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Adjusted Money's Worth Ratios in Life Annuities

  • Jaime Casassus
  • Eduardo Walker

The Money's Worth Ratio (MWR) measures an annuity's actuarial fairness. It is calculated as the discounted present value of expected future payments divided by its cost. We argue that from the perspective of annuitants, this measure may overestimate the value-for-money obtained, since it does not adjust for liquidity or risk factors. Measuring these factors is challenging, requiring detailed knowledge of assets, liabilities, and of the stochastic processes followed by them. Using a multi-factor continuous-time model, we propose a simple solution for an adjusted MWR (AMWR), which does consider illiquidity and default risk. We implement this solution for the competitive Chilean annuity market, which offers MWRs above 1, finding that indeed these ratios are biased upward 7 percent on average. We also present estimates of default option values, asset insufficiency probabilities and implied credit spreads for each annuity provider.

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Paper provided by Instituto de Economia. Pontificia Universidad Católica de Chile. in its series Documentos de Trabajo with number 434.

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Date of creation: 2013
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Handle: RePEc:ioe:doctra:434
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  1. Walker, Eduardo, 2009. "Los mercados de las rentas vitalicias en Chile. Competencia, regulación, ¿y miopía?," El Trimestre Económico, Fondo de Cultura Económica, vol. 0(301), pages 145-179, enero-mar.
  2. Thorburn, Craig & Rocha, Roberto & Morales, Marco, 2006. "An analysis of money's worth ratios in Chile," Policy Research Working Paper Series 3926, The World Bank.
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  13. Pierre Collin-Dufresne, 2001. "Do Credit Spreads Reflect Stationary Leverage Ratios?," Journal of Finance, American Finance Association, vol. 56(5), pages 1929-1957, October.
  14. Suzanne Doyle & Olivia S. Mitchell & John Piggott, 2004. "Annuity Values in Defined Contribution Retirement Systems: Australia and Singapore Compared," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 37(4), pages 402-416, December.
  15. Briys, Eric & de Varenne, François, 1997. "Valuing Risky Fixed Rate Debt: An Extension," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(02), pages 239-248, June.
  16. Rocha, Roberto & Morales, Marco & Thorburn, Craig, 2008. "An empirical analysis of the annuity rate in Chile," Journal of Pension Economics and Finance, Cambridge University Press, vol. 7(01), pages 95-119, March.
  17. Jaime Casassus & Pierre Collin-Dufresne, 2005. "Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates," Journal of Finance, American Finance Association, vol. 60(5), pages 2283-2331, October.
  18. Longstaff, Francis A & Schwartz, Eduardo S, 1995. " A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
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