FIN-02-063 |
NYU Stern School of Business |
Multiple Risky Assets, Transaction Costs and Return
Predictability: Implications for Portfolio Choice
December 2002
Anthony W. Lynch and Sinan Tan
ABSTRACT
Our paper contributes to the dynamic portfolio choice and transaction cost literatures by con-sidering
a multiperiod CRRA individual who faces transaction costs and who has access to multiple
risky assets, all with predictable returns. We numerically solve the individual’s multiperiod problem
in the presence of transaction costs and predictability. In particular, we characterize the investor’s
optimal portfolio choice with proportional and fixed transaction costs, and with return predictabil-ity
similar to that observed for the U.S. stock market. We also perform some comparative statics
to better understand the nature of the no-trade region with more than one risky asset. Throughout
our focus is on the case with two risky assets. We also perform some utility comparisons. The
calibration exercise reveals some interesting results about the relative attractiveness of the three
equity portfolios calibrated.
With proportional transaction costs and i.i.d. returns, we numerically find the rebalancing
rule to be a no-trade region for the portfolio weights with rebalancing to the boundary. With
zero correlation, the no-trade region is a rectangle irrespective of the investor’s age. When the
correlation of the risky assets is non-zero, the no-trade region becomes a parallelogram. With
positive correlation, the parallelogram distorts the associated rectangle in such a way as to take
advantage of the associated substitutability across the two assets that the positive correlation
induces. The converse is true for negative correlation. Turning to the allocations with return
predictability, our numerical results strongly suggest that it is the conditional return correlation
that determines the nature of the distortion to the no-trade parallelogram. Irrespective of the
investor’s age, the distortion always mirrors the no-trade parallelogram distortion that we find in
the i.i.d. case for return correlation of the same sign. The no-trade region is always larger late
in life than early in life. However, the difference in no-trade area between early and late in life
is less pronounced when returns are predictable, consistent with intuition that the benefits from
rebalancing today are more short-lived when returns are predictable than in the i.i.d. case.
Anthony W. Lynch
Institution: Stern School of Business, New York University, 44th West 4th Street, NY 10012
Email: alynch@stern.nyu.edu
Telephone: (212) 998-0350
Fax: (212) 995-4223
Homepage: http://www.stern.nyu.edu/~alynch/
Sinan Tan
Institution: Stern School of Business, New York University, 44th West 4th Street, NY 10012
Email: stan@stern.nyu.edu
Telephone: (212) 998-0560
Homepage: http://www.stern.nyu.edu/~stan/
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