Bitcoin production cost with hedging
Bitcoin is a decentralised, distributed piece of software that converts electricity and processing power into indisputably accurate records. Thus Bitcoin is allowing its users to utilise the Internet to perform the traditional functions of money like transacting value.
Mining machines are rewarded for supporting this process with a block reward and transaction fees. Since the introduction of mining pools, this process has become a statistical equation. The more hashpower a miner provides, the higher the reward. The amount of reward is simply distributed among all available hashrate. Hence if the hashrate increases, the single miner receives less reward with which he has to sustain himself.
As the figure below 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.
Figure: Bitcoin price and difficulty between 22-Jul-2010 and 21-Jul-2019.
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, the figure below shows 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 change = 1.05 + 0.703 x Bitcoin price change.
In other words, in the past the Bitcoin difficulty has increased 97.6% on average over 90 days without any Bitcoin price change, which we will call “Hardware appreciation”. On top of that, the difficulty increased by 96.8% 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 49.3% per year.
Figure: Bitcoin difficulty and price change over 90 day periods (not overlapping) between 18-Jul-2010 and 21-Jul-2019.
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
If we assume that the Hardware appreciation is driven by increasing hardware capacity according to Moore’s law, then this results in a constant factor. Moore’s law states a 100% increase every two years, but in Bitcoin mining that might be elevated due to the fact that radical new ground-breaking technology broke through multiple times. First Bitcoins were mined with CPUs, then GPUs and then lately with application-specific integrated circuits (ASICs, see here). 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 hashrate 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 analysing the relationship is to look at the traded future markets. FTX.com, a cryptocurrency exchange, launched a Bitcoin hashrate 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. The figure below shows the price development of the Bitcoin hashrate Q3 future versus the Bitcoin price (perpetual future).
Figure: Bitcoin hashrate future versus perpetual price future between 18-May-2020 and 15-June-2020.
Since the launch of the hashrate futures, 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 hashrate goes up, the miners are receiving less Bitcoins for their hashrate and their profit goes down.
The miners can hedge out the Bitcoin price risk using perpetual futures. FTX.com now also introduced Bitcoin hashrate 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 hashrate 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.
The most efficient machines for SHA256 (Bitcoin mining) are at the moment the Bitmain S19 Pro machines according to Asic Miner Value. The machines cost $3,010.22 and have a production of 0.0011 BTC per day. We can also assume a minimum operating cost of $0.02 per KWh according to Blockware solutions as a baseline. According to Asic Miner Value the profitability of the machine would then be around 77.3% today. Although that sounds like a great investment, we also have to assume a 3% drop in revenue per month due to increasing difficulty (see above), 1% pool costs, but an additional 5% mining reward from transactions.
The table below shows the revenue, operating costs and profit per month. The total profit accumulates to $3,148.41 and would allow the investor to generate 4.45% 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 $4,271.61 and a long hashrate future position with the same amount at a level of 3.4% per month versus the current difficulty level (see above for Q1 2021 hashrate 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 $9,900, while all other parameters remain unchanged (which of course is highly unlikely given our analysis above and difficulty changing accordingly).
Table: Estimated revenue, operating costs and profit per month for an Antminer S19 Pro (110 Th)
Summary
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 to hedge out the difficulty 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 hashrate of the machine and the global hashrate.
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 the 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.
