Bitcoin displacing Gold's monetary role

As a rapid power law of time

This is not investment advice. Your Bitcoin allocation should reflect your ability to handle risk and liquidity and your life circumstances.

Since inflation has been running so high recently, it seems useful to check Bitcoin’s value against gold as well as depreciating fiat. While gold prices are volatile, it is a scarce monetary asset, and really the only rival to Bitcoin in terms of scarcity of new supply in the monetary sphere. Currently both are growing in supply at roughly 1.8% per year, but as of Q2 next year Bitcoin’s supply growth will be cut to less than 1% with the next halving.

Gold is worth far more than Bitcoin in market cap, but Bitcoin has been closing the gap quickly on average since its creation moment in January, 2009.

The total amount of gold in existence is a little over 200,000 tons, and worth $13 trillion at current price of about $1950. Bitcoin’s market cap is just over $1/2 trillion, about two dozen times smaller.

Gold has monetary value, but also jewelry and industrial value. Private investment holdings are around $3 trillion, while government gold reserves in central banks and treasuries amount to a little over $2 trillion. Some of the jewelry demand should be included in the monetary premium, particularly in countries such as India and Thailand where gold is offered as a “bride price” at weddings and high quality 23K gold jewelry is readily pawned in a pinch. Overall the monetary demand seems to be roughly half of the total demand.

Figure 1. This graphic from Visual Capitalist showing gold reserves of various countries is wrong, although the numbers are thought to be accurate. It says central bank gold reserves. But America’s gold, the largest stockpile among all nations, is not owned by the Federal Reserve. It is owned by the US Treasury department and held at Fort Knox, West Point, and elsewhere, including 5% by the Fed. https://www.fiscal.treasury.gov/reports-statements/gold-report/21-02.html ; on the government’s books at $42 per ounce.

Bitcoin does not have industrial uses or a use case as jewelry, although people might ironically choose to make Bitcoin ‘tokens’ out of gold or other metals. Those aren’t Bitcoin of course, which is highly secured information held in a decentralized ledger. Bitcoin does have potential use as a security barrier for military, industrial, and general civilian use, but that would also reflect some monetary value for the security provided.

In order for Bitcoin to exceed gold’s monetary role for both national treasuries and investment by individuals it would need to grow in market cap by a factor of 10 times, to nearly $300,000 per Bitcoin.

In August 2021 I reported on Bitcoin’s progress toward matching the value of investment and national treasury gold holdings here:

Is Bitcoin Displacing Gold?

I examined four models of price history, that all had similar F-test statistics. The models are an exponential model, a power law model, and two S-curve models. In the early phases, an S-curve model (using the Weibull function) looks like a power law model. In those three cases we found that the price of Bitcoin denominated in gold ounces was rising as the fifth power of time.

BTC/Gold Models as of August 2021

Table 1. Table from August 2021 article on four models for Bitcoin vs. gold price. The exponential model had the best statistics at that time and was manifesting an 88% compound growth for Bitcoin relative to gold. The power law model showed Bitcoin rising relative to gold at nearly the fifth power of time since its birth. The S standard deviation statistic is in log10 terms for the first two models and natural log for the S-curve models. The timescale is the factor of 10 timescale for the exponential model and the time to the kneed of the curve in the S-models, starting from January 2009. The S statistic is the standard deviation of the log 10 (ln) of prices in the exponential (S-curve) models.

Figure 2. Best fit curves for the current exponential and power law model regressions, summarized in Table 2. This is a graph of log price in gold ounces vs. year elapsed since 2009 (the first two horizontal lines are 0.01 for the axis and 0.1 ounces respectively). The best fit power law model is closer to the current Bitcoin price in gold terms than the exponential model best fit, but both have good statistics.

The current best fit curves for the exponential model (green line) and the power law model (gray line), versus the monthly Bitcoin price in gold ounces, shown on a log scale in Figure 2 above. To the eye, the power law now seems like a better fit to the data. As I write this on 22 March 2023 the Bitcoin price is about 14.7 gold ounces.

Table 2 below updates the models with additional monthly data points since the prior August 2021 analysis. The power law and S-curve indices are approximately as before, while the timescale for the exponential fit has lengthened somewhat. Also notable is that the F-test statistics have improved substantially for all models, and the power law model now has a slightly higher F-test statistic than the others.

Table 2. Update through March 1, 2023. The R^2 correlation squared has improved for all models, as have the F-test, with a year and a half of additional data. The indices and timescales are similar for both the power law model and S-curve model. The S-curve is normalized to $2.4 Trillion maximal market cap, roughly equal to global government gold. The S-curve model reaches its knee in another two and a half years (if it doesn’t in actuality, Bitcoin will keep going higher like a power law for longer). The power law model now has the best F-test.

And here are the forecasts for each of the three models at the beginning of the years in the table, in ounces of gold. The exponential model is highly optimistic, to say the least, and would amount to a $3.5 million Bitcoin price by 2030 if gold stayed at its present price. The power law has Bitcoin reaching nearly a kilogram (32.15 ounces) of gold by the start of next year and almost 5 kilograms in 2030, some $300 thousand, if gold stays at its present price. The S-curve, that saturates at roughly 60 ounces and $2.4 trillion market cap, is more modest, reaching one kilogram of gold by 2025 and nearly two kilograms by 2030.

Table 3. Forecasts through 2030 for the exponential, power law, and $2.4 trillion market cap S-curve models. For now the power law model is slightly favored and has Bitcoin reaching 150 ounces or $300 thousand if gold’s price remains flat. If gold rises to $5000 over the next 7 years then the Bitcoin price would need to be around $750 thousand for this model to be successful.

Over the past decade, gold has provided about a 30% total return. This has provided some protection versus fiat inflation, but not enough. Whereas, over the past decade Bitcoin’s price in terms of gold ounces has increased from 0.062 ounces to 12.88 ounces, by over a factor of 200, far surpassing both gold and inflation.

Will it repeat that same extreme performance? Probably not, but the long-term trend is your long-term friend.