Asset Allocation Via The Conditional First Exit Time or How To Avoid Outliving Your Money

  • MOSHE ARYE Milevsky
  • KWOK Ho
  • CHRIS Robinson


The risk of outliving your money (or shortfall) with low risk, low return investments is very often more serious than the risk of losing money on high risk investments, until quite late in life. A stochastic process model incorporating mortality tables for men and women of retirement age, random rates of return and fixed initial wealth and desired level of consumption provides the analytical tool. A simulation using Canadian mortality tables and rates of return shows that almost all retirees should invest some of their wealth in equity, and for many the optimal allocation is 70–100% equity. The risk of shortfall is surprisingly high for a reasonable range of values of the variables, especially for an allocation of 100% in treasury bills. Women face much greater risk of shortfall than men. The analytical model also permits calculation of the distribution of the bequest and hence allows an individual to trade off changes in shortfall risk against changes in the expected bequest to the heirs.

asset allocation shortfall risk retirement planning 


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  1. Benari, Yoav, “Optimal asset mix and itslink to changing fundamental factors.” The Journal of Portfolio Management 11–18, (Winter 1990).Google Scholar
  2. Butler, Kirt, andDale Domian, “Risk, diversification, and the investment horizon.” The Journal of Portfolio Management 41–47, (Spring 1991).Google Scholar
  3. Butler, Kirt, and Dale Domian, #x201C;Long-Run Returns on Stock and bond Portfolios: Implications for Retirement Planning.” Financial Services Review 2(1), 41–50, (1992/93).CrossRefGoogle Scholar
  4. Crow, E.L., and K. Shimizu, Lognormal Distributions. Marcel Dekker Inc., 1985.Google Scholar
  5. Grauer, R., and Nils Hakansson, “Higher Return,Lower risk: Historical Returns on Long-Run, Actively-Managed Portfolios of Stocks, Bonds and Bills, 1936–1978.” Financial Analysts Journal 39–53, March–April 1982).Google Scholar
  6. Ho, K., and C. Robinson, Personal Financial Planning. Captus Press, 1996.Google Scholar
  7. Ho, K., M. A. Milevsky, and C. Robinson, “AssetAllocation, Life Expectancy and Shortfall.” Financial Services Review 3(2), 109–26, (1994).CrossRefGoogle Scholar
  8. ”Life Tables,Canada and Provinces 1985–87” Health Reports Supplement Statistics Canada (Can1 CS8.5 82–003S, No. 13) No. 13, Vol. 2, No. 4, 1990.Google Scholar
  9. Leibowitz, M., and Stanley Kogelman, #x201C;Asset allocation under shortfall constraints.” The Journal of Portfolio Management 18–23, (Winter 1991).Google Scholar
  10. Lloyd, W., and Naval Modani, “Stocks, bonds, billsand time diversification.” The Journal of Portfolio Management 7–11, (Spring 1983).Google Scholar
  11. Malkiel, B.G., ARandom Walk Down Wall Street. W. W. Norton & Co., 1990.Google Scholar
  12. Ross, S., R. Westerfield, B. Jordan, and G. Roberts,Fundamentals of Corporate Finance. Irwin, 1993.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • MOSHE ARYE Milevsky
    • 1
  • KWOK Ho
    • 2
  • CHRIS Robinson
    • 1
  1. 1.Schulich School of BusinessYork UniversityUSA
  2. 2.Atkinson College, York UniversityUSA

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