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Horizon Length and Portfolio Risk

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Abstract

In this paper, we compare the attitude towards current risk of two expected-utility-maximizing investors who are identical except that the first investor will live longer than the second one. It is often suggested that the young investor should take more risks than the old investor. We consider as a benchmark the case of complete markets with a zero risk-free rate. We show that a necessary and sufficient condition to assure that younger is riskier is that the Arrow-Pratt index of absolute tolerance (T) be convex. If we allow for a positive risk-free rate, the necessary and sufficient condition is T convex, plus T(0) = 0. It extends the well-known result that rational investors can behave myopically if and only if the utility function exhibits constant relative risk aversion.

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Authors and Affiliations

  1. Université de Toulouse, GREMAQ and IDEI, Place Anatole France, F-31042, Toulouse Cedex, France

    Christian Gollier

  2. Kennedy School of Government, Harvard University, Cambridge, MA, 02138, USA

    Richard J. Zeckhauser

Authors
  1. Christian Gollier
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  2. Richard J. Zeckhauser
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Correspondence to Christian Gollier.

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Gollier, C., Zeckhauser, R.J. Horizon Length and Portfolio Risk. Journal of Risk and Uncertainty 24, 195–212 (2002). https://doi.org/10.1023/A:1015697417916

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  • DOI: https://doi.org/10.1023/A:1015697417916

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