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Appendix Describing the Numerical Method Used in 'When Can Life-Cycle Investors Benefit from Time-Varying Bond Risk Premia?'

14 Pages Posted: 21 Nov 2006  

Ralph S. J. Koijen

New York University (NYU) - Department of Finance; Centre for Economic Policy Research (CEPR); National Bureau of Economic Research (NBER)

Theo Nijman

Tilburg University - Center and Faculty of Economics and Business Administration

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)

Date Written: August 2007

Abstract

We rigorously explain the numerical approach used in the above-mentioned paper. The methodology is based on Brandt, Goyal, Santa-Clara, and Stroud (2005) (Review of Financial Studies) and Carroll (2006) (Economics Letters). In addition to combining these numerical techniques, we suggest two extensions. First, the approach of Brandt, Goyal, Santa-Clara, and Stroud (2005) approximates the conditional expectations encountered in optimizing the utility function via polynomial expansions in the state variables. The coefficients in these expansions are estimated using cross-sectional regressions across a set of simulated trajectories of returns and state variables. We develop an accurate approximation of these regression coefficients to facilitate fast optimization over the portfolio weights. This allows us to deal with a large number of decision variables without relying on iterative procedures. Second, to approximate the conditional expectations that lead to the optimal consumption strategy, we ensure that the approximation remains strictly positive, while keeping the approximation computationally tractable.

Suggested Citation

Koijen, Ralph S. J. and Nijman, Theo and Werker, Bas J. M., Appendix Describing the Numerical Method Used in 'When Can Life-Cycle Investors Benefit from Time-Varying Bond Risk Premia?' (August 2007). Available at SSRN: https://ssrn.com/abstract=945720 or http://dx.doi.org/10.2139/ssrn.945720

Ralph S. J. Koijen (Contact Author)

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
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New York University (NYU) - Department of Finance ( email )

Stern School of Business
44 West 4th Street
New York, NY 10012-1126
United States

HOME PAGE: http://www.koijen.net

Centre for Economic Policy Research (CEPR) ( email )

77 Bastwick Street
London, EC1V 3PZ
United Kingdom

Theo E. Nijman

Tilburg University - Center and Faculty of Economics and Business Administration ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 466 2342 (Phone)
+31 13 466 3280 (Fax)

Bas J.M. Werker

Tilburg University - Center for Economic Research (CentER) ( email )

Econometrics and Finance Group
5000 LE Tilburg
Netherlands

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