Golden bubbles (Debasement Part I)

Key insights

Current levels of gold prices likely reflect a bubble that will result in multi-year, perhaps even multi-decade losses.
Gold prices over the floating-dollar period are well described by a fundamental model based on real interest rates, inflation expectations, changes in the dollar, and an “unobserved” component that captures speculation and changes in risk premia.
Corrections in gold price misalignments with “fair value” under the model are forecastable based on the degree of misvaluation and changes in the momentum of the unobserved component.
Conditioning 1-year-ahead and longer return distributions on current valuations and risk-premium/speculation momentum implies negative expected returns and low probabilities of positive returns.
Cross-market asset prices contradict the “debasement” narrative as a fundamental driver of gold prices, while central banks’ “de-dollarization” is limited and fading.
With real rates and the dollar likely to rise again this year, gold’s sharp rise may be in for a sharp correction.
A basket of non-precious metals and agricultural commodities may provide an alternative hedge to debasement, but equities likely provide the best alternative hedge.

Golden bubbles (Debasement Part I)

Gold has had a spectacular run and lately has dragged other precious metals in its wake. The yellow metal is up 122% (51% annualized) since it began its vertical ascent in March 2024. But even that likely understates its run. In the two years prior, the dollar ripped higher versus everything else, real discount rates surged, and still the nominal dollar price of gold held steady.

Like every bubble, gold has its evangelists, and they have a really good story: major central banks have lost their way, their emerging market counterparts are buying gold by the ton, fiscal debt is out of control nearly everywhere, unpopular governments are struggling to keep populists at bay amid already stretched budgets, and if that weren’t enough, the global order is undergoing a once-a-century unravelling, with arming for World War III accelerating. That perhaps explains why gold’s Starship-like rise hasn’t elicited the same concern bubble Cassandras typically show for US stocks, even after a year of uneven S&P 500 gains.

Yet, new or prospective gold buyers should contemplate that a gold buyer in January 1980 would have waited nearly 28 years to see a higher price – 29 years for a sustainably higher price – and had to pay storage or leasing costs the whole time. Given that cautionary tale, it is worth considering whether gold’s current prices are sustainable, what might happen to other, similar assets if it is not, and how you might hedge fiat debasement risks if that is your underlying concern. Valuing gold is the first in a three-part series on “debasement;” I’ll consider the future of the dollar and Bitcoin next.

A Hotelling model of gold prices

While it may seem counterintuitive, gold prices are little affected by gold mining and other variables that many would consider “fundamental.” The reason for that is that gold, although used in some manufacturing, is primarily a non-decaying, long-run store of value with a finite supply. Hence, unmined gold is best thought of as stored in an underground vault with a zero lease rate until it is mined. Seen that way, mining it is just transferring it to an overground vault and doesn’t affect its price. Instead, gold’s value is better described by a “Hotelling model.”¹ To understand the intuition behind a Hotelling model, imagine that we know the universe will end on date T and the end-of-times price of gold will be G. In that case, what would you want to pay for gold today if its only use is as a shiny store of value with fixed supply?

A (very) long-dated TIPS zero

The answer is the risk-adjusted net present value of G because its expected future appreciation would then pay you a competitive return. Since gold can never default, it should pay you a real risk-free return in perpetuity. Thus, the appropriate price of gold today would discount G by expected future inflation and real interest rates until the “end of days.” That effectively means that gold is a super-long duration, zero-coupon, inflation-indexed, risk-free bond, i.e. akin to a TIPS zero if the US government really were risk free. Hence, its price is dependent on expected future inflation and real interest rates, and if you are not a US resident, the exchange value of the dollar. Further, in the same way that super-long duration bonds are hypersensitive to changes in real interest rates and inflation expectations, gold’s price should be similarly volatile in those variables.

Fundamental determinants

Thus, under a Hotelling model, changes in the price of gold should reflect the accrual of real interest, inflation compensation, changes in the exchange value of the dollar, and capital gains (or losses) from shifts in the term structure of interest rates (both real and inflation components). These variables are readily observable and, indeed, gold prices do appear to fluctuate with each as expected: rising when interest rates fall and falling when interest rates rise (Figure 1); rising with inflation (particularly before inflation stabilized in the late 1980s and when it jumped during Covid, Figure 2); and varying inversely to the dollar (Figure 3).

And “other” things

But gold prices do not perfectly correlate with those variables. There are significant deviations over the last 55 years. (The departure of gold from its relationships with all three variables in the last two years is especially notable.) These nonconformities reflect factors that the simple Hotelling/TIPS framework misses: speculative demand – like the Hunt brothers’ cornering of the silver market in 1979² – risk premia that reflect both changes in risk tolerance and risk perceptions, and new discoveries of gold that change supply in the “underground vault.” These “other” factors, unlike interest rates and the dollar, are not directly observable in real time, or in the case of risk premia, ever.

Rudy Kálmán to the rescue!

Fortunately, there is a class of models that allows us to “infer” unobserved variables while estimating relationships in observable data: the Kalman filter. In the 1960s, a Hungarian-American mathematician, Rudolf E. Kálmán, developed a mathematical algorithm that optimally extracts a signal – even one that is not directly observed – from noisy data.³ The Kalman filter is widely used in signal processing to isolate or amplify signals hidden amid the noise. It also is increasingly used in economics and finance to estimate “unobserved” phenomena, like risk premia.

Seeing the unobservable

To estimate a Hotelling model of gold’s fair value based on “fundamentals” – real interest rates, inflation expectations and the dollar – but without ignoring unobserved changes in risk premia, speculative activity, and other factors affecting gold prices, I used a Kalman filter with a single, time-varying state variable to capture the unobservables.⁴ Unfortunately, over my chosen sample – gold prices since the dollar was floated in September 1971 – risk premia and speculation are not the only unobserved variables. Because TIPS (inflation-protected US Treasury securities) weren’t issued before 1997, real interest rates and market-implied inflation expectations (TIPS breakevens) didn’t exist for almost half my sample. I solved this problem by estimating a larger, multi-state Kalman filter with several variables that embed information about real interest rates (including gold) to extract “unobserved” TIPS yields and inflation expectations going back to 1971.⁵ (Actually, I estimated them back to 1870, but that’s for a different project.) I used those estimates of TIPS yields and breakevens for all observations before February 1997.

Navigating in the fog

“Unobserved” variables make the Kalman filter dangerous. A Kalman filter can fit anything if you allow it (just ask John Williams of the notorious “Laubach-Williams” model of neutral interest rates). So, it requires both significant caution and experimentation. My technique, using data through 2020, was to experiment with parameter constraints that maximized the explanatory power of “fundamental” (observed) variables, rather than the unobserved state variable, in fitting historic gold prices. Then, using expanding data windows from 1971 through the present, I estimated a new filter, month by month. Expanding windows are used to avoid look-ahead bias while allowing the model to adapt to structural change. With each iteration, I used the updated model’s coefficients to project gold prices forward 36 months with real-time real interest rates, inflation expectations and the dollar, but not the unobservable state variable.⁶ These rolling out-of-sample projections and their subsequent revisions were then used as “fair value” measures for gold prices.

Estimating “fair value”

Figure 4 presents gold prices with the rolling, 36-month projections of fair value and the root-mean squared error (RMSE) of the 36-month-ahead fair-value “forecast.” To facilitate viewing, only every 12^th projection (in alternating green and orange) are shown, and all variables are displayed in logarithms so that they are comparable through time in percentage terms. The first rolling estimation window (48 months and expanding by one each month thereafter) ends in 1975, where you can see the start of the first projection, and the first 36-month RMSE is aligned with the final point of that projection in 1978. The last orange projection and RMSE are associated with the last 36-month projection made for December 2025, based on a model estimated through December 2022.

Evaluating performance

Through the mid 1980s, projections capture gold’s dynamics, but are volatile and prone to large errors, especially around turning points. This likely reflects both gold traders learning how “floating” gold prices behave and the model learning how gold traders behaved. By the late 1980s, the model is nailing gold prices’ variation and level, and fair-value errors fall to near zero. Fair value projections again begin to break down in the 2005-‘15 period, first as the model misses the “permanent” shock of emerging markets’ rising demand for gold (discussed below), and later as it overestimates the permanence of their demand. But forecast errors drop sharply thereafter and the model even captures Covid’s effects well. It is only after 2022 that the model again begins to underestimate gold prices, and then quite dramatically. The question is whether the model went wrong, or gold prices have.

The definition of “permanent”

The answer to that question lies in how the model handles “permanence” and what that means. If a vast new seam of gold is discovered, increasing potential supply, the “end-of-time” price of gold (and current price) should permanently fall. If markets begin to fear – but not expect – a permanent rise in the rate of inflation, current and future prices of gold should jump to reflect compensation for the risk but perhaps not permanently: as fears subside, so should gold’s price. The unobserved, time-varying state variable captures these effects as fast-dissipating shocks to changes in gold prices.⁷ But those shocks become permanent in the level unless another shock offsets it. Hence, major gold discovery would imply a single negative shock that is not reversed, but a change in risk perception, if it reverses later, it requires two shocks: a positive one that raises the level of gold prices, then a negative one that later lowers it.

Shocks in motion

The forecast errors in the late 1970s and early 1980s represent both sides of the inflation-risks scenario. Throughout the 1970s, with inflation outpacing expected inflation priced into bonds, the model’s projections – which exclude the unobserved positive innovations to risk premia – underpredict gold prices. But as those risk premia are imprinted into the level of gold prices, the model then overpredicts gold in the 1980s as Fed Chairman Volcker quashed inflation risk fears and negative innovations to the unobserved variable permanently reduced the level of gold prices. Only after inflation expectations (and fears about them stabilized) did the model’s performance improve.

Crucially, this means that model revisions – comparing later projections to earlier projections – contain exploitable information about momentum in risk premia or speculation, and thus future gold prices. Because shocks to the unobserved state variable alter prices permanently unless reversed, revisions to long-horizon forecasts reveal whether shocks are still propagating or beginning to mean-revert.

Necessary but not sufficient conditions

The model thus provides two different metrics for value: (1) how much current prices deviate from projections of fundamental value; and (2) how fundamental projections update through time with unobserved shifts risk premia and speculation. The first describes the degree of potential misvaluation, potential because, depending on the nature of the shock, it could be permanent or temporary. The second factor describing the shock’s momentum provides information on both its permanence and timing, which is critical given John Maynard Keynes’ (supposed) warning that “Markets can remain irrational longer than you can remain solvent.” Hence, misvaluation may be a necessary condition for reversal, but it is not sufficient.

Conditioning expected returns

One way to see this is by comparing future gold returns conditioned on specific indicators with each other and with unconditional returns. Figure 5 presents the distributions of 1-year-ahead gold returns conditioning on current levels of implied gold misvaluation based on 12-, 24- and 36-month projections. Current misvaluations are extreme, 1.94, 1.68 and 1.38 standard deviations above their historic averages,⁸ respectively, and the implied return distributions are correspondingly miserable: average 1-year returns are -0.1%, -14.6% and -3.3% (versus an unconditional average return of 5.2%) and the probability of positive returns is only 0.67, 0.36, and 0.41, respectively. Figure 6 presents the same analysis for 10-year returns, showing the probability of positive returns over a decade are only 0.33, 0.18 and 0.15, respectively. However, a note of caution is necessary here: given the extremity of current misvaluation, the sample sizes are small: 6, 11 and 34 observations each.

Incorporating implied momentum

We can take this a step further and incorporate both the implied overvaluation and the projection revision indicator of momentum, i.e. conditioning expected returns on two indicators at once. The one wrinkle is that, as noted, overvaluation is now so extreme that there are too few past examples. To expand the historic comparables while still preserving a sense of the overvaluation, I lowered the threshold from current valuations to +1.5 standard deviations for the 12 and 24-month misvaluations and +1.0 standard deviation for the 36-month misvaluation.⁹ To measure “unobserved” momentum, I used the current 36-to-24-month projection revision, which is only 0.37 standard deviations above zero and falling, so I conditioned on its current value. But note that momentum, unlike misvaluation, is expected to positively covary with future returns, so I am conditioning on 36-to-24-month revisions being less than 0.37 standard deviations, which is almost two-thirds of the sample.¹⁰

Locking in losses

Figures 7 and 8 present the poor returns one can expect from gold over the next year and ten years, respectively, when conditioned on both valuation and momentum indicators. Each plot shows the annualized return distributions conditioning on both current 36-to-24-month revisions (momentum) and one misvaluation measure (12, 24 or 36 months), and, in the last column, returns conditioning on all four indicators (the projection revision and all three misvaluations). The distribution of unconditional returns is shown on the left for comparison. The bi-conditional distributions are depressing enough with average returns of -8.1%, -20% and -11%, respectively, at a one-year horizon and 0.4%, -3.2% and -1.9% annualized over a decade. But the all-conditions distribution suggests that buying into gold at current prices guarantees capital losses – if the Hotelling model and past data are representative – over every holding period from 1 to 10 years (on average, 35% for 1 year, and 5% annualized over 10 years). Note, these are price returns, not total returns, so they do not include lease or storage costs.

“This time is different…”

But what about the gold evangelists’ compelling story of fiscal dominance, monetary incompetence and forthcoming Armageddon? Surely this time is different? The problem is that none of these stories jibe with any other asset prices. If fiscal dominance and monetary debasement are the worry, why are medium- and long-term inflation breakevens near their long term average? Why are term premia, even after their expansion over the past year, still well below historic norms and the yield curve relatively flat? Why is the US dollar, even though off its 2022 highs, at an historically strong level? If the surge in gold prices reflects only the risk, rather than the expectation of “debasement,” or risks of global turmoil, why are option-implied volatility and butterfly pricing (the price of extreme moves) across asset classes including swaptions at such moderate levels? And why is every other commodity price at or near its 155-year low versus gold (Figure 9)?

De-dollarization?

The remaining narrative support for gold prices at current levels is “central bank buying” driven by “de-dollarization.” Except that the story is mostly a fable. Most central banks with large reserves haven’t adjusted their gold holdings in years (Figure 10). Only a handful of “BRICS” countries have and the vast majority of that has been done by just two countries: China and Russia (Figure 11). Furthermore, Chinese and Russian gold purchases have slowed as they have, by my calculations, already largely de-dollarized their foreign exchange reserves. (I’ll cover this in greater detail in Part II of this series.)

Warning signs

But there also is a worrying sign from one of the most aggressive central bank gold buyers of the post Covid period: Singapore. Given its immense reserves (and two large parallel sovereign wealth funds) the Monetary Authority of Singapore sometimes acts more like a hedge fund than a conservative central bank. It therefore is interesting that after doubling the volume of its gold holdings in the three years through March 2024, it has cut the number of troy ounces by 13.5% since. To the extent that it is front-running intelligence it has about the buying activity of its peers, that raises serious questions about official support for gold prices. Even if it just reflects sound asset allocation practices based on modeling similar to mine, it should be taken as a warning sign. In a year when I expect a rebound in both real interest rates and the dollar, slower central bank buying could be the straw that breaks the golden camel’s back.

Seeking alternatives

If it is debasement risk that you’re worried about there are alternatives to gold. Indeed, given the seizure of private gold holdings by the US when it last formally devalued the dollar under President Franklin Delano Roosevelt, there are probably much better alternatives to gold. Figures 12 and 13 present the 1-year and 10-year-ahead (annualized) returns of a variety of potential alternatives under the four conditions considered for gold in Figures 7 and 8. One thing is clear immediately: other precious metals, despite their significant relative undervaluation, are not good alternatives. In fact, that is true of most commodities, though random gains by selected industrial metals and agricultural commodities suggest that a basket of non-precious-metal commodities may be a reasonable alternative to gold. The Swiss franc has held its value over the long run, but note that Figures 12 and 13 do not include carry.

One note of caution is again necessary here: even with the expanded sample afforded by lowering the thresholds for the valuation indicators, these are still small-sample results that are heavily influenced by the experience of the 1980s. That said, lowering the thresholds for valuation to one standard deviation doesn’t change the results qualitatively.

The ultimate debasement hedge?

The standout performer in Figures 12 and 13 is equities. While some may dismiss that as a feature of the disinflationary bull-market of the Reagan deregulation, that would be a mistake. As long-time emerging markets’ investors know, equity prices are a natural hedge against large inflations because they are claims on earnings that rise with inflation. Developed market investors have been misled by the 1970s experience. Equities performed poorly as an inflation hedge then, because of the post-1973 negative productivity shock. The contrast with today is stark: the US is undergoing a productivity boom led by automated localization, AI and re-industrialization protected from China’s economic warfare by tariff walls.

The return of optionality?

The drop in volatility and butterfly option prices (tail-risk insurance) since last year also suggests increasing value in long-dated options. I will return to that topic after the completion of this series. In the meantime, institutional and annual subscribers interested in the full results of my gold analysis for all horizons from 1 to 10 years may request them.

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