Paper: arXiv 2411.13565

Authors: John Armstrong, James Dalby, Catherine Donnelly

Abstract

We evaluate the performance and level of intergenerational cross-subsidy in flat-accrual and dynamic-accrual collective defined contribution (CDC) schemes which have been designed to be compatible with UK legislation. In the flat-accrual scheme, all members accrue the benefits at the same rate irrespective of age. This captures the most significant feature of the Royal Mail Collective Pension Plan, which is currently the only UK CDC scheme. The dynamic-accrual schemes seeks to reduce intergenerational cross-subsidies by varying the rate of benefit-accrual in accordance to the age of members and the current funding level. We find that these CDC schemes can often be successful in smoothing pension outcomes post-retirement while outperforming a defined contribution scheme followed by annuity purchase at the point of retirement. However, this out-performance is not guaranteed in a flat-accrual scheme and there is little smoothing of projected pension outcomes before retirement. There are significant intergenerational cross-subsidies in the flat-accrual scheme. These qualitatively mirror the cross-subsidies seen in existing defined benefit schemes, but we find the magnitude of the cross-subsidies is much larger in flat accrual CDC schemes. The dynamic-accrual scheme design is intended to reduce such cross-subsidies, but we find they still arise due to the approximate pricing methodology used to determine the benefits accrued by each contribution. Although the cross-subsidies tend to cancel out over time, in any given year they can be large. Thus, the benefits accrued by contributions should be calculated rigorously to reduce cross-subsidies.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a rigorous mathematical and stochastic modeling framework for newly legal UK Collective Defined Contribution (CDC) pension schemes. It provides valuable insights into intergenerational cross-subsidies using both analytical constant-economic models and stochastic Black-Scholes risk-neutral pricing frameworks.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate Performance & Intergenerational Cross-Subsidies in UK CDC Schemes] --> B[Scheme Design & Inputs: Flat-Accrual vs. Dynamic-Accrual Models]
    B --> C[Simulation & Methodology: Model Accrual Rates, Funding Levels & Retirement Smoothing vs. Individual DC/Annuity]
    C --> D[Outcome 1: Performance & Smoothing]
    C --> E[Outcome 2: Intergenerational Cross-Subsidies]
    
    D --> F[CDC generally outperforms DC + Annuity & smoothes post-retirement income, but pre-retirement smoothing is limited]
    E --> G[Flat-Accrual creates very large cross-subsidies; Dynamic-Accrual reduces them overall, but year-to-year fluctuations remain due to approximate pricing]