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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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