Bitcoin vs. Gold Update
Post-Ukraine invasion environment
This is not investment advice. Bitcoin is highly volatile. Past performance of back-tested models is no assurance of future performance. Only invest what you can afford to lose. You must decide how much of your investment capital you are willing to risk with Bitcoin. No warranties are expressed or implied.
Uncertainty in the world is high
In the current macroeconomic and geopolitical environment, seemingly more dangerous than even the Great Recession, gold is catching a bid. Recent prices have risen nearly to $2000 per ounce. The Russian invasion of Ukraine has introduced great uncertainty and gold is an asset that benefits from such uncertainty.
In addition growth in the US and the West more generally is slowing down, a natural outcome with year-over-year comparisons to the exceptionally strong bounce as we began coming out of the COVID pandemic in 2021. We may have a little further post-Omicron bounce here, but the evidence that growth will slow through this year, even before the invasion, is rather clear.
Part of this is due to the high level of inflation starting to bite into growth potential. Gold, like Bitcoin, is typically considered an inflation hedge but it’s more complicated.
It is not simply the level of inflation that helps gold but the difference between interest rates and inflation. And currently, interest rates are very low with the 10-year Treasury rate below 2%. Given the 5% to 7.5% inflation the US is experiencing (depending on the metric), real interest rates are highly negative (real rate is calculated by subtracting the inflation rate from the interest rate).
Such negative real rates are supportive of gold’s price, since bond coupons and stock dividends become less valuable.
Bitcoin is flat this year
Bitcoin has been more uncertain in its direction this year, and more volatile, ranging between $35,000 and $48,000 and has been about flat since the invasion. Bitcoin is an alternative to dollars, and a path around the SWIFT system for those nations and individuals facing sanctions from Western central banks and governments. Russians are also facing greater internal capital controls and Western businesses exiting, plus a collapsing Ruble.
Bitcoin is a riskier, more volatile asset than gold, and investors de-risk in the face of slowing growth and greater geopolitical uncertainty. So it would not surprise me if gold performs better than Bitcoin this year, as both slowing growth and geopolitical worries will be around for some time.
Nevertheless, over the longer term, Bitcoin outperforms very considerably against gold. Over the past five years, the gold price has risen 59%. The Bitcoin price has risen by 3196%; the price is 33 times higher than in early 2017.
There are only two pristine collateral assets in the world today: gold and Bitcoin. Today’s fiat is based entirely on ever-increasing debt issuance. Gold is ancient technology and Bitcoin is 21st century technology that is steadily substituting itself for the monetary premium component of gold, at least in relative terms.
Table 1: Comparison of Gold, Fiat, and Bitcoin according to Aristotle’s key attributes of money (fungibility has been added to his four attributes).
We expect in the medium term that central banks or government treasuries will start adding Bitcoin to their reserves. El Salvador has already done this with their Bitcoin bond issuance and mining initiative. Private, corporate, and investment fund holdings of Bitcoin are expected to continue growing relative to gold holdings over the longer term.
Half a year ago, peace in Europe
In a prior article last August:
I showed the results of four model regressions for the price of Bitcoin measured in gold ounces, using monthly data since 2013. These models are a power law model, an exponential model, and a Weibull S-curve model using two different comparisons to gold, the government gold holdings of over $2 trillion, and all gold, which is about $12 trillion in market cap.
All of the models were statistically significant. The best fitting model was the exponential one which possessed a compound annual growth rate of just under 88%.
Updated regressions
Now that we have seven months of additional data points, how have these models held up?
Table 2 summarizes the power law, exponential, and S-curve Weibull model results (for the Weibull model this is the more conservative all government gold case, around $2.4 trillion as an asymptotic value). The table gives the model slope parameter k, either for ~ t^k for the power law and for the Weibull S-curve tangent, (where t is time in years since Bitcoin’s start in 2009) or for ~ 10^(kt) with the exponential model (that uses base10 logarithmic price in a linear regression against time).
Table 2: Slope, statistical parameters, current fair value, current CAGR, and one year forecast for the power law, exponential and S-curve models (government gold case).
The statistical certainty has improved, with similar R^2 values and with the F-test for the exponential case rising from 583 to 763 since 7 months ago. The other two models also have F-tests over 600 rather than less than 500 as before. So the F-test values rose much more than the 7% percentage increase in the number of data points.
The table shows the current fair value, current CAGR growth rate and the one year projection of model fair value. The current market price of 19 ounces is closest to the power law model fair value. The one year out forecast centroid range is from 26 ounces to 55 ounces.
It is important to ‘think logarithmically’ given Bitcoin’s high volatility. The one standard deviation for the power law and exponential models is about 0.29 and 0.27 respectively in log10 of price, corresponding to about a factor of 1.9. Thus if one year from now, as an example, if the price is 30 ounces of gold, it will still be consistent with the exponential forecast of 55 ounces.
The exponential model has the highest CAGR and highest one-year forecast at 55 ounces of gold by March 2023. The other two models predict Bitcoin will be equal to or close to one kilogram of gold (which is 32.15 ounces) next year.
It is worth noting that the Weibull S-curve model is approximated by a power law ~t^5.27 in its early years (and that the slope of that model and the power law model are similar).
Graph of exponential model fit
Our models are statistically better fits based on the additional data since August 2021, and as before we cannot discriminate between them. The exponential growth model continues to be slightly favored, but the current price agrees better with the power law model.
The graph (blue line) shows the exponential model as log10 of Bitcoin’s price in ounces of gold, plotted against years since the start of 2009. The green line is the best fit regression for the model, which is a straight line on this log-linear plot. Over the nine year period Bitcoin has increased in price from less than 1/10 of an ounce, through one ounce five years ago, and to around 20 ounces today. Bitcoin has increased by 2.5 orders of magnitude in nine years, when measured against gold.
Figure 1: Log10 of Bitcoin price in gold ounces versus years since 2009. The blue line shows monthly price and the green line the best fit regression with slope of 0.276 increase in log10 price per year (corresponds to 89% per annum).
Eyeballing the price curve there appears to be some flattening, perhaps the curve will shift toward a less steep power law or the S-curve formulation during the next few years.
Bitcoin is 21st century technology
There is nothing wrong with gold as a low volatility crisis hedge, it also behaves differently than Bitcoin over shorter time periods. Over long periods of time, decades, it just keeps up with inflation, while Bitcoin has radically outperformed during its 13 year history.
Bitcoin is a radical new information technology, often referred to as digital gold, and as such, has been growing in value considerably over time relative to both fiat currencies and gold. In addition it is much more fungible, divisible, and easier to verify than gold and is also much easier to move across the globe at much lower cost and much more quickly.
Bitcoin is the breakthrough 21st century monetary technology, created as an asset via a proof-of-work mining process, and secured by thousands of distributed ledger instances. Its adoption as an alternative pristine asset to gold continues to grow rapidly.