Bitcoin Stock-to-Flow Cross Asset Model Works Well on Housing

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Testudo Fortis Labs

6 min readMay 2, 2020

Plan₿,@100trillionUSD on Twitter, (or PlanB, if you are an iPhone browser and can’t see the ₿) has announced his updated stock to flow model, transforming it into a cross asset model. For those not familiar Plan₿’s excellent and extensive work on stock to flow and its relationship to the price of Bitcoin over time, you can read his most recent article here. To simplify (or, more accurately, oversimplify), Mr. ₿ (or is it Mr. Plan?) proposes that there is a correlation between the market capitalization of Bitcoin and the ratio of existing Bitcoin to annual production of Bitcoin. This relationship appears to hold with gold and other metals.

Plan₿ closes his most recent article by pointing out that a) his model implies a very high price future price for Bitcoin, $288,000, and b) it might be nice to compare other assets to the model.

Housing

I thought it might be fun to test the model on U.S. residential housing. To be clear, this is all based on the regressions run by Plan₿. I’m just plugging numbers into his formula.

Does stock to flow even make sense with regard to housing? Well, yes, actually. Economists have researched a number of housing markets using stock to flow models.

Naturally, I look at San Francisco (I’m looking at it right now). The Board of Supervisors has certainly increased the difficulty level and it is very hard to build. Everyone seems to be a HODLer. The stock is high, the flow is low, and the values are absurdly high. Meanwhile, in places where builders can supply housing to people who want it (known as “reasonable” or “functioning” markets) the flow is higher relative to the stock and prices are lower.

Housing is not a commodity in the same way that gold, silver, or oil are. It is not fungible on the unit or square footage level. On the other hand, if we look at the total production of housing in, say, the United States, we get a large and diversified sample.

Also, the annual production of housing is not limited in the same way as the production of gold, let alone the production of Bitcoin. It is still limited, however, by the availability of capital, labor and material and, often more importantly, local regulations. Vastly more housing could be built if the political will existed. But that will does not exist currently. Locations where housing production could be easily increased are not always the locations where it is most desired. So, at this particular moment in history, the flow of new housing is (or was pre-COVID) somewhat stable.

And we have good data for housing. The U.S. Census Bureau reports the total number of housing units completed each year. It also reports the average size of units, and whether they are single or multi-family. Further, there is data on the average sale price for built-for-sale housing. There are estimates for the total square footage of housing in the country. Finally, Zillow has a model for the total market capitalization of all the residential housing in the U.S. Put together, these provide the inputs to apply the stock to flow equation and test how well the total capitalization is predicted.

The Formula

Plan₿ ran the regression and came up with the following formula:

Market Value = exp(12.7598) * stock/flow ratio ^ 4.1167

So, once we calculate the correct ratio for U.S. housing, we can just plug it in and see how well housing market cap is predicted.

(Warning: Highly tedious recitation of numbers below. Feel free to skip ahead.)

Floor Space

There were, at the end of 2019, approximately 253.2 billion square feet of housing in the U.S. In a paper from 2015, Moura, Smith and Belzer calculated the total square footage from a combination of U.S. Census Bureau and HUD data. I have updated it to 2019 using Census data.

Further, Census Bureau data show us that 904,000 single family homes were completed in 2019, with an average size of 2,508 sq. ft. Additionally, 352,000 units were completed in multi-family buildings, with an average size of 1,138 sq. ft. That brings the production of floor space to 2,667,808,000 square feet in 2019.

So, dividing 253.2 billion sq. ft. by 2.67 billion sq. ft., we get a stock to flow ratio of 94.8.

Applying this to Plan₿’s formula, we get a market value projection of exp(12.7598) * 94.8 ^ 4.1167, or $47.8 trillion.

How well does this match the “actual” value? Zillow estimated the market value of all U.S. housing at $33.6 trillion.

Assuming Zillow’s numbers are correct, the model overestimates the value of housing by roughly 42%. That’s actually fairly close, but not exact.

But, wait a moment, are the square feet built in 2019 equal to the square feet that existed already? Unlikely. And while there are many beautiful old houses, on average old houses are inferior, if for no other reason than that they have more deferred maintenance than something built last month. So, the model should overestimate.

Value Added

Can we get a better estimate by looking at the dollar value of housing built? After all, if the Zillow estimate is right, it should include all the deferred maintenance, all the variance in location and amenities, all the differences in school districts. It’s price. Price knows all. Meanwhile, we do have the price at which the new housing sold. We’ll have a good, if not perfect, idea of the value of both the stock and the flow.

Now, the flaws. We don’t have a “price” for owner-built housing. We, or the Census Bureau anyway, know a lot about square footage, but not price. For built-for-sale real estate, we do have a price.

Examining the home size data, I arrive at a very rough calculation that owner-built housing is 6–8% smaller on average than built-for-sale housing.

More importantly, 24% of housing units completed were multi-family and the vast majority of those units were rentals. We don’t have a price for them. I’ll assume that a square foot of rental housing is equal to a square foot of a single-family home. This yields a weighted-average value for all housing units completed and sold of $320,700. This estimate is probably slightly too high, as multi-family, rental space and single-family home space are not really equivalent. But I cannot accurately quantify the difference. This difference does mean the stock to flow model should slightly underestimate the value of the housing stock.

Given the 1,256,000 units completed and/or sold at our average value of $320,700, we see $402.8 billion in housing added in 2019. Applying this to the Zillow estimate of total housing, we get a stock to flow of 83.4.

So, returning to our formula, we get a market value projection of exp(12.7598) * 83.4 ^ 4.1167 or $28.2 trillion.

The model undershoots Zillow’s $33.6 trillion estimate by 16%. Given that we expected an underestimate, this is fairly impressive.

Fitting the data to the Plan₿ graph

OK. You’ve stuck with me this far. You’ll probably want to see how our estimates look on the graph. And, frankly, you’ve earned it.

We’ll place the $33.6 trillion, Zillow estimate of U.S. housing value at two points on Plan₿’s graph, the “square footage” stock to flow of 94.8 (blue circle) and the “price” stock to flow of 83.4 (green circle). As you can see, both are very close to the regression line.

The green circle is U.S. Housing, value added based. The blue circle is U.S. Housing, square footage based. (Stole Plan₿’s graph, added to it.)

Conclusion

There you have it. Overall U.S. Housing value fits the value predicted by the Bitcoin Stock-to-Flow Cross Asset Model quite well. Fine tuning the value of housing added per year might even improve the fit.

Does this mean the projected 2020–2024 Bitcoin value of $288,000 will be correct? Well, you get to find out just as quickly as I do.