Money for nothing: Bitcoin Cash & the economics of hard-forks (part I)

Pricing a parallel universe

Over a month has passed since Bitcoin Cash has forked from the main Bitcoin chain. Short-lived anomalies observed in the aftermath of the split, such as very slow mining times due to widely miscalculated block difficulty, have mostly been resolved. While most exchanges have not opened order-books for BCH, sufficient liquidity exists and trading continues at non-zero prices. So much for the predictions of “experts” who projected a rapid decay to zero once the blockchain came up to speed, allowing people to move funds in any reasonable time frame. (Deja vu? Back in 2016 on the verge of the Ethereum hard-fork to bailout the DAO, so-called “experts” also predicted the minority chain Ethereum Classic would die out quickly.)

In fairness, the majority of Bitcoin proper trading does not hit the blockchain either, taking place on the internal ledgers of exchanges. That alone should have been a clue that mobility/velocity of fund movement can not be the deciding factor in determining market value of a cryptocurrency. But are there systemic ways of pricing a splinter faction such as Bitcoin Cash relative to its main chain?

BTC itself has significantly appreciated since August, going from below $3K to nearly crossing the $5K milestone before taking a hit in response to news from a crackdown in China. BCH has fluctuated significantly but continues to hold a valuation in the hundreds of dollars. In other words: the price of bitcoin after the fork plus that of bitcoin cash greatly exceeds that of bitcoin before the fork. Consider that every person who owned bitcoin before the fork still owns the same amount of bitcoin, plus a corresponding quantity of bitcoin cash.

On its face, the hard-fork has created value out of nothing.

Creating a new cryptocurrency out of thin air

Not to shabby for an initiative with modest beginnings as a strategic bluff to another threatened soft-fork. To recap: in response to the lukewarm reception by Bitcoin miners to the segregated witness feature, one of the factions in the never-ending scaling debate proposed a user-activated soft fork or UASF. This approach would effectively force the issue with miners, by disregarding blocks which do not include support for their favorite pet-feature. In response, an opposing faction threatened a user-activated hard-fork (UAHF) that would force miners to commit to a different criteria by disregarding chains that do not include support for their favorite pet-feature, namely 2MB blocks. UAHF was more deterrence than a coherent scaling plan: its proponents painstakingly pointed out the plan would only be invoked if segregated witness activation did not take place cleanly. Last minute developments appeared to render that unnecessary: segregated witness and large-blocks were merged into a Franken-design under the controversial “New York agreement.” Enough miners signaled for that version to reach its activation threshold. Crisis averted? Not quite: one die-hard group decided to run with the UAHF banner regardless of existing consensus, proceeding to create a new fork that supports 2MB blocks—Bitcoin Cash.

Before we go on to conclude that hard-forks are an unambiguous boon to the ecosystem and expect to have one every week, consider a few alternative explanations for the outcome:

  • Speculative bubble in the broader cryptocurrency space, a point many commentators have raised warnings about. No one has accused cryptocurrency investors of being too cautious in this day and age of oversubscribed ICOs. Bitcoin Cash may have been perceived as the next gold-rush by aggressive investors looking for another asset class to get in on the ground floor.
  • Creative conspiracy theories: secret cabals committing to a price floor for BCH in order to generate demand from exchanges or motivate miners to commit hash power. This could explain why BCH had a non-zero valuation but it can not account for why BTC itself started on a steady upwards trajectory.
  • Here is a more charitable interpretation for investor psychology: the community breathing a collective sigh of relief after segregate witness activation proceeding relatively “cleanly” by some definition. While the UAHF hard-fork came out of left field, it had incorporated lessons from past times when the network played a game of chicken with hard-forks. There was no risk of the alternative chain collapsing back on the main-chain, thanks to the deliberate introduction of an incompatibility at the fork point. There was replay protection: transactions from the main chain could not be broadcast on the alternative chain. (That was a critical lesson the Ethereum community learned during its DAO debacle. Compatibility between chains resulted in problems managing funds independently: by default sending ETH also resulted in sending ETC because someone else could—and did, as a matter of fact— take the transaction from the original chain and replay it on the Classic chain.) According to this explanation, bitcoin prices were artificially depressed before the fork due to collective investor anxiety and successful completion of the fork simply erased those worries.

Hash-rate follows valuation

Beyond the particular motivations that support the current price structure, the relative value of Bitcoin Cash to Bitcoin makes for an interesting experiment in comparing predictions from economic theory with observed market behavior of the participants. That goes for miners too: while it is common to accuse investors of tulip-mania irrational exuberance, miners are supposed to be rational actors maximizing subject to well-understood economics of mining. While Bitcoin Cash transactions are deliberately incompatible to Bitcoin transactions, the proof-of-work function used to mine blocks is identical on both sides. That means the chain split presents each miner with a continuous decision point: mine BTC, mine BCH or perhaps some mixture of both by dedicating partial capacity.

The relative profitability of mining—defined as rewards to amount of hash-rate expended— for BTC/BCH has fluctuated wildly during the initial few weeks. As profitability of the BCH blockchain soared, more miners were tempted to jump ship. Eventually the pendulum swung too far and BCH had too much competition, a form of the Yogi Berra saying applies: it is too crowded, no one mines there anymore. But the graph shows an unmistakable trend of converging towards 100%, the point where both chains are equally profitable. This same behavior was observed in the aftermath of ETH/ETC split. The price ratio between the chains was approximately equal to their difficulty ratio.

Is there a relationships between hash-rate and price? It is straightforward to argue for causality in one direction when two chains have compatible proof-of-work function. That compatibility is critical because it allows repurposing mining power. Recall that the majority of commercial mining is done using highly specialized hardware that has been painstakingly optimized for a specific proof-of-work function. It can not be used to support mining on a different blockchain unless that blockchain also uses the same proof-of-work. So an Ethereum miner can not easily switch to Litecoin without significant capital expense in acquiring new hardware, but they can turn around on a dime to mine Ethereum Classic using the same fixed assets.

This interoperability creates an opportunity to arbitrage hash power between blockchains. Suppose BTC is trading at $4000 and a mining pool has 1% of the hash-rate. Neglecting transaction fees, this pool would expect to collect on average 1% of the block reward of 12.5 BTC which comes out to $500 in fiat equivalent. Now suppose that BCH has one-tenth the total hash rate of Bitcoin network being a minority chain, but is valued at one-eighth of bitcoin at $500. In other words BCH is trading at a premium compared to its hash rate. In that case our mining pool can improve its profitability by shifting all power to mine BCH. After switching sides, the miner now accounts for roughly ~9% of the newly expanded BCH network capacity. That means on average they can count on collecting 9% of the 12.5 BCH reward per block. Converted to USD that comes out to ~$563. In other words defecting to BCH when it was trading at a premium to its hash-rate has improved the bottom line. (In fact until difficulty adjustment takes place, their actual profitability will be even higher because the network is still operating under the assumption of its original capacity. Blocks will arrive faster, so the reward per unit time is even more lucrative— considering that primary operational expense for mining is power consumption, that is a more relevant metric.)

Yet the same calculus does not work for a different mining pool which starts out with 5% of total hash-rate. That pool is looking at an average $2500 per block in earnings while operating on the main chain. Switching over to BCH, they become the big fish in a small pond, now accounting for one-third of the total BCH rate— and in the process posing a risk to decentralization due to having achieved critical mass for selfish-mining. But their expected earnings in steady state actually drops to less than $1700 USD per block. What went wrong? Shifting that 5% of mining capacity to the greatly under-powered BCH network destroys the condition that gave rise to the arbitrage opportunity in the first place: with the infusion of new hash power, BCH is no longer trading at a premium compared to its hash rate. (Of course this does not mean larger mining pools can not take advantage of the opportunity: it just means they have to shift some fraction of their resources over to BCH instead of their full capacity.)

Bottom line here is that rational miner behavior gives rise to a dynamic where hash-rate is naturally allocated between compatible blockchains in response to market valuation of those currencies. Put succinctly: hash-rate follows valuation.




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