Design Optimal Annuities

Annuities add welfare for retiring individuals. The design of optimal annuities will be considered and in more detail the interconnection with the optimal portfolio used for financing annuities. With the longevity risk of the aging population the importance of optimal annuities is more apparent than ever. First an optimal portfolio will designed for the stock market in the United States. The default equally weighted portfolio will be compared in detail with the minimum-variance and mean-variance portfolios in terms of the Sharpe ratio and the certainty equivalent return. The length of the rolling window is considered and afterwards it is investigated if bounding portfolio weights increase performance by reducing estimation errors. Fixed, graded and variable annuities based on the optimal portfolio will be solved and compared for different moments of pension in both financial measures and in terms of utility, as well as compared with the case of no annuity at retirement. Monte Carlo simulation will be used for the future. Afterwards it is investigated if deferred annuities add value. Variable annuities are found to outperform other annuities but have very low initial payouts. Graded annuities based on returns turn out to be the only viable option as the optimal design for annuities. The minimum-variance portfolio is found as the optimal portfolio design with a rolling window of 180 months and a bounding portfolio weight of 0.75. Annuities are found to add welfare over no annuity for retirement. Deferred annuities add value. Retirees in the United States are recommended to purchase annuities. Insurance companies should rely on the optimal minimum-variance portfolio with bounding portfolio weights for financing annuities.