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Optimal Portfolio Decision Rule Under Nonparametric Characterization of the Interest Rate Dynamics

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  • James J. Kung

    (Ming Chuan University)

Abstract

This study develops an optimal portfolio decision rule under nonparametric characterization of the interest rate dynamics. To proceed, we first derive an optimal decision rule based on the long rate and the spread (where $\mathrm{spread} = \mathrm{long\ rate} - \mathrm{short\ rate}$ ); then we employ nonparametric kernel regression to estimate, based on the Nadaraya–Watson (N–W) estimators, the parameters related to the two variables; and finally, using the N–W estimates as inputs, we implement our decision rule by the explicit finite difference scheme to find specifically the optimal allocation of wealth between short and long bonds for an investor with power utility at each time over a ten-year horizon. The following four stylized facts can be observed from our results: (i) the optimal fractions in short bond do not appear to vary with the short rate; (ii) the optimal fractions decrease as the long rate rises and increase as it falls; (iii) the optimal fractions increase as the horizon becomes shorter; and (iv) the optimal fractions generally decrease in the early part of the horizon for more risk-averse investor.

Suggested Citation

  • James J. Kung, 2014. "Optimal Portfolio Decision Rule Under Nonparametric Characterization of the Interest Rate Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 225-238, April.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:1:d:10.1007_s10957-013-0298-4
    DOI: 10.1007/s10957-013-0298-4
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    1. 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..
    2. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
    3. Brennan, Michael J. & Schwartz, Eduardo S. & Lagnado, Ronald, 1997. "Strategic asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1377-1403, June.
    4. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    5. 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.
    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    7. Michael Taksar & Michael J. Klass & David Assaf, 1988. "A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 277-294, May.
    8. Stanton, Richard, 1997. "A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
    9. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    10. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    11. Brennan, Michael J. & Schwartz, Eduardo S., 1980. "Analyzing Convertible Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(4), pages 907-929, November.
    12. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
    13. J. Lehoczky & S. Sethi & S. Shreve, 1983. "Optimal Consumption and Investment Policies Allowing Consumption Constraints and Bankruptcy," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 613-636, November.
    14. 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.
    15. 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.
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