Buyback to the Future: When Does Higher U.S. Debt Start to Matter?

U.S. bond markets have once again been at the front of market news in recent weeks and months. Federal debt hit a staggering $40 trillion the same week that Treasury Secretary Scott Bessent expanded a bond buyback program aimed at stemming the rise in 30-year Treasury yields .

The intervention was surprising. Usual stress markers, like volatility in inflation expectations, have been mostly absent, which makes it hard to read the buyback as a response to acute distress. Nonetheless, the sustainability of US debt was once again brought into question by observers. By the standards of any other country, the US runs huge deficits. In the 2025 fiscal year, the federal deficit was around $1.8 trillion, or almost 6% of GDP.

Is that number alarming? Not by itself. The more useful question, as Morgan Stanley's Andrew Sheets has argued, is not the size of the debt in isolation, but whether it is starting to act as a brake on the economy . Here, the picture is divided.

Private balance sheets tell a different story from the public ledger. US corporate debt relative to GDP has barely moved over the past decade and remains below its pre-pandemic peak. Household debt has fallen relative to both income and GDP, and much of it is locked in at low, fixed mortgage rates, even as household assets have climbed to record levels . The same divergence shows up abroad: Europe has offset higher government debt with deeper private deleveraging, while Japan has seen public borrowing rise against a stable private balance sheet .

None of this is accidental. Governments generally have chosen since the financial crisis to cut taxes and increase public borrowing. A widening gap between private balance sheets and public ones is the obvious consequence.

So where should investors watch for stress? The answer may lie beyond private debt burdens and instead be found in asset allocation. Thirty-year Treasuries currently yield roughly 3% above expected inflation; long-dated investment-grade corporates yield north of 6%. The real question is when investors decide bonds, at those yields, finally offer better value than equities (given their much lower risk). So far there is little evidence of that rotation: fund flows and cross-asset correlations have not shifted meaningfully, and strong earnings growth is still (for the moment) doing the work of justifying equity valuations . That is the metric worth tracking, not the debt stock itself.

That reallocation threshold is not just a matter of market sentiment. A simple extension of the standard debt-dynamics identity shows why a tipping point like this is a mathematical feature of the system, not merely a market mood. The intuition is straightforward: if the interest rate governments pay rises with the debt they carry, as investors demand more compensation for it, the debt path stops being a straight line and starts to bend. Below a certain level, growth and the primary balance are enough to pull the debt ratio back down. Above it, higher rates raise interest costs, which raise debt further, which raises rates again, a feedback loop that runs on its own, independent of any new policy failure. As shown below, this produces two equilibria rather than one continuous trend, and it is the reason debt crises so often look sudden in hindsight.

For now at least, the signals that would mark a genuine crossing of that threshold, such as a real rotation out of equities and into bonds, spiking inflation-expectation volatility, or disorderly Treasury auctions, remain largely absent. A more likely near-term consequence is slower moving: continued Treasury intervention and rising debt-service costs put gradual downward pressure on the dollar, particularly against higher-yielding, lower-debt currencies like the Australian dollar . The $40 trillion headline is just a number, after all. The consequential question is how the market decides to price (or re-price) all that debt.

Let $b_t$ denote the government debt-to-GDP ratio in period $t$, $r$ the effective interest rate on outstanding debt, $g$ the nominal GDP growth rate, and $s$ the primary surplus as a share of GDP (with $s<0$ denoting a primary deficit). The standard law of motion for the debt ratio over time is

Taking a first-order Taylor approximation for small $r,g$, the change in the debt ratio is

This yields the familiar result seen in first-year lectures: debt is stable ($\Delta b_t = 0$) when the primary surplus offsets the "interest-growth gap," $s = (r-g)\,b_t$. If $r<g$, a country can run a primary deficit and still see $b_t$ converge; if $r>g$, stabilization requires a primary surplus.

Simple models treat $r$ as fixed, but in practice the rate a government pays is itself a function of how much debt it carries: in simple words, investors demand compensation for rising credit and duration risk as the stock of debt grows. This can be modelled with a simple linear risk-premium specification,

where $r_f$ is the risk-free base rate (think a 10-year Treasury bill or similar) and $\lambda > 0$ measures the sensitivity of the borrowing rate to the debt ratio, in other words, how many additional basis points of yield the market demands per additional point of debt-to-GDP.

Substituting risk-premium into debt-approx gives

The key change relative to debt-approx is the quadratic term $\lambda b_t^2$: because higher debt raises the interest rate, which raises interest costs, which raises debt further, the dynamics are no longer linear in $b_t$. This convexity is what produces a genuine threshold rather than a smooth trend.

Setting $\Delta b_t = 0$ in debt-quadratic and solving the resulting quadratic in $b$ by the quadratic formula,

yields two roots:

These two roots are both important, albeit for different reasons:

• $b_{\text{low}}$ (stable equilibrium):for $b_t$ below this root, $\Delta b_t < 0$ whenever debt overshoots it, so the debt ratio is pulled back toward $b_{\text{low}}$. This is the "sustainable" region.
• $b_{\text{high}}$ (tipping point):above this root, $\Delta b_t > 0$ and grows without bound even absent any further deterioration in the primary balance - the risk-premium feedback loop dominates. Crossing $b_{\text{high}}$ is essentially equivalent to crossing a crisis threshold for the purposes of this illustration.

Between the two roots, the system is locally unstable: a small shock can tip the trajectory from converging toward $b_{\text{low}}$ to diverging past $b_{\text{high}}$, even with no change in underlying fiscal policy. This is essentially how debt crises, when they do occur, can appear sudden.

Sheets, A. (2026). "When Does Higher U.S. Debt Start to Matter?" Thoughts on the Market, Morgan Stanley Research, 26 August 2026.

CNBC (2026). "Treasury announces upscaled buyback operation for longer-term debt, sending yields lower." 19 August 2026.

Ritchie, G. (2026). "Bessent's Treasury Buyback Expansion Spurs Drop in 30-Year Bond Yields." Bloomberg, 19 August 2026.

CNBC (2026). "US government debt passes $40 trillion mark for the first time." 19 August 2026.

Remy, H. (2026). "Morgan Stanley has good news despite the yields and bad debt data." TheStreet, 30 August 2026.

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Congressional Budget Office (2026). The Budget and Economic Outlook: 2026 to 2036.