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Long Memory and the Term Structure of Risk


  • Schotman, Peter
  • Tschernig, Rolf
  • Budek, Jan


This paper explores the implications of asset return predictability on long-term portfolio choice when return forecasting variables exhibit long memory. We model long memory using the class of fractionally integrated time series models. Important predictor variables for U.S. data, like the dividend-price ratio and nominal and real interest rates, are non-stationary with orders of integration around 0.8. These time series properties lead to substantial increases of the estimated long-term risk of stocks, bonds and cash compared to earlier estimates obtained from a stationary VAR. Long-term risk increases because the fluctuations in the predictor variables imply that expected returns themselves become a significant source of long-term risk. We find that results are sensitive to the specification of the prediction equation of excess stock returns. The inclusion of the short-term nominal interest rate among the predictor variables has the most profound impact. Jointly with the dividend-price ratio it has significant predictive power, but contrary to the dividend-price ratio the nominal interest rate does not induce mitigating effects through mean reversion.

Suggested Citation

  • Schotman, Peter & Tschernig, Rolf & Budek, Jan, 2008. "Long Memory and the Term Structure of Risk," University of Regensburg Working Papers in Business, Economics and Management Information Systems 427, University of Regensburg, Department of Economics.
  • Handle: RePEc:bay:rdwiwi:5132

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    References listed on IDEAS

    1. Daniel J. Henderson & Christopher F. Parmeter & Subal C. Kumbhakar, 2007. "Nonparametric estimation of a hedonic price function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 695-699.
    2. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    3. Anglin, Paul M & Gencay, Ramazan, 1996. "Semiparametric Estimation of a Hedonic Price Function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 633-648, Nov.-Dec..
    4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    5. Hsiao, Cheng & Li, Qi & Racine, Jeffrey S., 2007. "A consistent model specification test with mixed discrete and continuous data," Journal of Econometrics, Elsevier, vol. 140(2), pages 802-826, October.
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    Cited by:

    1. Christian Rehring & Steffen Sebastian, 2011. "Dynamics of commercial real estate asset markets, return volatility and the investment horizon," Journal of Property Research, Taylor & Francis Journals, vol. 28(4), pages 291-315, June.
    2. Daniela Osterrieder & Peter C. Schotman, 2012. "The Volatility of Long-term Bond Returns: Persistent Interest Shocks and Time-varying Risk Premiums," CREATES Research Papers 2012-35, Department of Economics and Business Economics, Aarhus University.
    3. Ľuboš Pástor & Robert F. Stambaugh, 2012. "Are Stocks Really Less Volatile in the Long Run?," Journal of Finance, American Finance Association, vol. 67(2), pages 431-478, April.
    4. Carlo A. Favero & Andrea Tamoni, 2010. "Demographics and the Econometrics of the Term Structure of Stock Market Risk," Working Papers 367, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    5. Tschernig, Rolf & Weber, Enzo & Weigand, Roland, 2014. "Long- versus medium-run identification in fractionally integrated VAR models," Economics Letters, Elsevier, vol. 122(2), pages 299-302.
    6. Gündüz, Yalin & Kaya, Orcun, 2014. "Impacts of the financial crisis on eurozone sovereign CDS spreads," Journal of International Money and Finance, Elsevier, vol. 49(PB), pages 425-442.
    7. Gil-Alana, Luis A. & Moreno, Antonio, 2012. "Uncovering the US term premium: An alternative route," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 1181-1193.
    8. Daniela Osterrieder, 2013. "Interest Rates with Long Memory: A Generalized Affine Term-Structure Model," CREATES Research Papers 2013-17, Department of Economics and Business Economics, Aarhus University.

    More about this item


    Long-term portfolio choice; Term structure of risk; Linear processes with fractional integration;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models


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