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Financial Metrics & Modelling

Mean Reversion in Freight Rates and Vessel Values

Reviewed 2026-11-04

Summary

Mean reversion is a modelling hypothesis under which a variable tends to move back towards a long-run level after deviations. It is frequently used in shipping because freight earnings and vessel prices are cyclical, but the hypothesis is conditional: the equilibrium level can shift, structural breaks can occur and different market regimes may display different persistence.

Why this matters in ship finance

Mean-reverting models can inform medium-term earnings scenarios, ship valuation, investment timing and credit stress. The danger is false comfort. A model calibrated to a boom, crisis or obsolete trading structure may imply a rapid recovery that never materialises. For lenders, this can overstate future DSCR and collateral recovery; for investors, it can create premature buy signals.

The concept

A simple discrete specification is an AR(1) process around a long-run mean. A continuous-time analogue is the Ornstein-Uhlenbeck process. Both impose a pull back towards an equilibrium, but the variable being modelled - level, log-level, spread or return - must be specified and economically sensible.

Freight rates can in some markets approach zero or even become negative on particular routes, whereas vessel values are bounded below by scrap or alternative-use considerations. The same Gaussian process should therefore not be applied indiscriminately to all shipping variables.

Quantitative formulation

AR(1): x_t - mu = phi * (x_(t-1) - mu) + epsilon_t
Stationary mean reversion requires |phi| < 1; half-life is usually meaningful for 0 < phi < 1
AR(1) half-life = ln(0.5) / ln(phi)
Ornstein-Uhlenbeck: dx_t = kappa * (mu - x_t) dt + sigma dW_t ; half-life = ln(2) / kappa, kappa > 0

Worked example

If a monthly AR(1) estimate gives phi = 0.90, the implied half-life is approximately 6.6 months. That statement is conditional on the fitted process being stable. A structural break in trade demand, fleet supply, regulation or financing conditions may shift the long-run mean and make the historical half-life misleading.

Data and calibration

Segment- and size-specific freight indices; second-hand and newbuilding price series; consistent frequency; orderbook and fleet-supply data; trade-demand indicators; fuel prices; interest rates and financing conditions. Structural-break tests and rolling-window estimates should be considered where the series spans different market regimes.

Practical issues and limitations

  • Do not impose mean reversion because shipping is described as cyclical; test the statistical specification and economic plausibility.
  • Avoid estimating half-life from a process that is non-stationary or has an unstable coefficient.
  • Transformations matter: levels, log-levels and returns answer different questions.
  • Parameter uncertainty and regime changes should be carried into forecasts rather than hidden behind a single long-run mean.

How ShipFinance.ai uses this concept

ShipFinance.ai can use mean-reversion models as one candidate scenario generator, compare them with alternative processes, and expose fitted long-run means, persistence, half-life and break diagnostics. The model should be treated as a hypothesis to stress, not as a guaranteed recovery mechanism.

Key takeaways

  • Mean reversion is an empirical modelling assumption, not a law of shipping markets.
  • Half-life is meaningful only under a stable, correctly specified process.
  • Structural breaks and regime changes can dominate historical equilibrium estimates.

Primary methodological and shipping sources