Central Bank Bitcoin

or Government Treasury Bitcoin

CC-BY-SA 4.0 Stephen Perrenod, 2022 with Wonder app

This article is not financial or investment advice.

Cryptocurrency in central banks would mean Bitcoin

A very interesting paper has recently been written by Matthew Ferranti, an economics Ph.D. student at Harvard.

Titled “Hedging Sanctions Risk: Cryptocurrency in Central Bank Reserves” it looks at the optimal mix of Treasuries, Euro-denominated bonds, a global stock market index, Bitcoin, and gold under different assumptions, using recent price history and a dynamic Bayesian copula model (with Student-t distributions).

Ferranti examines the possibility of central banks adding Bitcoin alongside their forex and gold reserves, especially if they face potential sanctions from the US or EU. Russia, Iran, and North Korea in particular are under multiple sanctions.

One major quibble I have is that he uses daily data over only a two and a half year interval. The four year Halving cycle has demonstrated a major impact on Bitcoin’s price over the last dozen years, with prices typically strongest the year prior to and the year subsequent to the Halving. Also he uses 253 trading days per year appropriate to stock and bond markets, ignoring the fact that Bitcoin trades 365 days a year. This ability to trade 24x7x365 could be a real benefit to a central bank wanting to accumulate Bitcoin reserves or intervene in markets when other markets are closed.

Ferranti chooses a recent interval because he is concerned about the unsustainably rapid rise in the early years of price discovery for Bitcoin. And also he notes the growing correlation of Bitcoin’s price with stocks but I would note that has moved around considerably over the past decade and depends as well on the macroeconomic backdrop that changes from quarter to quarter and over multi-year periods.

Early days still for Bitcoin

I assert, based on the price evidence, that Bitcoin is still in the early stages of its adoption and price discovery, with a characteristic time scale of two to three decades similar to that for broad adoption of the Internet. I have previously addressed the long-term reduction in returns directly with Lindy technology adoption power law models and S-curve adoption models based on a Weibull function. Such power law and S-curve models have an annual appreciation rate that continuously drops with time.

I find that a power law of blockchain age with index ~ 5.5 gives an excellent fit. For the S-curve models we cannot yet statistically distinguish between an ultimate market cap, of say $3 trillion similar to all gold held by governments, or one as high as $100 trillion, similar to the global M2 fiat supply; in either case the behavior in the first decade or so with these S-curve models also looks like a power law of index > 5. Actually there could be no ultimate limit on Bitcoin’s value relative to fiat and gold since its maximum supply is ultimately fixed at 21 million and fiat currencies and gold are almost always increasing in supply into the indefinite future.

In fact for a power law model the expected annual return is simply k/B, where k is the index of the power law and B is the age in block years (percentage return is obtained by differentiating the power law and writing δP/P). This evaluates to about 38% currently and was above 100% prior to B = 5.5 years. The expected return very naturally tapers off continuously with this model or the S-curve models..

In Figure 1 we show the value of k, the power law index, determined from regressions of available monthly data. The regressions start from B = 2 block years elapsed, and we plot the best fit for the power law index from B = 3 until the present at 14.5 block years.

A block year is 52,500 blocks of nominal 10 minutes each, and is quite close to a calendar year at present. Block years are a better temporal basis given Bitcoin’s impactful regular Halving schedule each 210,000 blocks. In the early years from block year 3 on, the index k ranged between 3 and 6, but for the last 5 years it has been much more stable and above k = 5. Currently we have 151 monthly data points used in the regression analysis with statistical parameters R^2 = 0.94 and F-score > 2200.

Block years elapsed

Figure 1: Index for Lindy power law price model P ~ B^k where B is number of block years elapsed. The x-axis shows block years elapsed on the Bitcoin blockchain, where block years are 52,500 blocks in duration, and to within a couple of weeks, equal to calendar years in duration. This chart shows best fit power law index k (y-axis) for regressions using available monthly data between B = 2 block years and the B value shown on the x-axis. The index bounces around a lot until about B = 7.5, since then it has been close to k = 5. Current best fit value is k = 5.49 with standard error 0.12 and R^2 = 0.94, F-test 2237 for 151 data points. The model fair value is $35,554 with one standard deviation (prior four year window) in the log10 of price equal to 0.238 (a multiplicative factor of 1.73, thus the current Z score is -1.4). It is interesting that k has actually been trending upward for almost 6 years. The expected annual return in fair value is the differential with respect to P, divided by P, or k/B and currently 38%.

One dollar to rule them all

China, Russia, and Iran would like to be insulated from the US dollar as the global reserve currency and sanctions put in place by the US. There is no obvious replacement and even China is far from having such a deep government bond market that is essential for global financial collateral including trade finance. China is pursuing a Central Bank Digital Currency e-Yuan and hoping to use it extensively in their Belt and Road trading block initiative as well as domestically.

China has banned Bitcoin mining and yet there still seems to be significant hashrate there. Iran is allowing crypto mining, miners have to sell their output to the government. Russia has approved a national cryptocurrency exchange and is among the larger nations for Bitcoin mining. But the US has about 38% of all Bitcoin mining hashrate.

Only the dollar has the deep government bond market able to support global finance and trade, there are no ECB Bonds (just German, French, etc.) and China’s bond market is shallow and subject to capital controls. The Euro is the clear #2 global currency, not the Yuan or Yen, and the ECB looks to strengthen its position alongside EU expansion and economic health, but does not actively seek to replace the dollar.

China, Russia, Iran, and other nations have been adding to their gold holdings. What about Bitcoin alongside gold? It is much easier to ‘transport’ and offers fast settlement (one hour with six confirmations on the blockchain).

Many people think the Federal Reserve owns America’s gold, it does not. The US Treasury holds America’s gold in Fort Knox and at West Point and the Denver mint, the Fed holds gold for other nations in its vaults. The Fed itself only has gold certificates (paper) issued by the US Treasury. US Treasury gold is worth about $450 billion at current prices, higher than Bitcoin’s market cap of $315 billion.

‘None of the gold stored in the vault belongs to the New York Fed or the Federal Reserve System.’ - NewYorkFed.Org

If the US were to add Bitcoin to its reserves, it should happen through the US Treasury that manages the gold that belongs to the American people collectively.

Governments could use their central banks or sovereign wealth funds to procure Bitcoin or they could place it directly in their Treasury or Finance Ministry. That is really a matter of domestic politics and operational convenience. They may very well not want to announce their holdings, or understate them as they already appear to do with their gold holdings in a number of cases.

Despite some data limitations in Ferranti’s evaluation with his relatively short term span of price data his results appear reasonable and intuitive.

Ferranti model results for optimal share of reserves

Figure 2: Figure 17 from Ferranti’s paper. Under modest risk of sanctions, optimal shares in his model increase for both gold and bitcoin. The optimal share is a function of volatility or variance risk aversion, and exceeds 10% for Bitcoin (see blue line) if risk aversion is low (if acceptance of variance risk is moderate to high).

He found it is optimal for all central banks (or treasuries) to hold Bitcoin but due to price volatility at present it would be substantially less than optimal gold holdings. Total government gold in the world is 36,000 tons (at $55 million per, so $2 trillion) and 13% of all reserves (mostly in fiat treasury paper). The author finds optimal holdings around a few percent of reserves.

However, under his assumptions for the probability of sanctions, it can make sense for central banks to hold substantially more Bitcoin, which is essentially sanctions-proof when held off exchanges in wallets under control of an individual or organization. (It is still possible to track Bitcoin movement with chain analytics and seize it through court order if the keys can be located within a given jurisdiction. Bitcoin is held in the Internet in decentralized fashion but the keys are in hardware or software wallets). That percentage could easily be over 10% of all reserve holdings according to his models.

The total amount of central bank reserves is well over $10 trillion. China, Russia, and Iran hold about $4 trillion. And 10% of the sum of China, Russia, Iran reserves is greater than Bitcoin’s market cap. Of course if central banks were to buy in significant volumes the market cap could be pushed up considerably.

One can think of Bitcoin as a hedge and enhanced return alpha position relative to the gold holdings of central banks and governments in this context, and also as a replacement when gold is not available. Bitcoin is much more easily moved and sold, at very low transaction fees.

Without consideration of sanctions for moderate risk aversion (variance aversion parameter 150) the favored assets are short-term US treasuries, a global stock portfolio, and Bitcoin, in that order, with Bitcoin having an allocation under 10%.

But when the risk of sanctions is taken into account (as shown in Figure 2) the top three portfolio shares go to gold, Euro-denominated bonds, and global stocks. Bitcoin is fourth in this model despite its sanctions avoidance properties, with a share of around 10% at the middle value (150) of risk aversion.

Summary

I would say the general conclusion from Ferranti’s research is that central banks or government treasuries and sovereign wealth funds should start considering Bitcoin as a portfolio component, with shares up to 10% or more if they have high risk acceptance and concerns about a sanctions regime being imposed.

The foreign exchange reserves of the top 20 nations currently amount to $10.7 trillion (https://en.wikipedia.org/wiki/List_of_countries_by_foreign-exchange_reserves). One percent is about $100 billion and 10 percent about $1 trillion. So that is the order of magnitude of buying potential by larger nations. These are significant numbers relative to the current $320 billion market cap of Bitcoin.

In fact we are likely to see adoption more rapidly with smaller countries: El Salvador has a position in Bitcoin, as do Norway and Singapore through their sovereign wealth funds. It’s easier for them to buy without disrupting the market and they have less at stake with the current global system than do the US and Canada and Australia, and European nations. But a move to put Bitcoin in their reserves by Russia or China, likely in stealth mode at first, should not be discounted. It could already be in progress, secretly.