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Lifetime ruin minimization: should retirees hedge inflation or just worry about it?*

Published online by Cambridge University Press:  20 May 2011

HUAXIONG HUANG  and
MOSHE A. MILEVSKY
HUAXIONG HUANG
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto
MOSHE A. MILEVSKY
Affiliation:
Schulich School of Business, York University, 4700 Keele Street, Toronto (e-mail: milevsky@yorku.ca)
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Abstract

Inflation for retirees is different from and mostly higher than the macro-economic (average) inflation rate for the entire population. In the U.S.A, for example, the Consumer Price Index for the Urban population (CPI-U) calculated and reported by the Bureau of Labor Statistics (BLS) has a lesser known cousin called the CPI-E (for the elderly) in which the sub-component weights are based on the consumption patterns of Americans above the age of 62. This suggests that Inflation-Linked Bond Funds (ILBFs) – whose individual component bond adjustments are based on broad population (CPI-U) inflation – might not be the best hedge for individual retirees’ cost of living. But then again, broad shocks to inflation are likely to impact both indices. So, motivated by the question – is it good enough? – the current paper uses lifetime ruin minimization (LRM) techniques to investigate the optimal allocation between an ILBF and a nominal investment fund for a retiree facing an exogenous liability. Our model trades off the benefit of an imperfect hedge against the cost of lower investment growth. However, our numerical results suggest that although ILBFs can be a large part of the optimal retirement portfolio, it should be treated as just another asset class in the broad optimization problem as opposed to a special or unique category.

Type
Articles
Information
Journal of Pension Economics & Finance , Volume 10 , Issue 3 , July 2011 , pp. 363 - 387
Copyright
Copyright © Cambridge University Press 2011

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References

Albrecht, P. and Maurer, R. (2002) Self-annuitization, consumption shortfall in retirement and asset allocation: the annuity benchmark. Journal of Pension Economics and Finance, 1(3): 269–288.CrossRefGoogle Scholar
Amble, N. and Stewart, K. (1994) Experimental price index for elderly consumers. Bureau of Labor Statistics Monthly Labor Review, 117(5): 11–16.Google Scholar
Aziz, A., Katz, E. and Prisman, E. Z. (2001) Managing the risk of relative price changes by splitting index-linked bonds. Journal of Risk, 3(4): 69–88.CrossRefGoogle Scholar
Bayraktar, E. and Young, V. R. (2007) Correspondence between lifetime minimum wealth and utility of consumption. Finance and Stochastics, 11(2): 213–236.CrossRefGoogle Scholar
Bjork, T. (1998) Arbitrage Theory in Continuous Time. Oxford University Press, UK.CrossRefGoogle Scholar
Bodie, Z. and Clowes, M. J. (2005) Worry-Free Investing: A Safe Approach to Achieving Your Lifetime Financial Goals. 1st edition, Financial Times/Prentice Hall, New Jersey.Google Scholar
Browne, S. (1995) Optimal investment policies for a firm with a random risk process: exponential utility and minimizing the probability of ruin. Mathematics of Operations Research, 20(4): 937–958.CrossRefGoogle Scholar
Browne, S. (1999) The risk and reward of minimizing shortfall probability. Journal of Portfolio Management, 25(4): 76–85.CrossRefGoogle Scholar
Cairns, A. J. G., Blake, D. and Dowd, K. (2006) Stochastic lifestyling: optimal dynamic asset allocation for defined contribution pension plans. Journal of Economic Dynamics and Control, 30: 843–877.CrossRefGoogle Scholar
Campbell, J. and Viciera, L. (2002) Strategic Asset Allocation: Portfolio Choice for Long Term Investors. Oxford University Press, Oxford, UK.CrossRefGoogle Scholar
Ernst, B., Cockburn, I., Douglas, C., Epstein, A. and Grilliches, Z. (1997) Is price inflation different for the elderly? A empirical analysis of prescription drugs. National Bureau of Economic Research (NBER) Working Paper, No. 6182.Google Scholar
Gao, J. (2009) Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model. Insurance: Mathematics and Economics, 45(1): 9–18.Google Scholar
Gupta, A. and Li, Z. (2007) Integrated optimal annuity planning with consumption-investment selections in retirement planning. Insurance: Mathematics and Economics, 41(1): 96–110.Google Scholar
Haberman, S. and Vigna, E. (2002) Optimal investment strategies and risk measures in defined contribution pension schemes. Insurance: Mathematics and Economics, 31(1): 35–69.Google Scholar
Hobijn, B. and Lagakos, D. (2003) Social Security and the Consumer Price Index for the Elderly. Current Issues in Economics and Finance, Volume 9, No. 5, Federal Reserve Bank of New York, pp. 1–6. http://www.newyorkfed.org/research/current_issues/ci9-5.pdfGoogle Scholar
Hoevenaars, P. M. M., Molenaar, R. D. J., Schotman, P. C. and Steenkamp, T. B. M. (2008) Strategic asset allocation with liabilities: beyond stocks and bonds. Journal of Economic Dynamics and Control, 32: 2939–2970.CrossRefGoogle Scholar
Horneff, W. J., Maurer, R. H. and Stamos, M. Z. (2008) Lifecycle asset allocation with annuity markets. Journal of Economic Dynamics and Control, 32: 3590–3612.CrossRefGoogle Scholar
House of Representatives (2001) Consumer Price Index for the Elderly Consumers Act, H.R. 2035 (107th Congress).Google Scholar
Huang, H., Milevsky, M. A. and Wang, J. (2004) Ruined moments in your life: how good are the approximation. Insurance: Economics and Mathematics, 34: 421–447.Google Scholar
Ibbotson, R. G., Milevsky, M. A., Chen, P. and Zhu, K. (2007) Lifetime Financial Advice: Human Capital, Asset Allocation and Insurance. CFA Institute, Charlottesville, VA, USA.Google Scholar
Jarrow, R. and Yildirim, Y. (2003) Pricing treasury inflation protected securities and relative derivatives using HJM model. Journal of Financial and Quantitative Analysis, 38(2): 337–358.CrossRefGoogle Scholar
Jennings, W. (2006) Disaggregated TIPS: the case for disaggregating inflation linked bonds into bonds linked to narrower CPI components. Journal of Pension Economics and Finance, 5(3): 325–343.CrossRefGoogle Scholar
Kothari, S. P. and Shanken, J. (2004) Asset allocation with inflation-protected bonds. Financial Analysts Journal, 60(1): 54–70.CrossRefGoogle Scholar
Merton, R. C. (1971) Optimum consumption and portfolio rules in a continuous time model. Journal of Economic Theory, 3(December): 373–413.CrossRefGoogle Scholar
Milevsky, M. A. (2006) The Calculus of Retirement Income: Financial Models for Life Insurance and Pension Annuities. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Milevsky, M. A. and Robinson, C. (2000) Self-annuitization and ruin in retirement. North American Actuarial Journal, 4(4): 112–129.CrossRefGoogle Scholar
Moore, K. S. and Young, V. R. (2006) Optimal and simple: nearly optimal rules for minimizing the probability of financial ruin in retirement. North American Actuarial Journal, 10(4): 145–162.CrossRefGoogle Scholar
Robinson, C. and Tahani, N. (2007) Sustainable retirement income for the socialite, the gardener and the uninsured. Atkinson College Working Paper. SSRN. Available at http://ssrn.com/abstract=989165 CrossRefGoogle Scholar
Wang, Y. (2009) Quantile hedging for guaranteed minimum death benefits. Insurance: Mathematics and Economics, 45(3): 449–458.Google Scholar
Young, V. R. (2004) Optimal investment strategy to minimize the probability of lifetime ruin. North American Actuarial Journal, 8(4): 106–126.CrossRefGoogle Scholar