Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T14:04:51.354Z Has data issue: false hasContentIssue false
  • English
  • Français

Welfare analysis of conditional indexation schemes from a two-reference-point perspective*

Published online by Cambridge University Press:  01 October 2008

RENXIANG DAI  and
J.M. SCHUMACHER
RENXIANG DAI*
Affiliation:
Netspar, CentER, Tilburg University, PO Box 90153, 5000 LE Tilburg, The Netherlands
J.M. SCHUMACHER*
Affiliation:
Netspar, CentER, Tilburg University, PO Box 90153, 5000 LE Tilburg, The Netherlands
*
e-mail: [email protected]
[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Conditional indexation has recently attracted interest with pension funds that are looking for a middle way between defined benefit and defined contribution. In this paper, we analyze conditional indexation schemes from a life-cycle investment perspective. Welfare analysis is applied to investigate the performance of such schemes relative to alternative investment strategies such as fixed-mix policies. We carry out this analysis in the context of a broad family of utility functions, which takes into account the possible presence of two benchmark levels corresponding to a minimum guaranty and to full indexation, respectively. For the purpose of comparability, we construct a self-financing continuous-time implementation of the conditional indexation scheme. The implementation involves continual adjustment of the parameters of the contingent claim representing final payoff. Our findings indicate that, in situations where large weight is placed on the benchmark levels, conditional indexation is fairly close to being optimal.

Type
Articles
Information
Journal of Pension Economics & Finance , Volume 8 , Issue 3 , July 2009 , pp. 321 - 350
Copyright
Copyright © 2008 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Previous versions of the paper were presented at the ‘Insurance: Mathematics and Economics’ conference held in Piraeus, Greece, and the Netspar Pension Days in Tilburg, The Netherlands. We thank Lans Bovenberg, An Chen, Frank de Jong, Joost Driessen, Bertrand Melenberg, Theo Nijman, Michael Orszag (the Coordinating Editor) and two anonymous reviewers for helpful comments.

References

Ait-Sahalia, Y. and Brandt, M. (2001) Variable selection for portfolio choice. Journal of Finance, 56: 1297–1351.CrossRefGoogle Scholar
Ballotta, L., Haberman, S. and Wang, N. (2006) Guarantees in with-profit and unitized with-profit life insurance contract: fair valuation problem in presence of the default option. Journal of Risk and Insurance, 73: 97–121.CrossRefGoogle Scholar
Barberis, N., Huang, M. and Santos, T. (2001) Prospect theory and asset prices. Quarterly Journal of Economics, 116: 1–53.CrossRefGoogle Scholar
Benartzi, S. and Thaler, R. (1995) Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics, 110: 73–92.CrossRefGoogle Scholar
Berkelaar, A., Kouwenberg, R. and Post, T. (2004) Portfolio choice under loss aversions. Review of Economics and Statistics, 64: 973–986.CrossRefGoogle Scholar
Bikker, J. and Vlaar, P. (2007) Conditional indexation in defined benefit pension plans. The Geneva Papers on Risk and Insurance Issues and Practice, 32: 494–515.CrossRefGoogle Scholar
Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy, 81: 637–659.CrossRefGoogle Scholar
Browne, S. (1999) The risk and rewards of minimizing shortfall probability. Journal of Portfolio Management, 25: 76–85.CrossRefGoogle Scholar
Campbell, J. Y. and Cochrane, J. H. (1999) By force of habit: a consumption-based explanation of aggregate stock market behavior. Journal of Political Economy, 107: 205–251.CrossRefGoogle Scholar
Cox, J. and Huang, C. (1989) Optimum consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory, 49: 33–83.CrossRefGoogle Scholar
Dai, R. and Schumacher, J. M. (2008) Valuation of contingent pension liabilities and implementation of conditional indexation. Mimeo, Tilburg University.Google Scholar
Duffie, D. (2001) Dynamic Asset Pricing Theory. 3rd edn. Princeton, NJ: University Press, 2001.Google Scholar
Gatzert, N. and Kling, A. (2007) Analysis of participating life insurance contract: a unification approach. Journal of Risk and Insurance, 74: 547–570.CrossRefGoogle Scholar
Gomes, F. J. (2005) Portfolio choice and trading volume with loss-averse investors. Journal of Business, 78: 3675–3706.Google Scholar
Grosen, A. and Jørgensen, P. (2002) Life insurance liabilities at market value. Journal of Risk and Insurance, 69: 63–91.CrossRefGoogle Scholar
Kahneman, D. and Tversky, A. (1979) Prospect theory: an analysis of decision under risk. Econometrica, 47: 263–290.CrossRefGoogle Scholar
Karatzas, I. and Shreve, S. E. (1998) Methods of Mathematical Finance. New York: Springer-Verlag.Google Scholar
Kocken, T. P. (2006) Curious contracts: pension fund redesign for the future. PhD Thesis, Vrije Universiteit, Amsterdam.Google Scholar
Kocken, T. P. (2007) Constructing sustainable pensions. Life and Pensions, (July–August): 35–39.Google Scholar
Lusardi, A. and Mitchell, O. (2006) Financial Literary and Planning: Implication for Retirement Wellbeing. Dartmouth College and University of Pennsylvania.Google Scholar
March, J. G. and Shapira, Z. (1987) Managerial perspectives on risk and risk taking. Management Science, 33: 1404–1419.CrossRefGoogle Scholar
Merton, R. C. (2006) Observations on innovation in pension fund management in the impending future. PREA Quarterly, (Winter): 61–67.Google Scholar
Merton, R. C. (1969) Lifetime portfolio selection under uncertainty: the continuous-time case. Review of Economics and Statistics, 51: 247–257.CrossRefGoogle Scholar
Samuelson, P. A. (1969) Lifetime portfolio selection by dynamic stochastic programming. Review of Economics and Statistics, 51: 239–246.CrossRefGoogle Scholar
Segal, U. and Spivak, A. (1990) First order versus second order risk aversion. Journal of Economic Theory, 51: 111–125.CrossRefGoogle Scholar
Sharpe, W. F. (1998) Morningstar's risk-adjusted ratings. Financial Analysts Journal, 55: 21–33.CrossRefGoogle Scholar
Sullivan, K. and Kida, T. (1995) The effect of multiple reference points and prior gains and losses on managers' risky decision making. Organizational Behavior and Human Decision Process, 64: 76–83.CrossRefGoogle Scholar
Sundaresan, S. M. (1989) Intertemporally dependent preferences and the volatility of consumption and wealth. Review of Financial Studies, 2: 73–89.CrossRefGoogle Scholar
Tversky, A. and Kahneman, D. (1981) Decisions and the psychology of choice. Science, 211: 453–458.CrossRefGoogle ScholarPubMed
Tversky, A. and Kahneman, D. (1992) Loss aversion in riskless choice: a reference-dependent model. Quarterly Journal of Economics, 106: 1039–1061.CrossRefGoogle Scholar
van Rooij, M., Lusardi, A. and Alessie, R. (2006). Financial literacy and stock market participation. Mimeo, De Nederlandsche Bank.Google Scholar
von Neumann, J. and Morgenstern, O. (1944) Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press.Google Scholar