One complication in this model is that the impact of capacity stress on the market depends on the number of vessels available. The 2021-22 episode caught the industry at the bottom of an investment cycle, where few vessels were available to compensate for the lack of velocity in shipping due to port delays. Since then, more vessels have been put in circulation and the disruptions in the Red Sea happened with more capacity slack than in 2021-22, hence the apparent reduced impact on rates.

Therefore, the connection between rates and stress is non-linear such as: ) Where Slack represents the reserve capacity of the industry at the time of the disruption. RRmmttmmiim mmRR ≃bbmmbbmmqqiim qqmmttmm+ αα∗RRm RR(SSttqqmmb −SSqqmmS Hence rates increase above this threshold of maximum capacity absorption. The RRm RR(RR) = Scattered data points (Figure 12), illustrate that in this regime the relationship is linear. RR i RR≥0, mmqqbbmm 0 The capacity slack prior to a disruption is expected to change slowly over time unlike disruption and stress ΔRRmmttmmiim mmRR (UUSSDD) ≃2300 ∗ΔSSttqqmmb (MMiiq iiMMmm T UU) index, which see fast changes. Unfortunately, there is no good proxy for this threshold: slack is expectedly higher in 2024 than in 2020 due to ship delivered since. The empirical analysis will try explaining the slope α of the connection between stress and rate.

Annex 3 provides a model by which shippers' willingness to pay depends, inversely, on the value of their goods per container. According to this model, stress, and rate changes are proportional. M<sup>mmbb vvmmqmm RRmmqq TUU</sup> Typical value of a container is computed as an average mean across commodities, hence representative of ΔRRmmttmmiim mmRR (UUSSDD) ≃<sup>TTyyRRiiSSmmqq ggM</sup> ∗ΔSSttqqmmb (MMiiq iiMMmm T UU) vviimmgg SSmmRRmmSSiittyy (MM T UU) Typical value of a container is computed as an average mean across commodities, hence representative of lower end values.

With the moving capacity for vessels during the period of interest being 18MTEU, the typical value of goods implied by the observed connection is about **40,000 USD per TEU** . This value is indeed at the lower end of the value per TEU statistics (Annex 4). Therefore, capacity constraints and willingness to pay may explain the very high-rate bursts observed in recent periods of disruptions.

# **7. Conclusion**

The pandemic-induced crisis and other disruptions from 2020 onward significantly impacted shipping capacity and freight rates. While many regions experienced disruptions in their supply chains, the proposed metric and stress index effectively capture relative maritime supply chain disruptions despite their simplicity. Beyond measuring global trends, localized stress signals highlight chokepoints warranting a level of policy interventions. This framework could be extended to other scales (e.g., feeder loops or domestic shipping) and supply chains, where visibility data exists. Systematically producing the Stress Index, including disaggregated data at the regional or port level, could automatically inform productivity and capacity bottlenecks, flagging needs for infrastructure or operational improvements. Port productivity benchmarks like the World Bank’s CPPI, or dwell time made available in the World Bank’s Logistics Performance Index (2023) could be complemented with recurrent localized stress series, with ‘bursts’ flagging port investment 17