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Author Topic: An Explanation of Stock-to-Flow, and How it Applies to Bitcoin  (Read 55 times)
anon241469
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November 10, 2019, 03:40:24 PM
 #1

Copied from Saifedean Ammous’ book, The Bitcoin Standard:
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“The simplest way for people to exchange value is to exchange valuable goods with one another. This process of direct exchange is referred to as barter, but is only practical in small circles with only a few goods and services produced. In a more sophisticated and larger economy, the opportunity arises for individuals to specialize in the production of more goods and to exchange them with many more people—people with whom they have no personal relationships, strangers with whom it is utterly impractical to keep a running tally of goods, services, and favors. The larger the market, the more the opportunities for specialization and exchange, but also the bigger the problem of coincidence of wants—what you want to acquire is produced by someone who doesn’t want what you have to sell. ... From examining such human choices in market situations, Carl Menger, the father of the Austrian school of economics and founder of marginal analysis in economics, came up with an understanding of the key property that leads to a good being adopted freely as money on the market, and that is salability—the ease with which a good can be sold on the market whenever its holder desires, with the least loss in its price. The relative salability of goods can be assessed in terms of how well they address the three facets of the problem of the lack of coincidence of wants mentioned earlier: their salability across scales, across space, and across time. It is the third element, salability across time, which is the most crucial.

A good’s salability across time refers to its ability to hold value into the future, allowing the holder to store wealth in it, which is the second function of money: store of value. For a good to be salable across time it has to be immune to rot, corrosion, and other types of deterioration. For the good to maintain its value, it is necessary that the supply of the good not increase too drastically during the period during which the holder owns it.

A common characteristic of forms of money throughout history is the presence of some mechanism to restrain the production of new units of the good to maintain the value of the existing units. The relative difficulty of producing new monetary units determines the hardness of money: money whose supply is hard to increase is known as hard money, while easy money is money whose supply is amenable to large increases. We can understand money’s hardness through understanding two distinct quantities related to the supply of a good: (1) the stock, which is its existing supply, consisting of everything that has been produced in the past, minus everything that has been consumed or destroyed; and (2) the flow, which is the extra production that will be made in the next time period. The ratio between the stock and flow is a reliable indicator of a good’s hardness as money, and how well it is suited to playing a monetary role.

A good that has a low ratio of stock-to-flow is one whose existing supply can be increased drastically if people start using it as a store of value. Such a good would be unlikely to maintain value if chosen as a store of value. The higher the ratio of the stock to the flow, the more likely a good is to maintain its value over time and thus be more salable across time. If people choose a hard money, with a high stock-to-flow ratio, as a store of value, their purchasing of it to store it would increase demand for it, causing a rise in its price, which would incentivize its producers to make more of it. But because the flow is small compared to the existing supply, even a large increase in the new production is unlikely to depress the price significantly. On the other hand, if people chose to store their wealth in an easy money, with a low stock-to-flow ratio, it would be trivial for the producers of this good to create very large quantities of it that depress the price, devaluing the good, expropriating the wealth of the savers, and destroying the good’s salability across time. I like to call this the easy money trap: anything used as a store of value will have its supply increased, and anything whose supply can be easily increased will destroy the wealth of those who used it as a store of value. The corollary to this trap is that anything that is successfully used as money will have some natural or artificial mechanism that restricts the new flow of the good into the market, maintaining its value across time. It therefore follows that for something to assume a monetary role, it has to be costly to produce, otherwise the temptation to make money on the cheap will destroy the wealth of the savers, and destroy the incentive anyone has to save in this medium.” – Saifedean Ammous, The Bitcoin Standard
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Copied from Plan B’s article on Medium.com:
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Saifedean Ammous talks about scarcity in terms of stock-to-flow (SF) ratio. He explains why gold and bitcoin are different from consumable commodities like copper, zinc, nickel, brass, because they have high SF.
"For any consumable commodity [..] doubling of output will dwarf any existing stockpiles, bringing the price crashing down and hurting the holders. For gold, a price spike that causes a doubling of annual production will be insignificant, increasing stockpiles by 3% rather than 1.5%."
"It is this consistently low rate of supply of gold that is the fundamental reason it has maintained its monetary role throughout human history."
"The high stock-to-flow ratio of gold makes it the commodity with the lowest price elasticity of supply."
"The existing stockpiles of Bitcoin in 2017 were around 25 times larger than the new coins produced in 2017. This is still less than half of the ratio for gold, but around the year 2022, Bitcoin's stock-to-flow ratio will overtake that of gold" — Ammous[5]
So, scarcity can be quantified by SF.
SF = stock / flow
Stock is the size of the existing stockpiles or reserves. Flow is the yearly production. Instead of SF, people also use supply growth rate (flow/stock). Note that SF = 1 / supply growth rate.
Let’s look at some SF numbers.

Gold has the highest SF 62, it takes 62 years of production to get current gold stock. Silver is second with SF 22. This high SF makes them monetary goods.
Palladium, platinum and all other commodities have SF barely higher than 1. Existing stock is usually equal or lower than yearly production, making production a very important factor. It is almost impossible for commodities to get a higher SF, because as soon as somebody hoards them, price rises, production rises, and price falls again. It is very hard to escape this trap.
Bitcoin currently has a stock of 17.5m coins and supply of 0.7m/yr = SF 25. This places bitcoin in the monetary goods category like silver and gold. Bitcoin's market value at current prices is $70bn.
Supply of bitcoin is fixed. New bitcoins are created in every new block. Blocks are created every 10 minutes (on average), when a miner finds the hash that satisfies the PoW required for a valid block. The first transaction in each block, called the coinbase, contains the block reward for the miner that found the block. The block reward consists of the fees that people pay for transactions in that block and the newly created coins (called subsidy). The subsidy started at 50 bitcoins, and is halved every 210,000 blocks (about 4 years). That's why 'halvings' are very important for bitcoins money supply and SF. Halvings also cause the supply growth rate (in bitcoin context usually called 'monetary inflation') to be stepped and not smooth.

Stock-to-Flow and Value
The hypothesis in this study is that scarcity, as measured by SF, directly drives value. A look at the table above confirms that market values tend to be higher when SF is higher. Next step is to collect data and make a statistical model.
Data
I calculated bitcoin's monthly SF and value from Dec 2009 to Feb 2019 (111 data points in total). Number of blocks per month can be directly queried from the bitcoin blockchain with Python/RPC/bitcoind. Actual number of blocks differs quite a bit from the theoretical number, because blocks are not produced exactly every 10 minutes (e.g. in the first year 2009 there were significantly less blocks). With the number of blocks per month and known block subsidy, you can calculate flow and stock. I corrected for lost coins by arbitrarily disregarding the first million coins (7 months) in the SF calculation. More accurate adjusting for lost coins will be a subject for future research.
Bitcoin price data is available from different sources but starts at Jul 2010. I added the first known bitcoin prices (1$ for 1309 BTC Oct 2009, first quote of $0.003 on Bitcoin Market Mar 2010, 2 pizza's worth $41 for 10,000 BTC May 2010) and interpolated. Data archeology will be a subject for future research.
We already have the data points for gold (SF 62, market value $8.5trn) and silver (SF 22, market value $308bn), which I use as a benchmark.
Model
A first scatter plot of SF vs market value shows that it is better to use logarithmic values or axis for market value, because it spans 8 orders of magnitude (from $10,000 to $100bn). Using logarithmic values or axis for SF as well reveals a nice linear relationship between ln(SF) and ln(market value). Note that I use natural logarithm (ln with base e) and not common logarithm (log with base 10), which would yield similar results.

Plot:
https://miro.medium.com/max/4200/1*jOLs8eLLbY2yTfk93-a1-Q.png
 
Fitting a linear regression to the data confirms what can be seen with the naked eye: a statistically significant relationship between SF and market value (95% R2, significance of F 2.3E-17, p-Value of slope 2.3E-17). The likelihood that the relationship between SF and market value is caused by chance is close to zero. Of course other factors also impact price, regulation, hacks and other news, that is why R2 is not 100% (and not all dots are on the straight black line). However, the dominant driving factor seems to be scarcity / SF.
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November 10, 2019, 04:50:13 PM
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I am skeptical of the stock-to-flow model applied to market cap. The presentation of the statistics looks convincing, but it is deceiving.

1. The price has gone up exponentially over time, but that is all the stock-to-flow graph really shows. The price is correlated with any data that increases exponentially, such as stock-to-flow.

2. The stock-to-flow vs. market cap graph is becoming less relevant over time. If you look at the data, you will see that the shape of the graph is changing over time, with the points lining up more vertically after each halving. After the next halving, the points will begin to form a nearly vertical line. The long term graph may still still show correlation (because market cap and stock-to-flow are both exponential), but after the first halving, the graphs between halvings show almost no correlation.

3. The stock-to-flow model predicts that the price will increase exponentially to infinity. Not only is that impossible, but the price is already diverging from the model.  If you look at a price graph, you can see that the price is increasing exponentially, but you can also see that the price is starting to flatten out. That is the opposite of what the model predicts.

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November 10, 2019, 04:58:52 PM
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I am skeptical of the stock-to-flow model applied to market cap. The presentation of the statistics looks convincing, but it is deceiving.

1. The price has gone up exponentially over time, but that is all the stock-to-flow graph really shows. The price is correlated with any data that increases exponentially, such as stock-to-flow.

2. The stock-to-flow vs. market cap graph is becomes less relevant over time. If you look at the data, you will see that the shape of the graph is changes over time, with the points are lining up more vertically after each halving. After the next halving the points will begin to form a nearly vertical line. The long term graph may still still show correlation (because market cap and stock-to-flow are both exponential), but after the first halving, the graphs between halvings show no correlation.


 - no no no no, a million times no. The price is only diverging from the model because overall it is converging to the model. That's what my research has been about and I've written a couple articles about it already!  https://medium.com/@AJC241469/on-bitcoins-convergence-simplified-part-1-3e521b0b1515

3. The stock-to-flow model predicts that the price will increase exponentially to infinity. Not only is that impossible, but the price is already diverging from the model.  If you look at a price graph, you can see that the price is increasing exponentially, but you can also see that the price is starting to flatten out. That is the opposite of what the model predicts.


 - Again, nooooo. You are wrong, sir! read my articles!

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November 10, 2019, 07:41:52 PM
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I am skeptical of the stock-to-flow model applied to market cap. The presentation of the statistics looks convincing, but it is deceiving.
1. The price has gone up exponentially over time, but that is all the stock-to-flow graph really shows. The price is correlated with any data that increases exponentially, such as stock-to-flow.
2. The stock-to-flow vs. market cap graph is becomes less relevant over time. If you look at the data, you will see that the shape of the graph is changes over time, with the points are lining up more vertically after each halving. After the next halving the points will begin to form a nearly vertical line. The long term graph may still still show correlation (because market cap and stock-to-flow are both exponential), but after the first halving, the graphs between halvings show no correlation.
- no no no no, a million times no. The price is only diverging from the model because overall it is converging to the model. That's what my research has been about and I've written a couple articles about it already!  https://medium.com/@AJC241469/on-bitcoins-convergence-simplified-part-1-3e521b0b1515

I agree that it looks like it is converging, but I believe that is more of a reduction in volatility than a convergence to the the stock-to-flow model. Consider that in the STF multiple graph, the upper limit is falling faster than the lower limit is rising. I expect that at some point the lower limit will flatten out and start to fall as the price diverges from the STF line.

3. The stock-to-flow model predicts that the price will increase exponentially to infinity. Not only is that impossible, but the price is already diverging from the model.  If you look at a price graph, you can see that the price is increasing exponentially, but you can also see that the price is starting to flatten out. That is the opposite of what the model predicts.

 - Again, nooooo. You are wrong, sir! read my articles!

What your model predicts as the price of a bitcoin in 2136 when the subsidy is 0.00000001 BTC and the supply is 20.99999 million BTC, and the STF is 2.1x1015? What does it predict when the subsidy is 0 and the STF value is NaN?

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November 10, 2019, 08:09:51 PM
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I agree that it looks like it is converging, but I believe that is more of a reduction in volatility than a convergence to the the stock-to-flow model. Consider that in the STF multiple graph, the upper limit is falling faster than the lower limit is rising. I expect that at some point the lower limit will flatten out and start to fall as the price diverges from the STF line.

 - The difference in the logarithmic rate of change of those bounding curves is negligible. In fact, those bounding curves are quite symmetric about a model multiple of 1.0. Regarding your expectation.... well, given the current trend, your expectation will not be met; it seems the price of Bitcoin has been moving in 2019 such that it is converging toward the price implied by the model in the next subsidy era, just like it did prior to the previous two halvings.


What your model predicts as the price of a bitcoin in 2136 when the subsidy is 0.00000001 BTC and the supply is 20.99999 million BTC, and the STF is 2.1x1015? What does it predict when the subsidy is 0 and the STF value is NaN?


 - Again, you are not thinking. Yes, I know what the price is predicted to be. It's quadrillions, or quintillions, right? You should be smarter than this! What is the value of the total fiat money supply, measured in USD? Maybe $50 trillion? $100 trillion? $200 trillion? Okay, now just think for a minute... when the value of Bitcoin continues to converge to the S/F model, and in 2, or 3, or 4 more halvings the total value of Bitcoin inevitably surpasses the total value of fiat money (measured in USD), what does that imply???

I don't want to spoil it for you, you deserve to have that "aha!" moment! But here's a hint: what is the basis of your valuation?? Are you sure you, personally, don't want to change your basis?! Perhaps you should re-read the excerpt from Saifedean Ammous' book!

Think!
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November 10, 2019, 09:02:37 PM
 #6

The stock-to-flow model predicts that the price will increase exponentially to infinity. Not only is that impossible, but the price is already diverging from the model.  If you look at a price graph, you can see that the price is increasing exponentially, but you can also see that the price is starting to flatten out. That is the opposite of what the model predicts.

I agree that the model doesn't work at the margins -- the returns should eventually diminish. However, I don't think we have enough historical price data to say it's diverging from the model yet.

What if we are following a normal probabilistic distribution, as the technology adoption life cycle is often viewed? That would mean we haven't yet experienced the steepening curve where adoption crosses the chasm between "early adopter" and "early majority." At that point, price could accelerate beyond the stock-to-flow model's projection before reversing back below. Like any regression model, price should be expected to stay at the lower end some of the time.

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