The inevitable mathematics of sovereign debt

Central banks understand it, so should individual investors

There is a point in any debt spiral at which the question stops being political and becomes arithmetic. The US – and much of the developed world – has reached that point. Understanding why requires no ideological priors. It requires only a calculator.

Start with the global picture. Public debt across the world’s major economies has been rising for decades, but the pace accelerated sharply after the pandemic. Global public debt rose to just under 94% of world gross domestic product in 2025, according to the International Monetary Fund, and is projected to reach 100% by 2029. Among the G7, Japan carries debt above 260% of GDP, Italy above 138%, France above 110%, the UK above 100%. This is no longer a handful of fiscal outliers. It is the architecture of the global financial system.

For most of the past two decades, large debt burdens were uncomfortable but manageable. The reason was simple: interest rates were near zero. When a government borrows at 0.5% and its economy grows at 3%, the debt burden shrinks automatically, even without running a surplus. Low rates made a generation of fiscal excess feel consequence-free. That era is over.

What changed

The rate-hiking cycle that began in 2022 as a response to inflation permanently changed the arithmetic on sovereign balance sheets. Governments do not borrow once and hold that debt forever. They issue securities across a range of maturities, and when those bonds mature, they must be refinanced at whatever rate prevails at that time.

The US has approximately $9tn in debt maturing in the next 12 months. That debt was largely issued at rates between 0.5% and 2%. Refinancing it at current rates of 4%-5% embeds that higher cost for the life of the newly issued security – and even future rate cuts would reverse it only gradually. The Congressional Budget Office estimates the average interest rate on federal debt held by the public to be 3.4% in 2026, rising towards 3.9% later in the decade as older low-coupon debt rolls over. Each refinancing ratchets the cost higher.

The consequence is that the US will spend more than $1tn on net interest in fiscal year 2026 alone – more than the entire defence budget (even as the US is at war with Iran). A decade ago, annual net interest expense was roughly one-quarter of today’s level. By 2036, the CBO projects that figure will more than double to $2.1tn. By 2056, it will reach 6.9% of GDP – exceeding both Social Security and Medicare. The federal government will be devoting an extraordinary share of national income to servicing claims accumulated in the past.

Gross US federal debt now exceeds $40tn – approximately 126% of GDP on the IMF’s internationally comparable measure – and is projected to reach 142% by 2031, the steepest trajectory among any advanced economy. The deficit stands at approximately 5.8% of GDP in fiscal 2026, nearly double the 50-year historical average of 3.8%. These are not independent problems. Rising interest costs drive rising deficits, which require more borrowing, which increases the debt stock, which raises future interest costs. The spiral is self-reinforcing.

Is the debt sustainable?

One test is the debt-dynamics equation associated with economist Evsey Domar. The rule is this: for a debt burden to be sustainable, the interest rate on government borrowing must be lower than the nominal growth rate of the economy. When borrowing costs rise above growth, the debt-to-GDP ratio rises automatically. To hold it flat, a government must run a primary surplus: that is, revenues must exceed spending before interest payments are counted.

In other words, a country with debt at 100% of GDP and an interest-growth differential of 1% must run a primary surplus of 1% of GDP just to keep the ratio stable. Nothing could be further from the truth in the US today. The US currently runs a total deficit – the full gap between all spending and all revenue – of approximately 5.8% of GDP. Even stripping out interest payments entirely, the so-called primary deficit is approximately 2.6% of GDP.

Under Domar’s framework, the US would need to swing from a 2.6% primary deficit to a surplus of roughly 1% – a fiscal adjustment of nearly 4 percentage points – simply to stop the debt ratio from rising. It is moving in the opposite direction, meaning the debt ratio rises automatically.

Four ways out, none easy

There are four broad ways to change the arithmetic of an unsustainable debt trajectory: faster growth, fiscal adjustment, default or restructuring, and erosion of the debt’s real value through inflation and financial repression. None is painless, and in practice governments often use some combination of them.

The first is growth. Sustained nominal economic growth above the effective interest rate makes a given debt burden easier to carry and can reduce the debt-to-GDP ratio without requiring as much fiscal adjustment. It is the most politically appealing solution. The difficulty is that trend growth across most advanced economies is modest relative to today’s debt burdens. The IMF projects US real growth slowing towards roughly 1.8% later in its forecast period.

The second is fiscal adjustment: raise taxes, restrain spending or do both until the government produces a sufficiently large and durable primary surplus. This is the cleanest solution mathematically and the hardest one politically. The required adjustment would touch constituencies that voters are accustomed to protecting – taxpayers, retirees, healthcare beneficiaries, defence and other major spending programmes. Elected governments have repeatedly shown little appetite for imposing that pain pre-emptively. Meaningful consolidation tends to become politically possible only when an emergency – a market revolt, an inflation shock, a funding crisis or some comparable constraint – makes the cost of inaction unmistakable. The option exists. The political will to use it before a crisis is much less evident.

The third is default or restructuring. For a major reserve-currency sovereign, an explicit default would be profoundly disruptive to credit markets and the financial system. It is possible. It is not the base case.

The fourth is inflation or financial repression: reducing the real burden of debt by allowing nominal growth and inflation to outpace the effective interest paid on the debt, often while regulation or central-bank policy helps contain funding costs. This is not a prediction of hyperinflation. History repeatedly shows that, when fiscal adjustment proves politically insufficient, governments often resort to some combination of inflation, monetary accommodation and financial repression. The form varies. The incentive does not.

What the institutions are telling you

Central banks do not publish op-eds, they publish balance sheets. And the balance sheets of the world’s central banks have been making the same statement, in the same direction, for 15 consecutive years.

Official-sector gold purchases exceeded 1,000 tonnes in each of 2022, 2023 and 2024 – more than twice the 2010-21 annual average. This is not a trade or a sentiment call on the gold price. These are institutions with access to the same fiscal data discussed above, executing a sustained reallocation towards an asset that carries no counterparty risk, cannot be printed and sits outside the liability structure of another sovereign.

During a session I participated in this summer as part of OMFIF’s Gold and Precious Metals Working Group, a reserve manager from a central bank that had recently begun accumulating gold was asked to describe the motivation. The answer was one word: diversification. It is always described as diversification. But the diversification is away from something specific – away from the sovereign paper of governments whose fiscal trajectories are described above. Central banks are not panicking; they are solving a mathematical problem.

The individual investor corollary

Everything that is true for a reserve manager is true for an individual with savings. The scale is different. The arithmetic is identical. If the most likely resolution of the sovereign debt problem involves some combination of inflation, financial repression and currency debasement – and the mathematics above suggest it does – then the real value of cash and fixed-income savings is the thing at risk. Not as a prediction, but as the arithmetic consequence of the policy options that remain available.

Gold is not a trade on that view. It is the asset that has no liability on the other side of it. In an era of too many liabilities, that is not a small thing.

Steven Feldman is Co-founder and Chief Executive Officer of GBI, the institutional infrastructure for physical precious metals, serving global wealth managers, banks, and fintechs. GBI is a member of OMFIF’s Gold and Precious Metals Working Group.

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