arXiv 4 Jul 2026 · Theoretical Economics
arXiv:2607.03933 · PDF · DOI · OpenAlex · Extracted main text
When markets move more and more in lockstep, are they drifting towards the point where a price bubble becomes possible, and can that drift be measured before the crossing? This paper joins two long-separate ideas, that a rational bubble is a price outgrowing its dividends and that a crisis threshold can be read off the strength of a market's single dominant factor, onto one object recovered from the data: a summary of how asset returns move together, paired with a discount rate. We call this crossing point the fragility edge and show it plays three roles at once. A stated discipline says what the data support: the edge firmly, with a margin of error; whether a bubble exists, only roughly; which asset carries it, not at all. Across eighteen global equity indices from 2004 to 2024, that dominant factor strengthens in every documented crisis, the market collapsing from about six to about four independent factors; once the discount is set so that calm markets sit at the edge, this strength crosses it in crisis. These readings coincide with crises, not forecasts.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Baik, Jinho and Ben Arous, Gérard and Péché, Sandrine (2005) Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices | 1.000 | 10 | 5 | 100% |
| 2 | Andersen, P. K. and Gill, R. D (1982) Cox's Regression Model for Counting Processes: A Large Sample Study | 1.000 | 9 | 3 | 100% |
| 3 | Phillips, Peter C. B. and Shi, Shuping and Yu, Jun (2015) Testing for multiple bubbles: Historical episodes of exuberance and collapse in the S&P 500 | 1.000 | 8 | 3 | 100% |
| 4 | Acemoglu, Daron and Carvalho, Vasco M. and Ozdaglar, Asuman and Tahb… (2012) The Network Origins of Aggregate Fluctuations | 0.928 | 4 | 3 | 100% |
| 5 | Reed, Michael and Simon, Barry (1980) Methods of Modern Mathematical Physics. I: Functional Analysis | 0.928 | 4 | 3 | 100% |
| 6 | Lin, D. Y. and Wei, L. J (1989) The Robust Inference for the Cox Proportional Hazards Model | 0.874 | 6 | 2 | 100% |
| 7 | Cox, D. R (1972) Regression Models and Life-Tables | 0.843 | 3 | 3 | 100% |
| 8 | Montrucchio, Luigi (2004) Cass transversality condition and sequential asset bubbles | 0.843 | 3 | 3 | 100% |
| 9 | Campbell, John Y. and Shiller, Robert J (1988) The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors | 0.737 | 3 | 2 | 100% |
| 10 | Lucas, Jr., Robert E (1987) Models of Business Cycles | 0.644 | 4 | 1 | 100% |
Showing the top 10 of 61 scored citations.