Net Disagreement and the Limits of Long-Term Bond Pricing
New research suggests that unbounded disagreement over growth forecasts can make long-term bonds mathematically non-existent.
Bond valuation depends on net disagreement between investors regarding aggregate endowment growth. When this disagreement grows without bound, the long-forward measure and the long bond cease to exist. This creates a theoretical ceiling on the maturity of tradable instruments in environments where market participants cannot converge on long-run growth expectations.
Yields may appear to converge along a specific belief path, but this convergence is deceptive. The long yield alone does not indicate whether valuation weights and bond returns are actually stabilizing across different maturities. This disconnect means that observing a stable long-end yield does not guarantee that the underlying pricing mechanisms are consistent.
Fixed-income markets rely on the assumption that long-dated bonds provide a reliable anchor for the term structure. If net disagreement remains unbounded, the mathematical foundation for these instruments collapses. This suggests that extreme divergence in growth forecasts does more than just increase volatility; it removes the theoretical possibility of a long-term equilibrium price.
Institutional portfolios heavily weighted toward ultra-long durations face a structural risk when beliefs about the distant future diverge. The research provides finite-maturity error bounds for bond prices and forward densities, offering a way to quantify the pricing inaccuracies that emerge as maturities lengthen under these conditions.
This framework shifts the focus from the average belief of the market to the net disagreement between participants. The stability of the long end of the curve depends less on the specific growth forecast and more on the limit of the disagreement between the most optimistic and pessimistic actors.
Market participants should monitor the gap between different growth regimes to determine if the long-forward measure remains viable. When disagreement exceeds certain bounds, the traditional tools for pricing long-dated liabilities may fail to produce meaningful values.