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Autocorrelated Returns and Optimal Intertemporal Portfolio Choice

Author

Listed:
  • Ronald J. Balvers

    (Department of Economics, West Virginia University, Morgantown, West Virginia 26506-6025)

  • Douglas W. Mitchell

    (Department of Economics, West Virginia University, Morgantown, West Virginia 26506-6025)

Abstract

In recent years it has been shown empirically that stock returns exhibit positive or negative autocorrelation, depending on observation frequency. In this context of autocorrelated returns the present paper is the first to derive an explicit analytical solution to the dynamic portfolio problem of an individual agent saving for retirement (or other change of status, like the purchase of a house or starting college). Using a normal ARMA(1,1) process, dynamic programming techniques combined with the use of Stein's Lemma are employed to examine "dollar-cost-averaging" and "age effects" in intertemporal portfolio choice with CARA preferences. We show that with a positive moving average parameter and positive riskfree rates, if first-order serial correlation is nonnegative, then the expected value of the optimal risky investment is increasing over time, while if first-order serial correlation is negative this path can be increasing or decreasing over time. Thus a necessary but not sufficient condition to obtain the conventional age effect of increasing conservatism over time is that first-order serial correlation be negative. Further, dollar-cost averaging in the general sense of gradual entry into the risky asset does not emerge as an optimal policy. Simulation results for U.S. data are used to illustrate optimal portfolio paths.

Suggested Citation

  • Ronald J. Balvers & Douglas W. Mitchell, 1997. "Autocorrelated Returns and Optimal Intertemporal Portfolio Choice," Management Science, INFORMS, vol. 43(11), pages 1537-1551, November.
    • Handle: RePEc:inm:ormnsc:v:43:y:1997:i:11:p:1537-1551
    DOI: 10.1287/mnsc.43.11.1537
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    Citations

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    Cited by:

    1. Shubhangi Sikaria & Rituparna Sen & Neelesh S. Upadhye, 2019. "Bayesian Filtering for Multi-period Mean-Variance Portfolio Selection," Papers 1911.07526, arXiv.org, revised Aug 2020.
    2. Alois Geyer & Michael Hanke & Alex Weissensteiner, 2009. "A stochastic programming approach for multi-period portfolio optimization," Computational Management Science, Springer, vol. 6(2), pages 187-208, May.
    3. Dirk Ulbricht, 2014. "John Doe's Old-Age Provision: Dollar Cost Averaging and Time Diversification," Discussion Papers of DIW Berlin 1376, DIW Berlin, German Institute for Economic Research.
    4. Wu, Hui & Ma, Chaoqun & Yue, Shengjie, 2017. "Momentum in strategic asset allocation," International Review of Economics & Finance, Elsevier, vol. 47(C), pages 115-127.
    5. Anna Battauz & Alessandro Sbuelz, 2018. "Non†myopic portfolio choice with unpredictable returns: The jump†to†default case," European Financial Management, European Financial Management Association, vol. 24(2), pages 192-208, March.
    6. Balvers, Ronald J. & Mitchell, Douglas W., 2000. "Efficient gradualism in intertemporal portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 24(1), pages 21-38, January.
    7. Mitchell, Douglas W., 2001. "Effects of decision interval on optimal intertemporal portfolios with serially correlated returns," The Quarterly Review of Economics and Finance, Elsevier, vol. 41(3), pages 427-438.
    8. Dirk Ulbricht, 2013. "Stock Investments for Old-Age: Less Return, More Risk, and Unexpected Timing," Discussion Papers of DIW Berlin 1324, DIW Berlin, German Institute for Economic Research.
    9. Ralph S. J. Koijen & Juan Carlos Rodríguez & Alessandro Sbuelz, 2009. "Momentum and Mean Reversion in Strategic Asset Allocation," Management Science, INFORMS, vol. 55(7), pages 1199-1213, July.
    10. Balvers, Ronald & Wu, Yangru, 2010. "Optimal transaction filters under transitory trading opportunities: Theory and empirical illustration," Journal of Financial Markets, Elsevier, vol. 13(1), pages 129-156, February.

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