Longevity Risk

Adaptive Strategies for Pension Fund Management ArXiv ID: 2508.13350 “View on arXiv” Authors: Raphael Chinchilla, Thomas D. Rueter, Timothy R. McDade, Peter R. Fisher, Emmanuel Candes, Trevor Hastie, Stephen Boyd Abstract This paper proposes a simulation-based framework for assessing and improving the performance of a pension fund management scheme. This framework is modular and allows the definition of customized performance metrics that are used to assess and iteratively improve asset and liability management policies. We illustrate our framework with a simple implementation that showcases the power of including adaptable features. We show that it is possible to dissipate longevity and volatility risks by permitting adaptability in asset allocation and payout levels. The numerical results show that by including a small amount of flexibility, there can be a substantial reduction in the cost to run the pension plan as well as a substantial decrease in the probability of defaulting. ...

A 4% withdrawal rate for American retirement spending, derived from a discrete-time model of stochastic returns on assets and their sample moments ArXiv ID: 2508.10273 “View on arXiv” Authors: Drew M. Thomas Abstract What grounds the rule of thumb that a(n American) retiree can safely withdraw 4% of their initial retirement wealth in their first year of retirement, then increase that rate of consumption with inflation? I address that question with a discrete-time model of returns to a retirement portfolio consumed at a rate that grows by $s$ per period. The model’s key parameter is $γ$, an $s$-adjusted rate of return to wealth, derived from the first 2-4 moments of the portfolio’s probability distribution of returns; for a retirement lasting $t$ periods the model recommends a rate of consumption of $γ/ (1 - (1 - γ)^t)$. Estimation of $γ$ (and hence of the implied rate of spending in retirement) reveals that the 4% rule emerges from adjusting high expected rates of return down for: consumption growth, the variance in (and kurtosis of) returns to wealth, the longevity risk of a retiree potentially underestimating $t$, and the inclusion of bonds in retirement portfolios without leverage. The model supports leverage of retirement portfolios dominated by the S&P 500, with leverage ratios $> 1.6$ having been historically optimal under the model’s approximations. Historical simulations of 30-year retirements suggest that the model proposes withdrawal rates having roughly even odds of success, that leverage greatly improves those odds for stocks-heavy portfolios, and that investing on margin could have allowed safe withdrawal rates $> 6$% per year. ...

Optimal mutual insurance against systematic longevity risk ArXiv ID: 2410.07749 “View on arXiv” Authors: Unknown Abstract We mathematically demonstrate how and what it means for two collective pension funds to mutually insure one another against systematic longevity risk. The key equation that facilitates the exchange of insurance is a market clearing condition. This enables an insurance market to be established even if the two funds face the same mortality risk, so long as they have different risk preferences. Provided the preferences of the two funds are not too dissimilar, insurance provides little benefit, implying the base scheme is effectively optimal. When preferences vary significantly, insurance can be beneficial. ...