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Robust Asset Allocation For Long-Term Target-Based Investing

Author

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  • P. A. FORSYTH

    (David R. Cheriton School of Computer Science, University of Waterloo, 200 University Avenue West, Waterloo ON, N2L 3G1, Canada)

  • K. R. VETZAL

    (School of Accounting and Finance, University of Waterloo, 200 University Avenue West, Waterloo ON, N2L 3G1, Canada)

Abstract

This paper explores dynamic mean-variance (MV) asset allocation over long horizons. This is equivalent to target-based investing with a quadratic loss penalty for deviations from the target level of terminal wealth. We provide a number of illustrative examples in a setting with a risky stock index and a risk-free asset. Our underlying model is very simple: the value of the risky index is assumed to follow a geometric Brownian motion diffusion process and the risk-free interest rate is specified to be constant. We impose realistic constraints on the leverage ratio and trading frequency. In many of our examples, the MV optimal strategy has a standard deviation of terminal wealth less than half that of a constant proportion strategy which has the same expected value of terminal wealth, while the probability of shortfall is reduced by a factor of two to three. We investigate the robustness of the model through resampling experiments using historical data dating back to 1926. These experiments also show much lower standard deviation and shortfall probability for the MV optimal strategy relative to a constant proportion strategy with approximately the same expected terminal wealth.

Suggested Citation

  • P. A. Forsyth & K. R. Vetzal, 2017. "Robust Asset Allocation For Long-Term Target-Based Investing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-32, May.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:03:n:s0219024917500170
    DOI: 10.1142/S0219024917500170
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    1. Elena Vigna, 2014. "On efficiency of mean--variance based portfolio selection in defined contribution pension schemes," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 237-258, February.
    2. Dang, D.M. & Forsyth, P.A., 2016. "Better than pre-commitment mean-variance portfolio allocation strategies: A semi-self-financing Hamilton–Jacobi–Bellman equation approach," European Journal of Operational Research, Elsevier, vol. 250(3), pages 827-841.
    3. Ledoit, Oliver & Wolf, Michael, 2008. "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 850-859, December.
    4. Cong, F. & Oosterlee, C.W., 2016. "Multi-period mean–variance portfolio optimization based on Monte-Carlo simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 23-38.
    5. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    6. Annaert, Jan & Osselaer, Sofieke Van & Verstraete, Bert, 2009. "Performance evaluation of portfolio insurance strategies using stochastic dominance criteria," Journal of Banking & Finance, Elsevier, vol. 33(2), pages 272-280, February.
    7. Bertrand, Philippe & Prigent, Jean-luc, 2011. "Omega performance measure and portfolio insurance," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1811-1823, July.
    8. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    9. Narayana R. Kocherlakota, 2001. "Looking for evidence of time-inconsistent preferences in asset market data," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 25(Sum), pages 13-24.
    10. Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
    11. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    12. Jean-Luc Prigent & Philippe Bertrand, 2011. "Omega performance measure and portfolio insurance," Post-Print hal-01833064, HAL.
    13. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    14. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    15. Philippe Cogneau & Valeri Zakamouline, 2013. "Block bootstrap methods and the choice of stocks for the long run," Quantitative Finance, Taylor & Francis Journals, vol. 13(9), pages 1443-1457, September.
    16. K. Ko & Zhijian Huang, 2012. "Time-inconsistent risk preferences in a laboratory experiment," Review of Quantitative Finance and Accounting, Springer, vol. 39(4), pages 471-484, November.
    17. Gilles Sanfilippo, 2003. "Stocks, bonds and the investment horizon: a test of time diversification on the French market," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 345-351.
    18. Tomasz R. Bielecki & Hanqing Jin & Stanley R. Pliska & Xun Yu Zhou, 2005. "Continuous‐Time Mean‐Variance Portfolio Selection With Bankruptcy Prohibition," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 213-244, April.
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    Cited by:

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