June 23rd 2020
Founder at www.protosmanagement.com. Senior portfolio manager and quant. PhD in Comp Neuro. SU Alumn
Bitcoin is a decentralized, distributed piece of software that converts electricity and processing power into indisputably accurate records. Thus Bitcoin is allowing its users to utilize the Internet to perform the traditional functions of money like transacting value.
The more hash power a miner provides, the higher the reward. The amount of reward is simply distributed among all available hash rates. Hence if the hash rate increases, the single miner receives less reward with which he has to sustain himself.
As the figure shows, both the Bitcoin mining difficulty and the Bitcoin price increased massively in the past. However, the difficulty increased magnitudes more than the Bitcoin price. While the Bitcoin price increased 123,365.64 times since 2010, the difficulty increased 49,928,366,166.79 times.
For a company engaged in Bitcoin mining, that creates a headache as its profitability depends on the relationship between the Bitcoin price and difficulty. The Bitcoin difficulty drives the production volume, while the Bitcoin price determines the value of the production.
If, for example, the difficulty increased by 10%, a Bitcoin mining company produces 10% less Bitcoin. If the price stays equal, then of course, the revenue decreased by 10%.
The company will then have to cover expenses from that decreased production. The expenses normally include electricity as well as hosting costs and are usually fixed.
One mitigating factor is the Bitcoin price. If the Bitcoin price rallied over the same time period 10%, then of course the profitability stays the same. However, in the past, the Bitcoin price only mitigated partially the loss in production (see above) and therefore mining companies faced a continuous deterioration of profitability.
To analyse the impact, we calculated the change in Bitcoin price versus the change of difficulty over periods of 90 days. Interestingly, the correlation between the two variables is 59.4% and the regression analysis finds the linear relationship of
Bitcoin Difficulty = 1.05 + 0.703 x Bitcoin price.
In other words, in the past, the Bitcoin difficulty has increased 105% on average over 90 days without any Bitcoin price change, which we will call “Hardware appreciation”. On top of that, the difficulty increased by 70.3% for every 100% change in the Bitcoin price, which we will call “Bitcoin appreciation”.
While the Bitcoin appreciation is neutral for the miner, the hardware appreciation is not and therefore the miners have faced an average decrease of their mining production of 51% per year.
What are the drivers for the difficulty level?
We suggest that the difficulty level and therefore the production level of a given miner is determined by the hardware appreciation and Bitcoin price changes:
Difficulty change = hardware appreciation + Bitcoin price change
ASICs were introduced in 2013 and since then the increase has dropped off to about 10% per 30 days. Moore’s law would forecast an even lower level of 3% per month ((100% production + 100% increase)^(1/24 months)-100% production).
We suggest that going forward the hardware appreciation will probably be close to 3% since the hardware is already at a very high-efficiency level with a lower bound from Moore’s law. In fact, the Bitcoin hash rate futures for Q1 2021 are trading at 3.4% per month above the level of mid-May 2020 (level of 21.137 T versus 16.104 T over a 9 month period).
On top of the hardware appreciation, we suggest that the difficulty is manipulated by the Bitcoin price as well (see linear regression above). The regression analysis above indicates that the difficulty went up and down with the Bitcoin price almost linearly.
In other words, when the Bitcoin price rallied over 90 days, the difficulty went up almost with the same amount.
Another way of analyzing the relationship is to look at the traded futures markets. FTX, a cryptocurrency exchange, launched a Bitcoin hash rate future on 15-May-2020 that settles to the average difficulty of Bitcoin blocks mined during the quarter, divided by 1,000,000,000,000.
Since the launch of the hash rate future, it seems to be mean reverting around the change of the Bitcoin price and vice versa. That is in fact exactly what our model would predict on short time frames such as days because Bitcoin price movements are changing much faster than hardware changes. On the other hand, hardware changes should have a slow diverging effect on the two curves in that the difficulty should end up higher than the Bitcoin price.
Putting it all together
The driving forces behind the profitability of Bitcoin mining are the global difficulty and the Bitcoin price. Simply put, if the Bitcoin price goes up, the miners can sell their produced Bitcoins for a higher price and make a larger profit. However, if the global hash rate goes up, the miners are receiving fewer Bitcoins for their hash rate and their profit goes down.
The miners can hedge out the Bitcoin price risk using perpetual futures. FTX.com now also introduced Bitcoin hash rate futures to hedge out the difficulty risk. In this article, we analysed the relationship between the two futures and introduced a simple model driving the Bitcoin hash rate future.
We suggest that the difficulty is driven by a combination of hardware appreciation and Bitcoin price changes. The hardware appreciation is driven by improving hardware described by Moore’s law and can be considered a fixed variable of around 3% per month. On top of that, the Bitcoin price is driving the difficulty up and down with its volatility.
If the difficulty is driven by hardware appreciation and Bitcoin price, and the Bitcoin price risk can be hedged out by taking a short position in the Bitcoin price future, then the profitability of mining hardware should depreciate with about 3% per month until it drops below the operating costs.
We calculated the revenue, operating costs, and profit per month. The total profit accumulates to $3,038.62 and would allow the investor to generate 0.80% profit on the original investment over 24 months.
The model also assumes that the produced bitcoins are fully hedged by taking a short bitcoin perpetual future position (at a level of $9,500) in the amount of $4,723.42 and a long hash rate future position with the same amount at a level of 3.4% per month versus the current difficulty level (see above for Q1 2021 hash rate future and then roll over in next contract).
However, for an investor that would like a return of at least 10% over the period of 24 months, he would need to wait until the Bitcoin price increases to $10,100, while all other parameters remain unchanged.
Bitcoin allows its users to utilise the Internet to perform traditional functions of money like transactions. Bitcoin mining machines are rewarded for supporting this process with a block reward and transaction fees. We wanted to analyse the profitability of mining machines given the current status of the Bitcoin mining network and new derivative products to hedge out risk.
For example, FTX.com has introduced a new set of futures that allow us to hedge out the difficulty of risk for Bitcoin miners. Bitcoin mining depends on three variables: the cost of the machine, the price of Bitcoins that are being produced, and the production amount. The production amount depends simply on the global difficulty and is a function of the hash rate of the machine and the global hash rate ate.
We found that mining is profitable over a period of 24 months assuming very cheap energy and operating costs (total of $0.03 per kWh). The main drag on the profitability is arguably the decreasing production due to the expected increase in difficulty over time (at the moment traded at 3.4% increase per month).
Overall, an investment in the latest hardware of Antminer S19 Pro (110 Th) results in a 0.8% return on the invested capital fully hedged against bitcoin and difficulty changes that is probably not very appealing and an interested investor would probably want to wait until Bitcoin increases to about $10,100 to generate at least a 10% return over 2 years.