Time Diversification, Safety-First and Risk

  • Moshe Arye Milevsky
Article

Abstract

The purpose of this article is to demonstrate the effect of investment time horizon on the choice of risky assets in a portfolio when the investor in question is optimizing a Safety-First (downside risk-aversion) utility function. It is shown, under standard assumptions, that although shortfall risk decreases exponentially with investment time horizon, the portfolio asset allocation proportions remain invariant. In fact, in some instances, the optimal allocation will not even depend on the drift of the underlying assets. Thus, we extend the classical results of Samuelson and Merton, derived under conventional utility assumptions, to an individual optimizing an A.D. Roy Safety-First objective; a discontinuous utility function that has been extolled as conforming to observed investor behaviour. A numerical example is provided.

Asset allocation investment 

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References

  1. Butler, K.C. and D.L. Domian, “Risk, Diversification and the Investment Horizon.” Journal of Portfolio Management 17, 41–48, (1991).Google Scholar
  2. Butler, K.C. and D.L. Domian, “Long-run returns on Stock and Bond Portfolios: Implications for Retirement Planning.” Financial Services Review 2(1), 41–49, (1993).Google Scholar
  3. Gunthorpe, D. and H. Levy, “Portfolio Composition and the Investment Horizon.” Financial Analysts Journal51–56, (1994).Google Scholar
  4. Kritzman, M., “What Practitioners Need To Know About Time Diversification.” Financial Analysts Journal 14–18, (1994).Google Scholar
  5. Hull, J.C. Options, Futures and other Derivative Securities 2nd Edition, Prentice Hall, New Jersey, (1993).Google Scholar
  6. Marshall, J.F., “The Role of the Investment Horizon in Optimal Portfolio Sequencing.” The Financial Review 29(4), 557–576, (1994).Google Scholar
  7. McEnally, R.W., “Time Diversification: Surest Way to Lower Risk?” Journal of Portfolio Management 11, 24–26, (1985).Google Scholar
  8. Merton, Robert C., “Optimum Consumption and Portfolio Rules in a Continuous Time Model” Journal of Economic Theory 3, 373–413, (1971).Google Scholar
  9. Milevsky, M.A., K. Ho and C. Robinson, “Asset Allocation via the Conditional First Exit Time or How To Avoid Outliving Your Money.” Review of Quantitative Finance and Accounting 9(1), (1997).Google Scholar
  10. Roy, A.D., “Safety-First and the Holding of Assets.” Econometrica 20(3), 431–449, (1952).Google Scholar
  11. Samuelson, Paul C., “Lifetime Portfolio Selection by Dynamic Stochastic Programming.” Review of Economic and Statistics 51, 239–246, (1969).Google Scholar

Copyright information

© 1999 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. 1999

Authors and Affiliations

  • Moshe Arye Milevsky
    • 1
  1. 1.Schulich School of BusinessYork UniversityNorth YorkCanada

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