Wharton Pension Research Council Working Papers

Document Type

Working Paper

Date of this Version



We analyse portfolio policies for investors who invest optimally for given investment horizons with respect to Conditional Value-at-Risk constraints. We account for nonnormally distributed, skewed, and leptokurtic asset return distributions due to regime shifts. The focus is on standard CRRA utility with a money back guarantee at maturity, which is often augmented to individual retirement plans. Optimal solutions for the unconstrained as well as the constrained policy are provided and examined for risk management costs calculated as welfare losses. Our results confirm previous findings that money back guarantees yield mild downside protection at low economic costs for most long term investors.


Portfolio choice, Risk management, Downside risk

JEL Code

G11, G17

Working Paper Number


Copyright/Permission Statement

All opinions, errors, findings, interpretations, and conclusions of this paper represent the views of the authors and not those of the Wharton School or the Pension Research Council. © 2013 Pension Research Council of the Wharton School of the University of Pennsylvania. All rights reserved.


This research reported herein was supported by a grant from the Bundesverband für Investment and Asset Management (BVI). The authors appreciate helpful comments from Ralph Rogalla and Alexander Schaefer.

Included in

Economics Commons



Date Posted: 26 June 2019