A CPT-Based Comparison of Retirement Products

Abstract

We compare a variety of retirement products under cumulative prospect theory (CPT), including both well-known (variable) annuity products and some innovative, tontine-like retirement products, in which longevity risks are shared between insurers and policyholders. Following Hu and Scott (2007), an agent determines the overall CPT value by evaluating the total discounted payoffs over time compared to the initial investment made. Regarding the mortality-linked products, we find that tontines are widely preferred to annuities, tontines with guarantees and portfolios of annuities and tontines. Only in a few special cases, annuities deliver the highest CPT value. The reasons for the relative superiority of tontines is the presence of safety loadings or subjective mortality beliefs. Including financial market risk, variable annuities are found to be the most attractive source of retirement income under the majority of parameters considered. In some exceptional cases with safety loadings and some guarantee constraints, tontines with minimum guarantees can outperform variable annuities. Our results suggest that agents with CPT preferences prefer risk-carrying products with potentially higher returns to guaranteed annuities, providing alternatives to agents who are not fond of purchasing annuities.