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Optimal Consumption and Investment Strategies with Stochastic Interest Rates

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  • Sørensen, Carsten

    (Department of Finance, Copenhagen Business School)

  • Munk, Claus

    (Dept. of Accounting, Finance & Law, SDU - Odense University)

Abstract

We study the consumption and investment choice of a time-additive power utility investor and demonstrate how theinvestor should optimally hedge changes in the op- portunity set. The investor is allowed to invest in stocks and interest rate dependent assets in a continuous-time dynamically complete market. In particular, we demon- strate that under stochastic interest rates the investor optimally hedges changes in the term structure of interest rates by investing in acoupon bond, or portfolio of bonds, with a payment schedule that matches the forward-expected (i.e certainty equivalent) consumption pattern. This is of conceptual importance since the hedge portfolio does not depend on the speci c term structure dynamics (only through the consequences for the optimal consumption pattern). We consider two explicit examples where the dynamics of the term structure of interest rates are given by theVasicek-model and a three-factor non-Markovian Heath-Jarrow-Morton model.

Suggested Citation

  • Sørensen, Carsten & Munk, Claus, 2001. "Optimal Consumption and Investment Strategies with Stochastic Interest Rates," Working Papers 2000-9, Copenhagen Business School, Department of Finance.
  • Handle: RePEc:hhs:cbsfin:2000_009
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    File URL: http://openarchive.cbs.dk/cbsweb/handle/10398/7175
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    References listed on IDEAS

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    1. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Sørensen, Carsten, 1999. "Dynamic Asset Allocation and Fixed Income Management," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 513-531, December.
    4. Shiller, Robert J. & Beltratti, Andrea E., 1992. "Stock prices and bond yields : Can their comovements be explained in terms of present value models?," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 25-46, October.
    5. 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(01), pages 63-91, March.
    6. Brown, Stephen J & Goetzmann, William N & Ross, Stephen A, 1995. " Survival," Journal of Finance, American Finance Association, vol. 50(3), pages 853-873, July.
    7. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    8. Kaushik I. Amin & Robert A. Jarrow, 2008. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 15, pages 327-347 World Scientific Publishing Co. Pte. Ltd..
    9. 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.
    10. Fama, Eugene F. & French, Kenneth R., 1989. "Business conditions and expected returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 25(1), pages 23-49, November.
    11. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    12. 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: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    13. LuisM. Viceira & John Y. Campbell, 2001. "Who Should Buy Long-Term Bonds?," American Economic Review, American Economic Association, vol. 91(1), pages 99-127, March.
    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. 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.
    16. Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283.
    17. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    18. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    19. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    20. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, June.
    21. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312.
    22. Cox, John C. & Huang, Chi-fu, 1991. "A variational problem arising in financial economics," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 465-487.
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    Cited by:

    1. Maj-Britt Nordfang & Mogens Steffensen, 2017. "Portfolio Optimization and Mortgage Choice," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 10(1), pages 1-21, January.
    2. Konermann, Patrick & Meinerding, Christoph & Sedova, Olga, 2013. "Asset allocation in markets with contagion: The interplay between volatilities, jump intensities, and correlations," Review of Financial Economics, Elsevier, vol. 22(1), pages 36-46.
    3. Zhou, Y., 2014. "Essays on habit formation and inflation hedging," Other publications TiSEM 4886da12-1b84-4fd9-aa07-3, Tilburg University, School of Economics and Management.
    4. Muck, Matthias, 2010. "Trading strategies with partial access to the derivatives market," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1288-1298, June.
    5. Munk, Claus, 2008. "Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3560-3589, November.
    6. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 32.
    7. Jakub Trybu{l}a & Dariusz Zawisza, 2014. "Continuous time portfolio choice under monotone preferences with quadratic penalty - stochastic interest rate case," Papers 1404.5408, arXiv.org.
    8. Branger, Nicole & Mahayni, Antje & Schneider, Judith C., 2010. "On the optimal design of insurance contracts with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 485-492, June.
    9. Yao, Haixiang & Li, Zhongfei & Li, Duan, 2016. "Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability," European Journal of Operational Research, Elsevier, vol. 252(3), pages 837-851.
    10. Claus Munk & Alexey Rubtsov, 2014. "Portfolio management with stochastic interest rates and inflation ambiguity," Annals of Finance, Springer, vol. 10(3), pages 419-455, August.
    11. Larsen, Linda Sandris, 2010. "Optimal investment strategies in an international economy with stochastic interest rates," International Review of Economics & Finance, Elsevier, vol. 19(1), pages 145-165, January.
    12. Christian Flor & Linda Larsen, 2014. "Robust portfolio choice with stochastic interest rates," Annals of Finance, Springer, vol. 10(2), pages 243-265, May.
    13. Larsen, Linda Sandris & Munk, Claus, 2012. "The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts," Journal of Economic Dynamics and Control, Elsevier, vol. 36(2), pages 266-293.
    14. Paolo Guasoni & Scott Robertson, 2012. "Portfolios and risk premia for the long run," Papers 1203.1399, arXiv.org.
    15. Sami Attaoui & Pierre Six, 2014. "Hedging demand and the certainty equivalent of wealth," Economics Bulletin, AccessEcon, vol. 34(3), pages 1742-1750.
    16. Mellios, Constantin & Six, Pierre & Lai, Anh Ngoc, 2016. "Dynamic speculation and hedging in commodity futures markets with a stochastic convenience yield," European Journal of Operational Research, Elsevier, vol. 250(2), pages 493-504.
    17. Branger, Nicole & Kraft, Holger & Meinerding, Christoph, 2009. "What is the impact of stock market contagion on an investor's portfolio choice?," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 94-112, August.
    18. Chang, Hao & Chang, Kai, 2017. "Optimal consumption–investment strategy under the Vasicek model: HARA utility and Legendre transform," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 215-227.
    19. Branger, Nicole & Hansis, Alexandra, 2015. "Earning the right premium on the right factor in portfolio planning," Journal of Banking & Finance, Elsevier, vol. 59(C), pages 367-383.
    20. Escobar, Marcos & Ferrando, Sebastian & Rubtsov, Alexey, 2016. "Portfolio choice with stochastic interest rates and learning about stock return predictability," International Review of Economics & Finance, Elsevier, vol. 41(C), pages 347-370.
    21. Munk, Claus & Sørensen, Carsten, 2010. "Dynamic asset allocation with stochastic income and interest rates," Journal of Financial Economics, Elsevier, vol. 96(3), pages 433-462, June.
    22. Chen, An & Vellekoop, Michel, 2017. "Optimal investment and consumption when allowing terminal debt," European Journal of Operational Research, Elsevier, vol. 258(1), pages 385-397.
    23. Lioui, Abraham, 2007. "The asset allocation puzzle is still a puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1185-1216, April.
    24. Chen, An & Pelsser, Antoon & Vellekoop, Michel, 2011. "Modeling non-monotone risk aversion using SAHARA utility functions," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2075-2092, September.

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    Keywords

    Investment; Strategies;

    JEL classification:

    • A00 - General Economics and Teaching - - General - - - General

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