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

See all articles by Ralph S. J. Koijen

Ralph S. J. Koijen

University of Chicago - Booth School of Business; Centre for Economic Policy Research (CEPR); National Bureau of Economic Research (NBER)

Theo Nijman

Tilburg University - Tilburg University School of Economics and Management

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 E. 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)

University of Chicago - Booth School of Business ( email )

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HOME PAGE: http://faculty.chicagobooth.edu/ralph.koijen/

Centre for Economic Policy Research (CEPR) ( email )

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National Bureau of Economic Research (NBER) ( email )

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Theo E. Nijman

Tilburg University - Tilburg University School of Economics and Management ( email )

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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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