Smart Bitcoin miners should manage their computing power like an investment

How do we ensure that miners continue to generate hashrate? The answer is to maintain a steady flow of ongoing investments in mining hardware to increase the network’s security budget.

Written by: Leo Zhang, Jack Koehler, and Cai Da. The former two are from Anicca Research, a computing power and derivative product research institution, and the latter is from General Mining Research.

Compiled by: Perry Wang

This article was written by Anicca Research in collaboration with General Mining Research (GMR), a Singapore-based hashrate and derivatives investment and trading agency. GMR provided its proprietary mining machine market data and supported this article with hashrate growth forecasts based on aggregated data from mining machine manufacturers for sales in the coming months.

If you recognize how much is beyond your control, you will be able to gain more control.

_ Benjamin Graham, author of "The Intelligent Investor", the father of value investing_

Hashrate valuation is one of the oldest and most esoteric topics in the cryptocurrency space. Several academic papers and industry research reports have explored the economic and game-theoretic aspects of Proof-of-Work, but most of them oversimplify or make unrealistic assumptions about how hashrate markets work in practice.

In this article, we explain that the operation of computing power is essentially equivalent to managing an investment portfolio, and that computing power pricing includes the difficulty of pricing all aspects of the portfolio. We will introduce the mechanisms of popular pricing and their flaws. We parameterize the computing power portfolio and further explain how various assumptions in the test will affect the results. The importance of the valuation framework is not only to practice theory, but also to lay the foundation for the development of professional risk management practices in the computing power industry.

The fair value of computing power

Since you can buy coins from the open market, why run your own mining?

This is the most common reaction when people first hear about cryptocurrency mining. As we all know, the huge financial rewards sparked the initial interest in mining and matured the industry into a billion-dollar behemoth. A successful miner can produce Bitcoin at a price below the spot price, thus building a position at a significant discount compared to buying the coins on the open market.

However, low production costs are by no means permanent. Competition in the mining industry has been increasing over the years, and market cycles have become increasingly unpredictable. The "discounts" that miners love so much can deteriorate into painful losses at any time. In today's market, is mining still more profitable than buying from the open market? Given the many variables involved in this question, it is futile to try to give a once-and-for-all generalization. But we can divide the market cycle into several archetypal stages and observe how the profitability of common mining and trading strategies evolves in each stage.

Let’s start with 2018. In the memory of most miners, it was an extremely bleak year. In our previous article in this series, “ Understanding the “Alchemy” of Hash Rate: Reflexivity and Seasonal Changes in the Cryptocurrency Computing Power Market ”, we classified the first three quarters of 2018 as inventory-flush in the mining cycle. At that time, the price of coins fell, but the hash rate growth rate was still strong.

Assuming that a miner purchased a Bitmain Ant S9 mining machine with a computing power of 10 Ph/s in early 2018, and the unit price of each mining machine was about US$2,675 at the time, the total expenditure on 690 mining machines was US$1.85 million. Assuming a linear depreciation rate of 24 months for the hardware and a miner's electricity cost of US$0.0507 per kWh (about RMB 0.33, data provided by GMR) , we can backtest the performance of three common strategies:

• Neutral strategy: miners sell enough tokens to cover daily electricity costs ($941.38) and daily mining machine depreciation ($2,563.54) . If the mining revenue for the day is less than the total fee ($3,709.01) , only the tokens sufficient to cover the electricity costs are sold. All other BTCs are held.

• Coin hoarding strategy: The miner's sales revenue is enough to pay the daily electricity bill (941.38 yuan) , and all remaining BTC will continue to be held.

• Arbitrage strategy: The miner immediately sells all the mined BTC for fiat currency. The only goal is to use the difference between the spot price and the production cost to conduct arbitrage transactions. It is worth mentioning that this strategy will cause tax burdens and will be subject to transaction frictions constrained by liquidity. In order to simplify the modeling, these factors are not taken into account.

Next, we compare the performance of the above mining strategy with two common strategies of buying coins through the open market:

• One-time purchase: The mining evaluation period starts on the same day (January 1, 2018) , and the notional value of the tokens is equal to the total mining capital expenditure + annual operating expenditure (1,845,750 USD + 941.38 * 365 USD) at the BTC spot price of that day (13,465 USD) , and the tokens are held until the end of the evaluation period. For simplicity, we do not consider the transaction friction caused by purchasing this amount of Bitcoin.

• Regular fixed-amount purchases: The nominal value of the purchased tokens is still equal to mining capital expenditure + annual operating expenditure, but the specific strategy is to purchase a fixed value of tokens every day during the entire evaluation period ($2.26 million/365) .

Over the next year, the daily production cost per token ($3,709.01 spent divided by the number of tokens mined that day) exceeded the market price around July and continued to climb in the second half of the year, making the miner unprofitable for a long time. From the results, it can be seen that after a year of bear market, the "arbitrage strategy" suffered the least loss, while the "hoarding strategy" was hit the hardest.

This is because the "coin hoarding strategy" is the only strategy with no unrealized P&L. All other strategies hold long positions to varying degrees. In the mining machine inventory dumping phase when mining revenue continues to decrease, unrealized positions are likely to result in losses at the end of the valuation period.

In practice, a sensible miner would have shut down their mining machines after a long period of losing money. If this miner had stopped operations at the end of June, their losses would have been much smaller. If the miner had been using an "arbitrage strategy" before, the miner could even be profitable:

Neutral and hoarding strategies will remain unprofitable, although the losses will be less than buying coins from the open market. The losses are mainly due to the capital expenditure of purchasing mining machines. The miner previously purchased these mining machines for a total price of $1.84 million, but can only resell them for $738,000 (excluding transaction friction, shipping costs and taxes) . The income from the BTC he mined does not make up for the depreciation of the hardware.

In both examples, the arbitrage strategy seems to be the safest strategy. But what happens during the opposite phase of the market cycle, when overall mining revenue is increasing?

After the torment of the shakeout phase at the end of 2018, miners had a bumper harvest in the first half of 2019. The same analysis from January 1, 2019 to June 30, 2019 shows that the arbitrage strategy has the least profit, while the high-risk aggressive strategy (coin hoarding strategy and one-time purchase) has an income of more than 50% higher than the low-risk defensive strategy.

The life cycle was adjusted to 12 months at the beginning of 2019

With the benefit of hindsight, it’s easy to see which strategies have long-term success. But when the overall market is in a long-term downturn, taking an aggressive approach requires a firm belief and deep understanding of macro conditions. This is especially true for one-time purchases, where the timing of the position is everything.

Mid-2019 was a period of hardware iteration. Miners sold old mining machines and purchased newer, more efficient models. In this example, given the soaring BTC price, which drove up the price of mining machines, miners were able to sell mining machines at a premium over the initial purchase price.

Assume that the miner sold 690 Antminers and used the $271,000 in revenue to purchase a new Shenma M20 miner in the second half of the year:

In 2019, this miner earned:

If the miner does not replace the mining machine and continues to use the Antminer S9 mining machine for mining throughout the year, the miner's income will be significantly less than that of the miner who updated the mining machine:

In fact, miners are not bound to a fixed strategy throughout the mining cycle. Whenever they think the market trend is changing, they have the flexibility to change their strategy. In addition, they can use trading strategies to cover mining costs, or lend tokens to increase the profit of inventory. For example, miners can sell tokens for profit on days when mining profits exceed production costs, and buy tokens from the open market on days when mining profits are lower than production costs. Taking the right tactics at different stages of the mining cycle will have a significant impact on performance results. The purpose of these cases is not to summarize a universal money-making strategy, nor to prove that mining is definitely better than buying tokens, but to illustrate that managing a mining business is essentially managing an investment portfolio.

These strategies represent the simplest and most common strategies. A lazy miner who employs only one simple strategy throughout a market cycle can earn different value than a miner who actively employs multiple strategies. There are endless ways to manage hashrate, but mining manufacturers price everyone the same regardless of the strategy the buyer adopts. While price is an absolute data point, value is relative. Ideally, the price of a mining machine should represent the average of the value distribution of all available strategies, but this is impossible. So how should the hashrate industry be priced? What exactly does the price of hashrate represent? More importantly, how should miners value hashrate in a way that best suits their situation?

Heuristics for Hash Power Pricing

In today’s market, the price of hashrate is mainly controlled by hardware manufacturers such as Bitmain, MicroBT, and Canaan Creative, which occupy the vast majority of the market share of new mining machines and fully control the initial issuance rights of mining hashrate hardware.

The primary task of manufacturers is to make sure that production pays off, which has less to do with the cryptocurrency market and more to do with supply chain management. The price at which they sell their products can be adjusted based on market demand, but they must ensure a certain production profit. Sometimes manufacturers artificially lower their prices to make them more expensive than their competitors. In short, manufacturers' pricing does not represent the theoretical fair value of hashrate. It is mixed with external factors that reflect the status of the mining machine manufacturing company.

In the first article of the Alchemy of Calculation Power, " Understanding the Alchemy of Hash Rate: Characteristics and Challenges of Bitcoin Calculation Power Assets ", we discussed that the most popular indicator for evaluating calculation power is the static break-even days (Chain News Note: Generally referred to as payback days in China, static days-to-breakeven) . This indicator takes into account the current instant price of BTC, mining difficulty, fees, and full operating expenses, and can measure how many days it takes for the purchased mining machine to break even. Each miner has a different payback day on the same mining machine because each miner operates differently. Miners calculate their own payback days based on the electricity costs they use and the electricity costs of installed capacity. However, mining machine manufacturers cannot take into account the costs of all miners, so the starting point for the payback day calculation is the average electricity cost of the entire market.

Since it is extremely challenging to collect electricity cost data from each miner, the average cost can only be a rough estimate, and the electricity cost also changes with the seasons. Miners with different cost structures rise and fall like the waves. Mining machine manufacturers make this calculation based on their best guess at electricity costs and finalize the price of mining machines based on a reasonable payback period range.

But what is the industry-wide electricity cost that mining machine manufacturers use as an input parameter? We can use the historical price data of mining machines to reversely estimate it.

We can use the discounted cash flow method to backtest historical mining machine prices to find out the underlying assumptions that manufacturers made when pricing their mining machines. For example, the Antminer S9 retailed for $2,675 in January 2018.

Assuming that the life cycle of an Antminer S9 mining machine is 24 months, we can calculate the historical revenue of a mining machine:

Next we work backwards from the electricity cost so that the sum of all present values ​​of daily free cash flows equals the total purchase price. Assuming an annual weighted average cost of capital (WACC) of 12.5%, we get:

To ensure that the average daily expenditure does not exceed $1.57, the electricity cost of the S9 mining machine needs to be $1.57/24/1.365 = $0.048/kWh. This means that unless the miner can obtain electricity at no more than $0.048 (about RMB 0.33) per kWh, the mining machine is considered expensive. The above results are calculated based on Strategy 3 (arbitrage strategy) . Using other strategies for this analysis, Strategy 1 Neutral Strategy requires an electricity cost of $0.017 per kWh, and Strategy 2 Hoarding Strategy requires an electricity cost of $0.01 (about RMB 0.07) per kWh. This means that in practice, the actual "break-even" electricity cost is in the range of $0.01-0.048 per kWh.

The electricity costs that most miners actually paid in early 2018 were far beyond this range. However, this level of premium is not unreasonable. BTC prices have just hit a record high, network difficulty has not yet started to catch up, and Antminer S9 is in short supply in the market. The ultimate determinant of price is still supply and demand.

Applying the same method to the pricing of mining machines at other points in time, the following table shows the corresponding "break-even" electricity costs for miners. The electricity cost here is the average of the costs derived from the three strategies:

From another perspective, if the electricity cost of the entire industry is $0.0507 per kilowatt-hour, what is the fair value of these mining machines at that time? The fair value here is still the average of the fair values ​​of the three strategies:

The premium/discount ratio is the mining machine price divided by the fair value. Data source: hashrateindex.com

Note that this analysis does not account for changes in industry-wide average electricity costs or WACC due to the difficulty in accurately estimating industry-wide average costs and WACC.

This analysis is not intended to calculate an absolutely objective fair value. Fair value relative to each miner varies due to different operating expenses and different strategies. But even assuming an industry-wide average fee, we can still observe inefficiencies in mining machine pricing. During the bull market, mining machine manufacturers significantly increased the price of mining machines, and during the BTC decline, manufacturers were forced to liquidate their inventory at a discount below cost. This is consistent with historical evidence we have observed in the mining market. When the price of BTC rises rapidly, the price of mining machines sometimes rises faster than the price of the token.

In theory, rising prices also mean that the network difficulty will increase faster in the future, so the price of mining machines should rise more slowly than the price of coins. However, in reality, market pricing often deviates from the theoretical mechanism under such conditions. In the final analysis, the prices of these mining machines are driven by supply and demand, and the liquidity of the mining machine market is extremely poor.

By backtesting the historical pricing of mining machines, we can see that the intuitive inference method of pricing based on static payback days is not enough to capture the volatility of mining profit margins. In order to assess the current fair value of mining machines, we need to model mining profits in a forward-looking manner so that our tools or theoretical frameworks can describe the drastic fluctuations of variables.

A more advanced approach is to view hashrate as a call option. The principle of this approach starts with considering the mining revenue of the miners as the underlying asset. Mining revenue is divided into three components: price, mining difficulty and fees. Call options on the price of Bitcoin are esoteric enough, but derivatives that encapsulate these three components are much more complex. It is simple to describe options built on multiple underlying assets using the Black-Scholes model: the additional considerations are the correlated random walks and the corresponding multi-factor version of Ito's Lemma. However, building a correlation matrix between the three variables is a difficult task.

As discussed in the Hashrate Alchemy series, price and hashrate are correlated but with an ever-changing lag. Due to reaction delays, when examining the relationship between hash power and price over shorter time windows, the correlation is minimal. It is therefore easy to simplify modeling the hash rate path as a process that is completely independent of price. From a financial theory perspective, hashrate is a derivative of Bitcoin, and over long enough time frames, the two time series are positively correlated.

On the other hand, transaction fee dynamics are more difficult to model. Although transaction fees are somewhat correlated with price and network hashrate (inversely) , they are primarily driven by on-chain activity, which is an exogenous factor. This is why a correlation matrix does not produce meaningful results.

But once assumptions are made about the distribution of the underlying assets, pricing hash power over a period of N is equivalent to pricing a series of zero-strike European call options that expire daily. In other words, as long as the mining machine is turned on, the hash power is a contract that is executed every day and converted into the underlying asset, i.e. mining revenue. The cost of the contract is the depreciation of the hardware plus operating expenses. The option premium for the entire asset package should theoretically be the price of the mining machine plus the present value of all operating expenses incurred during the N period.

In the formula:

• V is equal to the fair value of the mining machine.

• Ci is the value of a call option based on mining revenue and expiring on day I.

• T is the average daily operating expense.

This approach has a serious flaw. The formula evaluates the contracts on day i and day i-1 independently. In reality, the revenue on day i-1 should set the initial conditions for the contract expiring on the next day. Any method of computing power evaluation based on option pricing and simply summarizing all trials during the period will face this path dependency problem. Each trial is an unrelated evaluation.

Numerical method estimation

For numerical methods, the problem of path dependence does not exist. Instead of evaluating 10,000 trials per day, the same 10,000 trials are used for all experiments. Monte Carlo simulation can help model complex dynamics by generating random numbers. Using a sampling procedure, the expected income in a risk-neutral world is calculated. It is then discounted at the risk-free rate. With Monte Carlo simulation, we are able to simulate the mining profitability of the latest generation of mining machines over the next two years and compare their fair value with the price on the market today.

As a first step, we need to make some assumptions about price movements. Several studies have shown that the jump diffusion model is best suited to describe BTC price distribution. We use the jump diffusion model to simulate 10,000 possible price movements over the next two years. In a random simulation, each movement takes a different path.

The jump-diffusion model has two basic parts: diffusion (geometric Brownian motion) and jumps (usually Poisson distribution) . To simplify the modeling, we assume that there is a threshold probability for jumps. When a jump is triggered, the amplitude follows a normal distribution.

Calibrated against historical price data, we use the following as parameters for the model:

• Constant drift: 0.10%

• Drift standard deviation: 2.50%

• Jump probability: 5.00%

• Jump mean: 0.10%

• Jump standard deviation: 5.00%

In addition to token prices, we also need to forecast the network’s hashrate in order to calculate mining revenue. Modeling hashrate is more complex than price trajectory because each unit of hashrate is different. While every miner on the network is computing hashes for the same algorithm, the amount of electricity consumed varies from miner to miner. The simplified model of the current network hashrate abstracts away several hardware efficiency categories that will behave differently as the market evolves. Categorizing the model by energy efficiency class shows us the makeup of the mining machines on the market, and therefore gives us a rough prediction of how they will evolve in the future.

Unlike price data, mining information is extremely challenging to collect. The only way to solve this problem is to interview as many miners, distributors, and manufacturers as possible. GMR surveyed major Chinese mining machine manufacturers and distributors and came up with an estimate of the market composition as of November 1, 2020:

This structure is used as the basis for the initial conditions of the forecast model. Using the estimated industry-wide average total electricity price, we can calculate the break-even threshold for each layer and get a rough idea of ​​how many miners may drop prices if the BTC price drops below break-even. Using $0.0507 per kWh as the industry-wide average total electricity price estimate, we can plot four possible scenarios based on different price levels:

Source: GMR provided its proprietary data

Note that this only gives a baseline for hash rate forecasts. If the BTC price rises dramatically, miners may put cheaper older mining machines into production through the secondary market, and mining machine manufacturers may speed up production.

Based on the above scenario, we can find a linear function y = 4,544x + 6e07 to describe the relationship between price and network hash power. For simplicity, we assume that the growth of hash power over the next six months follows a function of the 14-day average BTC price, with a drift term dW. The drift term parameters are set to a mean of 2.5% and a standard deviation of 5%. In addition, based on our estimates of manufacturer mining machine sales, assume that the hash rate will increase by 200 Ph/s per day over the next six months. We simulate hardware reaction delays by adding a constant reaction delay of 20 days. This means that the hash rate only reacts to price actions that occurred at least 20 days ago. The full function formula is as follows:

A sample trajectory is as follows:

In reality, the relationship between hashrate and price is a messy and complex tangle. Using a linear function to describe it is like projecting a chaotic system onto a low-dimensional subspace. This function can break down for a variety of reasons. This is the same correlation matrix problem we described in our options pricing approach. However, this architecture allows us to easily add lags, so it is a significant improvement over assuming hashrate and price are two completely independent distributions. This makes forecasting much more manageable.

To further improve our estimates, we can use the Markov Chain Monte Carlo algorithm model. Unlike the Monte Carlo algorithm, which draws independent samples from a distribution, the Markov Chain Monte Carlo algorithm draws samples where the next sample depends on the previous samples. This solves multidimensional problems better than the general Monte Carlo simulation. The exact construction of the algorithm will be explored in the next article.

Once we have a prediction for BTC price and hash rate for the next two years, we can calculate the profitability of mining just like we did with backtesting historical hash power prices. There was very little lending activity backed by crypto assets two years ago, but today the crypto lending market has grown into a massive industry. Collateralized lending is one of the most common services that miners often rely on. Evaluating the current WACC, it should be significantly higher. Instead of the 12.5% ​​in the 2018 analysis, we can reduce it to 10%

Using $0.0507 per kWh for electricity costs and assuming a 10% risk-free rate, we can generate a distribution of fair values. The final result is the average of all 10,000 trials. In addition, we assume that after two years, the Antminer S19 Pro and Shenma M30s still retain 20% of their residual value.

Needless to say, this should not be the final word on whether the mining machine in question is overpriced or underpriced. The mean and standard deviation of the price distribution, the function of hashrate and price, lag time, electricity costs, discount rates, and residual values ​​are all factors that can heavily influence this assessment. For example, running the simulation with electricity costs of $0.07/kWh and $0.03/kWh:

We can see that when electricity costs are high (left) , the prices of more efficient miners (Ant S19 and Shenma M30s) are closer to fair value. When electricity costs are low (right) , the prices of less efficient miners (Ant S17 and Shenma M20s) are more favorable. This proves that if electricity costs are competitive enough, miners can benefit from running less efficient miners.

In our model, we built a switch that turns off a rig if mining revenue is consistently lower than spending over a 14-day period. In the real world, miners don’t often turn rigs on and off based on short-term profitability.

Most of the time, miners have agreements with data centers where they host their assets, stipulating the minimum amount of electricity they need to consume each month. Even if profit margins fall below zero, most miners prefer to wait for a confirmed downward trend in the price of the currency before taking action.

Due to the labor-intensive nature of data center operations and the lack of liquidity in the mining machine market, miners are forced to observe longer-term coin price trends rather than short-term price trends. The increase in the number of lending service providers in recent years has also enhanced miners' tolerance during the winter. Miners can pledge their tokens or mining machines to borrow fiat currency to pay fees instead of selling a large number of tokens. Nevertheless, this is the theoretical lower limit of mining losses. Miners' losses cannot exceed capital expenditures plus accumulated operating expenses.

As with call options, the greater the volatility of the underlying index, the higher the theoretical value of the instrument. We can see that the results vary as the parameters of the jump-diffusion model vary. When volatility is suppressed, the theoretical valuation of the miner drops sharply. When volatility is high, the theoretical value increases rapidly:

Electricity cost based on $0.0507 per kWh

This analysis is based on the Strategy 3 daily sell strategy. As with the backtest analysis, the fair value that can be "unlocked" by running hash power is within the fair value range (Strategy 1, Strategy 2, Strategy 3) . Given that the Monte Carlo simulation runs 10,000 paths, each with a distinct path, running just one strategy is enough to cover every type of market phase.

A future with zero block rewards

Another variable that has a significant impact on mining revenue is transaction fees. Assuming fees increase linearly by 5% and 10% per year, the fair value of mining machines will increase significantly:

Electricity cost based on $0.0507 per kWh

In reality, transaction fee trends are very irregular and have only a vague relationship with other endogenous variables. Modeling fee trends requires completely independent distributions. There are many ways to improve their accuracy:

• As discussed in the paper, the Markov Chain-Monte Carlo algorithm model is used to alleviate the dimensionality barrier

• Dynamic lags are introduced based on four archetypal market cycles, and jumps are modeled using a Poisson process.

• Use a hash rate-weighted average electricity cost rather than the median cost across the industry.

• Calibration parameters using statistical methods

• Use the Miner Learning Tool to describe the relationship between hash power and price.

• Incorporating transaction fee forecasts into mining revenue calculations

• Use agent-based simulation for miner behavior. Agent-based modeling is a technique for modeling complex systems to gain a deeper understanding of system behavior. It is widely used in high-frequency trading or smart contract risk analysis. In this framework, each miner is a "user" with different strategies and different cost bases. We can then define some simple reaction types (buy more miners, sell miners, buy more miners but wait 30 days for them to arrive, etc.) and build a library of "user behaviors". This will allow us to simulate more complex interactions in the hash power market. For more background information, read Conway's Game of Life.

Nobel Prize-winning economist Myron Scholes once said, “All models are flawed, but that doesn’t mean you can’t use them as a decision-making tool.”

Like the Black-Scholes model, a simulation model is a mechanism that attempts to simplify the complexity of the real world by reflecting it in a short description. This reduction makes the model useful, but it also limits its usefulness. It is important to understand that its limitations are specific and that the simulation represents possibilities, not certainties.

But for users who have already formed a view on the market, the model is a benchmark. Like any predictive model, this simulation is only as good as the assumptions made by the user. One uses the modeling tools that translate those views of the future into appropriate prices today, in hopes of exploring what problems will be exposed when that version of the future emerges.

Why is this important? What is the significance of developing asset pricing theory in markets that are clearly driven by supply and demand?

Valuation is not just a theoretical exercise. For Bitcoin, once the mining industry is completely dependent on transaction fee income, competition produces only minimal profits, and there is no predictable element in the mining income calculation, how can we ensure that miners continue to generate hash power? The answer is to maintain the stability of continued investment in mining hardware to increase the network's security budget. This is critical because without sufficient hash power, the entire system is vulnerable to attack, at which point Bitcoin's settlement guarantee will become worthless.

A rigorous valuation framework is the first step to testing assumptions and market behavior, and planning accordingly. Valuation is fundamental to proper risk management for some mining companies, given that some are too big to fail. The purpose of this exercise is to start a conversation in this general direction. We will continue to work on further refining our framework in the coming years.