://drive.google.com/file/d/1bECqgijhgjdS782AB620gFjK5qx-vA99/view) [April, 2021].

You may know of the Squish report as the source of a spicy $150k price prediction for Eth. My friend mentioned that it was being well-received by people in the finance industry, so I decided to take a look. By my own (financial neophyte's) judgement it seems reasonably sophisticated, decently-reasoned and has compelling, time-sensitive predictions. I think reading Squish alongside Pfeffer is productive, as they have different foci and [potentially?] different conclusions. There may also be a conflict in their analysis of the impact of Proof of Stake on network value (and, ultimately, token value) which I'm curious to see folks unpack here.

Both are well-written, light on the jargon yet informationally dense, but not oppressively so. I was able to do a read-skim of both such that I got a Pareto 80/20 in a few hours. I'd highly recommend taking a look at both if you find these summary notes interesting -- my goal here is to provide a scaffold of their arguments, such that interested parties can have a conversation, rather than to reproduce them in detail.

I've inserted my own questions throughout this document -- I have more questions than opinions at this point.

# An Equilibrium valuation model of crypto 
*Note: Unless otherwise noted, pull quotes in this section are from Pfeffer.*

Pfeffer provides an equilibrium approach here, asking what the steady-state valuation of a crypto asset will be. He provides a simple mathematical model:

$$
M = \frac{PQ}{V_{elocity}}
$$

where M is the money supply, PQ is the sum of the product of the Price and Quantity of resources consumed by the currency (ie, compute PQ + bandwidth PQ + storage PQ + watts PQ + dank memes PQ, dank meme-lords PQ, etc). If T is the number of tokens that have been issued, we have a sweet little model for valuing a token: $V_{alue} = M/T$.

Pfeffer is primarily analyzing Bitcoin and Etherium here and seems close to being a bitcoin maximalist. Writing in 2017 he's quite skeptical of Etherium as an investment vehicle. Proof of Stake [PoS] was already being discussed in 2017; he models the outcome as follows:
- Because PoS is dramatically more computationally efficient, it will lower resources embodied in the network, ceteris paribus, lowering PQ.
- This will be slightly counterbalanced by tokens being tied up in staking pools, which will drop Velocity, but not enough to counter the drop in PQ.
- This problem will also be exacerbated by sharding and rollups which will dramatically increase transaction rates, increasing Velocity.

Pfeffer in 2017 feels this will wipe out Eth valuations, altho significantly, he's writing two years before [EIP1559](https://eips.ethereum.org/EIPS/eip-1559), which layouts a plan to "burn" network fees,  or details of the PoW merge were finalized.

## Forks
Pfeffer also has concerns about the future of crypto assets with codebases that can be forked, concluding that section:

> For a fork to succeed, there needs to be enough value available to arbitrage to incentivise users, some miners and a sufficiently credible developer group to support the fork. It should therefore be acknowledged that, to the extent the equilibrium outcome is arrived by way of one or more forks, there could be a sustainable level of network value economic rent premium above computing cost that is too small to provide adequate incentives for a fork to succeed. I would not, however, consider it to be a very compelling investment thesis when the best I can hope for is to keep an amount of value corresponding to an economic rent that’s too small for anyone to bother arbitraging it away from me despite relatively low barriers to doing so.

I don't offhand know how far into the ICO bubble this was, to be able to call this prescient or not. I also don't know what to think of it right now, possibly at the end of another bubble but with bitcoin and eth both having recently reached all-time highs.

GAS decouples ETH price from the underlying real costs, so may provide some protection from aggressive forks, bec it can be adjusted to remove arb opportunities, but the entire point of Pfeffer's argument is that scaling Eth will be great for the economy and end-users, but terrible for investors.

> On 23 December 2017, the total amount of ETH used to fuel transactions ... was ETH 1,388, worth about $1 million at $700 per ETH. Annualised... this is about $355m per year... let’s assume Ethereum network traffic grows from here at the same rate internet traffic grew from 1995 to 2005 (roughly 150% growth per year) and that the combined offsetting impact of declining computing costs is -20% per year (optimistic as this approximates only the effects of the average rate of decline in computing costs without a change in the consensus mechanism; implementation of proof-of-stakeor other scaling solutions could represent a step change down in the computing costs of the network by orders of magnitude). The combined net effect would imply ‘Ethereum GDP’ (PQ) doubles each year. At this rate, Ethereum GDP would grow from $355millionto $363billion in ten years, an over thousand-fold increase. **If we assume an ETH velocity of 7, the network value of ETH would be $52billion in 10 years, about 24% less than its current network value of approximately $68 billion.** [Emphasis mine]

__Q: How do these projections look 4 yrs later?__

Pfeffer also makes some arguments about BTC/Eth as likely stores of value vs units of exchange, opining that it's more likely that there will be specialization rather than one-coin-to-rule-all, with BTC very well positioned as a value-store. Eth, OTOH, may or may not win as unit-of-exchange, but whichever coin does become the exchange coin, it will likely be acquired on an as-needed basis and not be hodl'd. The vision is e-gold that you then convert to e-cash on demand. Pfeffer projects a $260 - 800k valuation of Bitcoin based on a network value estimate of $4.7 - 14.6 trillion.

> Regarding risk, an investment with a 20x – 60x upside only requires a probability of success of between 2% to 5% to be a positive net expected value investment. Each of us can reflect on his own view of what that the probability is of the foregoing scenario materialising. I’m personally pretty comfortable that,given where we are today in Bitcoin’s development and adoption, that the probability is higher than 2–5%, likely much higher. While there are many technical, political, regulatory and psychological hurdles ahead, the store-of-value use case is by far the simplest one, and already closest to reality.  I would argue therefore that here you have an investment with a downside:upside skew of -1x:60x and a positive net expected value. Investments with both those characteristics are extremely rare.

Looks pretty good in hindsight, what're the new odds now? Interestingly, we're about to see another prediction of a possible 30 - 50x upside.

__Q: Does Does Pfeffer's $M = PQ/V$ model empirically predict anything about crypto prices up until this point?__

# Squish
*Note: Unless otherwise noted, pull quotes and illustrations in this section are from Squish.*

Pfeffer's analysis is a fundamentally equilibrium and long-term one, whereas Squish's is a disequilibrium, flow-based, medium-term one. It's also the actionable one, if you think it's credible.

For Squish, the key factors are that decreases in liquidity of supply lead to increases in volatility and price spikes, combined with a strong claim that *certain types of supply illiquidity cannot be priced in ahead of time.*

In this flow based model, the projection is that the merger of EIP1559 and PoW [currently planned for June and December 2021, respectively] will lead to the lock up ~90% of coins, equivalent to three BTC halving events. These will be events that can precipitate a dramatic drop in Etherium sell-liquidity, which would then proceed to drive Eth's price up dramatically through 2023.

Okay. Why can't this be priced in? Squish spends considerable ink on this, I encourage you to consult them directly, but I'll include some relevant quotes below, as well as my own attempted illustration, here: in an elastic liquid market foreknowledge of decreased liquidity cannot be [fully?] priced in because by definition if it's liquid + elastic, there are people transacting at the current price, and pressure up or down is met by changes in supply/demand which dampen those movements. Image the hypothetical country of Examplestan. On Jan 1st everybody wakes up from their hangovers to news that for... Reasons, in one year, the supply of gas will drop by 90% for one month. What happens to prices over the next year? Maybe.. not much? Some ants prudently buy spare storage canisters and calmly fill them up; some grasshoppers procrastinate for eleven months. Probably in December lineups start to form at gas stations, but if supply is still unaffected, prices probably stay stable through December. But during January, if for some reason you do need to buy gas, you're screwed: illiquidity leads to massive volatility and price spikes. This is purely my gedanken, and should not be taken as dispositive of the broader case if it's somehow flawed.

Returning to Squish, they phrase it like this:

> For something like an apple, you can simply model demand increasing as price declines because consumers prefer lower prices. Investable assets are never so simple. Rather than thinking of elasticity of the asset itself, we can think about the elasticity of flows from investors. For example, short-term investment funds that quickly sell holdings on small increases in price can be considered a highly elastic source of supply flows, whereas long-term investment funds that hold assets regardless of increases in the price of their assets can be considered a highly inelastic source of supply flows... the concept of elasticity of supply and demand flows nicely captures the relationship between liquidity and volatility. If a $1 price increase in ethereum causes huge supply inflows as investors start selling, ethereum would not keep rising because prospective buyers would not need to pay up. When I say an asset is dominated by highly elastic flows, I am saying that whenever the price changes, there are huge supply and/or demand inflows that increase liquidity and dampen volatility for the asset.

Squish sees hardcore cypto investors as a large source of inelastic demand, extrapolating from Bitcoin hodlers who won't sell in the face of 10x or 100x gains, to an even higher level of fanaticism from eth stakers, because of the cash flows from staking. If bitcoin maximalists hodl through thick and thin when the only upside is capital gain, how much strong will that trend be when hodling also gets you a cash stream?


Behold: hodling!

![Graph of bitcoin wallet sizes vs BTC price. They are tightly correlated and grow expentially.](https://i.imgur.com/K95oB5N.png)

> In any ordinary asset, you would expect rebalancing out of such an insane amount of capital, but these large bitcoin wallets are all held by HODLers, so instead you continue to see the number of large wallets rise, showing the growth and stability of HODL culture in the Bitcoin community.

This is inelastic demand: stacking satoshis at any price. Note that this framework is consistent with prices falling one year after a Bitcoin halving event (ie, right god-damn now): in this view, we're simply shaking off the paper-handed fops who are spooked, which is unlocking a temporary pool of liquidity. The underlying process of transferring BTC to those with inelastic demand (hodlers) can continue through this.

This dynamic is combined with Bitcoin's build-in halving events to create cycles of illiquidity and volatility. Rather than "maturing" as some people have speculated, Bitcoin volatility is baked in and will likely grow over time:

>... all halving related money flows are long lasting, persistent, flows that don’t change in direction over time. My thesis is that this creates an edge in price action over a different time frame, and given illiquidity conditions of the underlying, can kick off a supercycle...

> ...these effects cannot be priced in because they are the flows themselves. The concept that the market “prices in information” is one we take for granted. But when you dig into it, what we mean is that money flows react to new information relative to current prices so as new information comes online, price rises and those new inflows decline until the price reflects that information. Structural flows, however, aren’t reflexively changing in response to information, so they can’t be priced-in ahead of time without the structure changing

Returning to Etherium: there's already almost 4m ETH staked before rewards have even started being issued, 3.3% of Eth market cap. These are people so committed to hodling that they've bound themselves to the mast. Additionally, three times as much Etherium has been locked into defi. For Squish these are leading indicators of a massive drop in sell pressure coming.

> Explicitly, I am making the case that future inelasticity of Ethereum’s supply will, for reasons of simple economic incentives, vastly outweigh current inelasticity of Bitcoin’s supply...

Squish points to other instances where flow changes that could have been anticipated ahead of time still lead to rapid price spikes. Squish references research on price drops as IPO lockup-periods expire[^1][^2][^3], none of which I've had a chance to look at yet, as well as this specific example of Tesla joining the S&P 500. I believe the implication here is that ETFs like SPY and other institutional investors were obligied to buy large amounts of Tesla following the listing, and Tesla holders tend to be hodlers because.. they have big Musk Lust?

![Graph of Tesla stock price pre and post joining the S&P500](https://i.imgur.com/GyjPnKR.png)

__Q: Is this joining-the S&P effect robust with other companies? If it isn't, how convincing is an "Elon fans are hodlers" story?__

The creation of a new etherium ETFs may also be an important source of buying pressure, leading to yet more volatility:

> between significant investor flows into staking, significant investor flows into locking up their Ether in DeFi, and significantly increased rates of Ether HODLing, these new funds aren’t going to find a lot of available supply - but they have no choice but to buy anyways, at any price. Again we’re back to our volatility model - Illiquidity breeds volatility.

Squish converges on their >$100k price ceiling a few different ways, although you may quibble with their logic. Eg:

> If I can buy 1000 ETH and stake them for a 25% yield (Justin Drake’s best guess for APR after Proof of Stake) and a 2% annual share repurchase (Justin Drake’s best estimate for supply deflation after Proof of Stake), then my 1000 ETH produces a pretax “owners earnings” of 270 ETH. Let’s assume I sell 40% to cover my tax bill, so I get an after tax earnings of 162 ETH per year on my 1000 ETH “loan” to secure the Ethereum network... As a bond, in this interest rate environment with the S&P 500 at an earnings yield of 2.3%, a discount rate of 3% seems fair. This yields 5400 ETH.

To make this explicit: this is the formula for valuing a perpetuity, $C/r$  with a 162 Eth Coupon and 3% return. This 5x factor is then used to multiple a $20k base price derived from a valuation model by Raoul Paul that doesn't factor in staking. Does it make sense to model staked Etherium as a perp with a fixed return? Maybe not. Is a 5x factor unreasonable? ¯\_(ツ)_/¯ Regardless, this leads to Squish's base-case price target of $30 - $50k based on illiquidity and flow analysis and a volatility induced ceiling of $150k.

Another derivation:

> Prior valuation models based on inferior comparables (BTC Stock to flow, Payment networks, Metcalfe’s law, DCF model on YTD fees) result in a 30-50k base case. In a flows-based market w/ triple halving catalyst, 150k is achievable... the catalysts don’t even really begin until July or really November 2021 when the merge to Proof of Stake occurs. These flows could take another 12 months to fully manifest, so my target price expiration date is January 2023

After 2023, Squish gestures to Pfeffer's concerns about equilibrium performance. Ie: don't expect >$100k to be stable, if we get there.

__Q: How do we reconcile Squish's analysis that Proof of Stake will lead to massive liquidity drops with Pfeffer's prediction that Eth's valuation will be eroded away?__

## Failure modes
I'm going to quote and lightly kibitz Squish's litany of how this could go wrong here:

> 1. EIP1559 or Proof of Stake doesn’t get passed. Similar to Merger Arbitrage risk. The main risk here is miners revolting.
    - https://our.status.im/vitalik-escalates-eth-2-0-merge-as-miners-plan-a-51-attack/
    - https://stopeip1559.org/

__Q: Does EIP-1559 actually guarantee deflation?__

The actual EIP document describes a mechanism to burn transaction fees, but doesn't fully specify the monetary policy implications:

> By burning the base fee, we can no longer guarantee a fixed token supply. This could result in economic instability as the long term supply of ETH will no longer be constant over time. While a valid concern, it is difficult to quantify how much of an impact this will have. If more is burned on base fee than is generated in mining rewards then ETH will be deflationary and if more is generated in mining rewards than is burned then ETH will be inflationary. Since we cannot control user demand for block space, we cannot assert at the moment whether ETH will end up inflationary or deflationary, so this change causes the core developers to lose some control over Ethereum’s long term monetary policy.
- Source: https://eips.ethereum.org/EIPS/eip-1559

__Q: If 1559 doesn't guarantee deflation, does something else codify it?__

> 2. EIP1559 and Proof of Stake get passed but there are issues with the upgrade
> 3. Proof of Stake is delayed more than 2-3 months.
> 4. Transaction fees are too low after scaling for fee burn to have an impact on price.
> 5. Scaling could fail to reduce fees.
> 6. Volatility doesn’t need to mean upside volatility. If illiquidity is created, but bitcoin peaks before demand can flow into Ethereum, maybe illiquid outflows tank the price too much for the triple halving to make a difference.
> 7. Ethereum is a “risk on” asset and a liquidation event in global markets would tank Ether
with all the rest of the world’s assets, just like in the 2020 COVID crash.
> 8. If Bitcoin has major outflows before Ethereum’s narrative is adopted, it would be a major headwind for Ethereum’s price that could acutely overcome the effect of the triple
halving.
> 9. The SEC could decide to never approve the [Etherium] ETF or the ETF doesn’t get expected inflows.
> 10. The SEC could approve the ETF before Ethereum becomes illiquid, reducing the
volatility when those flows enter the asset
> 11. Geopolitical regulatory risk could arise. If Ethereum at 100k is a ~10T market cap, this could easily become a new issue.
> 12. Ethereum’s monetary policy could change towards a more inflationary stance. It never has in Ethereum’s entire history, but many Bitcoin investors seem to think that’s a real risk they want priced so I figure I’d mention it.

__Q: What are reasons to think Eth might become inflationary?__

> 13. What if the triple halving can be priced in? What if everyone does know about Ethereum and DeFi and I just don’t see it in my information bubble? The unknown unknown is always a concern.
> 14. I could be *technically* wrong but incredibly close. With these kinds of flows and
illiquidity events, the confidence interval on price is obviously extremely high. I wanted a falsifiable price target, so I picked $150,000. Price could peak at $100,000 before Jan2023 because there just wasn’t enough fuel to move that extra distance.


I'd add to this list: technology risk from deploying Proof of Stake, a relatively new technique at scale.

## The Squish Edge

As part of their justification for what their edge might be, Squish gives that very few analysts are looking at Eth using a price flow basis, particularly on these longer-term timelines, plus relative freshness of the information: the report was written in April 2021, using information current to the last month.

## Some fancier strategies:

Squish ends with some ideas for folks who might want to get fancypants:

> Ethereum is a “risk on” asset, and if the market crashes, so will it. Knowing this, we can use non-linear hedges to increase purchasing power in the event that happens. Check out the short-term correlations of VIX to Ethereum. It might be worth hedging Ethereum with deep out of the money S&P 500 puts or VIX ETP call options with a small % of the Ethereum exposure (0.5%-1%) that is rolled every month or two. This will require thoughtful execution but could massively increase returns in the event a calamity does strike... You could try to time it... If you’re going to try that, and like me you don’t have the capital to just roll put options, check out Andrew Thrasher’s paper on the VIX Tsunami for optimal signals to take your shots128.

> Volatility is forecastable. Read Mandelbrot. It’s a structural force in markets. Per the model I’ve laid out, Bitcoin’s volatility is a function of algorithmic supply/demand dislocations caused by the halving event every 4 years along with HODLing to create illiquid supply. This effect cannot be priced in ahead of time by markets, and without any elasticity of supply, price must be volatile as it shifts from pocket of liquidity to pocket of liquidity. If bitcoin’s algorithm is never changed, and Bitcoin HODLers never sell, Bitcoin’s volatility cannot reduce. One rebuttal might be that every halving, the issuance reduction is lower. I agree with this, but unfortunately the commitment to HODLing means that in every halving that smaller supply/demand gap operates on more illiquidity. It may not perfectly balance out, but volatility isn’t going anywhere.

Squish ends their report with a "fun predictions" section but doesn't include probabilities, boooooooooooooo.

## Cruxes
- Is a deflationary policy actually codified anywhere? What are reasons to think it might or might not be pursued? Squish seems to be putting a *lot* of stock in 1559 as deflationary, and also points to other people who seem to have a similar certainty that Eth will become "Ultra Sound" deflationary currency. As I point out above, though, this specifically *isn't* codified in 1559 -- I don't know if it is somewhere else, though.
- Is it reasonable to think that some structural flows can't be priced in? If so, is Eth one of those cases?
- Does Pfeffer's bearish PQ valuation model need to be reconciled with Squishe's 1/8th turbobull model? The former is an equilibrium model and doesn't account for culture, flows or hype-cycles; can they both be right? Certainly they can both be wrong..
- *If* BTC and ETH have volatility fundamentally baked into their monitary policy, as Squish suggests, is an equalibrium approach even the correct way to think about them?

[^1]: Field, L.C. and Hanka, G. (2001), The Expiration of IPO Share Lockups. The Journal of Finance, 56: 471-500. https://doi.org/10.1111/0022-1082.00334
[^2]: Rajesh K. Aggarwal, Laurie Krigman, Kent L. Womack, Strategic IPO underpricing, information momentum, and lockup expiration selling,Journal of Financial Economics,Volume 66, Issue 1,2002, Pages 105-137, ISSN 0304-405X,https://doi.org/10.1016/S0304-405X(02)00152-6.
[^3]: Brau, J.C., Carter, D.A., Christophe, S.E. and Key, K.G. (2004), "Market reaction to the expiration of IPO lockup provisions", Managerial Finance, Vol. 30 No. 1, pp. 75-91.