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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.

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Bibliographic Info

Paper provided by Copenhagen Business School, Department of Finance in its series Working Papers with number 2000-9.

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Length: 42 pages
Date of creation: 01 May 2001
Date of revision:
Handle: RePEc:hhs:cbsfin:2000_009

Contact details of provider:
Postal: Department of Finance, Copenhagen Business School, Solbjerg Plads 3, A5, DK-2000 Frederiksberg, Denmark
Phone: +45 3815 3815
Email:
Web page: http://www.cbs.dk/departments/finance/
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Keywords: Investment; Strategies;

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References

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  1. Viceira, Luis & Campbell, John, 2001. "Who Should Buy Long-Term Bonds?," Scholarly Articles 3128709, Harvard University Department of Economics.
  2. Brown, Stephen J & Goetzmann, William N & Ross, Stephen A, 1995. " Survival," Journal of Finance, American Finance Association, vol. 50(3), pages 853-73, July.
  3. John Y. Campbell, 1985. "Stock Returns and the Term Structure," NBER Working Papers 1626, National Bureau of Economic Research, Inc.
  4. 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.
  5. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  6. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237.
  7. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
  8. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, 06.
  9. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  10. 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.
  11. 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.
  12. 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.
  13. 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 247-57, August.
  14. 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.
  15. 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.
  16. Robert J. Shiller & Andrea E. Beltratti, 1990. "Stock Prices and Bond Yields: Can Their Comovements Be Explained in Terms of Present Value Models?," NBER Working Papers 3464, National Bureau of Economic Research, Inc.
  17. 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.
  18. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  19. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312.
  20. 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.
  21. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-09, March.
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Citations

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Cited by:
  1. Muck, Matthias, 2010. "Trading strategies with partial access to the derivatives market," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1288-1298, June.
  2. 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.
  3. Paolo Guasoni & Scott Robertson, 2012. "Portfolios and risk premia for the long run," Papers 1203.1399, arXiv.org.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  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. 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.

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