Valuing variable annuities with guaranteed minimum lifetime withdrawal benefits |
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| Institution: | 1. School of Risk Management, Insurance, and Actuarial Science, St. John’s University, United States;2. Insurance/Risk Management & Business Economics/Policy, University of Pennsylvania - The Wharton School, United States;1. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1;2. Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, Canada, H3G 1M8;1. Schulich School of Business, York University, Canada;2. IFID Centre, Canada;3. Department of Mathematics and Statistics, York University, Canada;1. School of Finance and Statistics, East China Normal University, Shanghai, 200241, China;2. School of Risk and Actuarial Studies and CEPAR, UNSW Business School, The University of New South Wales, Sydney, NSW 2052, Australia;3. Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia;1. Department of Finance and Insurance, Lingnan University, 8 Castle Peak Road, Tuen Mun, Hong Kong;2. Department of Risk Management and Insurance, Georgia State University, 35 Broad Street (11th Floor), Atlanta, GA 30309, USA;1. School of Business, Stevens Institute of Technology, Babbio Center, 1 Castle Point on Hudson, Hoboken, NJ 07310, USA;2. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30318, USA;3. Department of Mathematics, Marist College, 3399 North Road, Poughkeepsie, NY 12601, USA |
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| Abstract: | Variable annuities with guaranteed minimum lifetime withdrawal benefits (VA/GLWB) offer retirees longevity protection, exposure to equity markets, and access to flexible withdrawals in emergencies. We model how risk-averse retirees optimally withdraw from the products, balancing returns and the embedded longevity protection. Assuming reasonable individual preferences, the resulting cash flow generates a Money’s Worth Ratio of around 0.9 for our stylized VA/GLWB in the post-crisis product, considerably lower than what was offered prior to 2008. Sensitivity analyses with respect to portfolio choice, mortality, fees, and guaranteed withdrawal rates show that MWRs range from 0.80 to 1.0, with the portfolio choice making the biggest difference. For most parameter choices, the utility value of the VA/GLWB exceeds that of a similar mutual fund, but it is less than for a fixed annuity. Interestingly, VA/GLWB withdrawals in early retirement can optimally exceed contract maximum withdrawals, despite the fact that this reduces future withdrawal guarantees. |
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| Keywords: | Annuity Guarantee Lifetime income Life cycle model Portfolio allocation Longevity protection |
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