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A Diffusion Model for Long-Term Optimization in the Presence of Stochastic Interest and Inflation Rates

Author

Listed:
  • Farid Mkaouar

    (Ecole Nationale d’Assurance (Enass))

  • Jean-Luc Prigent

    (Université de Cergy-Pontoise (THEMA) and Labex MME-DII)

  • Ilyes Abid

    (Institut Supérieur de Commerce de Paris)

Abstract

We consider the long term portfolio management problem, under stochastic rates and inflation risk. Five basic financial assets are considered: a money market account (the cash), an inflation-protected cash, a financial stock index and two different bonds with constant maturity. The first one corresponds to a nominal bond while the second one is an inflation-indexed bond. We consider constant maturation bonds, which allows to obtain a bond/stock ratio increasing with time (when there exists no inflation). This nice property is in accordance with popular advice. In this framework, we provide the general solution of the expected utility maximization. This intertemporal optimization problem is solved by using the martingale approach. We detail in particular the CRRA case. We determine also the optimal portfolio weights and analyze the solutions. We show in particular that the weight invested on the inflation-indexed bond increases with the relative risk aversion and also when the time horizon increases, which corresponds to a stronger demand for inflation hedging for longer maturities. Such feature illustrates the importance of introducing inflation-indexed bonds on financial markets.

Suggested Citation

  • Farid Mkaouar & Jean-Luc Prigent & Ilyes Abid, 2019. "A Diffusion Model for Long-Term Optimization in the Presence of Stochastic Interest and Inflation Rates," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 367-417, June.
    • Handle: RePEc:kap:compec:v:54:y:2019:i:1:d:10.1007_s10614-017-9742-0
    DOI: 10.1007/s10614-017-9742-0
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    as
    1. Darrell Duffie & Chi-Fu Huang, 2005. "Implementing Arrow-Debreu Equilibria By Continuous Trading Of Few Long-Lived Securities," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 4, pages 97-127, World Scientific Publishing Co. Pte. Ltd..
    2. Marie Brière & Ombretta Signori, 2012. "Inflation-Hedging Portfolios : Economic Regimes Matter," Post-Print hal-01494498, HAL.
    3. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1981. "A Re-examination of Traditional Hypotheses about the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 36(4), pages 769-799, September.
    4. Isabelle Bajeux-Besnainou & James V. Jordan & Roland Portait, 2001. "An Asset Allocation Puzzle: Comment," American Economic Review, American Economic Association, vol. 91(4), pages 1170-1179, September.
    5. LeRoy, Stephen F, 1984. "Nominal Prices and Interest Rates in General Equilibrium: Endowment Shocks," The Journal of Business, University of Chicago Press, vol. 57(2), pages 197-213, April.
    6. Cartea, Álvaro & Saúl, Jonatan & Toro, Juan, 2012. "Optimal portfolio choice in real terms: Measuring the benefits of TIPS," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 721-740.
    7. Canner, Niko & Mankiw, N Gregory & Weil, David N, 1997. "An Asset Allocation Puzzle," American Economic Review, American Economic Association, vol. 87(1), pages 181-191, March.
    8. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    9. Marie Briere & Ombretta Signori, 2012. "Inflation-hedging portfolios: Economic regimes matter," ULB Institutional Repository 2013/253373, ULB -- Universite Libre de Bruxelles.
    10. LeRoy, Stephen F, 1984. "Nominal Prices and Interest Rates in General Equilibrium: Money Shocks," The Journal of Business, University of Chicago Press, vol. 57(2), pages 177-195, April.
    11. Jules Binsbergen & Michael Brandt, 2007. "Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function?," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 355-367, May.
    12. Carl Chiarella & Chih-Ying Hsiao & Willi Semmler, 2007. "Intertemporal Investment Strategies Under Inflation Risk," Research Paper Series 192, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Nicole El Karoui & Monique Jeanblanc-Picqué, 1998. "Optimization of consumption with labor income," Finance and Stochastics, Springer, vol. 2(4), pages 409-440.
    14. 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.
    15. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, June.
    16. Lioui, Abraham & Poncet, Patrice, 2001. "On optimal portfolio choice under stochastic interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1841-1865, November.
    17. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    18. André Palma & Jean-Luc Prigent, 2009. "Standardized versus customized portfolio: a compensating variation approach," Annals of Operations Research, Springer, vol. 165(1), pages 161-185, January.
    19. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    20. Wachter, Jessica A., 2002. "Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(1), pages 63-91, March.
    21. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    22. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    23. Michael J. Brennan & Yihong Xia, 2000. "Stochastic Interest Rates and the Bond-Stock Mix," Review of Finance, European Finance Association, vol. 4(2), pages 197-210.
    24. repec:dau:papers:123456789/9296 is not listed on IDEAS
    25. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    26. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    27. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    28. Benninga, Simon & Protopapadakis, Aris, 1983. "Real and Nominal Interest Rates under Uncertainty: The Fisher Theorem and the Term Structure," Journal of Political Economy, University of Chicago Press, vol. 91(5), pages 856-867, October.
    29. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
    30. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    31. Cvitanic, Jaksa & Goukasian, Levon & Zapatero, Fernando, 2003. "Monte Carlo computation of optimal portfolios in complete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 971-986, April.
    32. Wachter, Jessica A., 2003. "Risk aversion and allocation to long-term bonds," Journal of Economic Theory, Elsevier, vol. 112(2), pages 325-333, October.
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    More about this item

    Keywords

    Portfolio optimization; Stochastic interest rate; Stochastic inflation; Inflation-indexed bonds;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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