×

Managing contribution and capital market risk in a funded public defined benefit plan: impact of CVaR cost constraints. (English) Zbl 1231.91216

Summary: Using a Monte Carlo framework, we analyze the risks and rewards of moving from an unfunded defined benefit pension system to a funded plan for German civil servants, allowing for alternative strategic contribution and investment patterns. In the process we integrate a Conditional Value at Risk (CVaR) restriction on overall plan costs into the pension manager’s objective of controlling contribution rate volatility. After estimating the contribution rate that would fully fund future benefit promises for current and prospective employees, we identify the optimal contribution and investment strategy that minimizes contribution rate volatility while restricting worst-case plan costs. Finally, we analyze the time path of expected and worst-case contribution rates to assess the chances of reduced contribution rates for current and future generations. Our results show that moving toward a funded public pension system can be beneficial for both civil servants and taxpayers.

MSC:

91B30 Risk theory, insurance (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] ABP, 2006. ABP Annual Report 2006. ABP Investments, Heerlen; ABP, 2006. ABP Annual Report 2006. ABP Investments, Heerlen
[2] Artzner, P.; Delbaen, F.; Eber, J.; Heath, D., Thinking coherently, Risk, 10, 11, 68-72 (1997)
[3] Artzner, P.; Delbaen, F.; Eber, J.; Heath, D., Coherent measures of risk, Mathematical Finance, 9, 3, 203-228 (1999) · Zbl 0980.91042
[4] Blake, D., Pension Finance (2006), Wiley: Wiley Chichester
[5] Bogentoft, E.; Romeijn, H. E.; Uryasev, S., Asset/liability management for pension funds using CVaR constraints, Journal of Risk Finance, 2, 3, 57-71 (2001)
[6] Brandt, M. W.; Santa-Clara, P., Dynamic portfolio selection by augmenting the asset space, Journal of Finance, 61, 5, 2187-2217 (2006)
[7] Bundesministerium des Innern, 2005. Dritter Versorgungsbericht der Bundesregierung. Berlin; Bundesministerium des Innern, 2005. Dritter Versorgungsbericht der Bundesregierung. Berlin
[8] Campbell, J. Y.; Chan, Y. L.; Viceira, L. M., A multivariate model for strategic asset allocation, Journal of Financial Economics, 67, 41-80 (2003)
[9] Campbell, J. Y.; Shiller, R. J., Stock prices, earnings and expected dividends, Journal of Finance, 43, 661-676 (1988)
[10] Campbell, J. Y.; Shiller, R. J., Yield spreads and interest rate movements: A bird’s eye view, Review of Economic Studies, 58, 495-514 (1991)
[11] Campbell, J. Y.; Viceira, L. M., The term structure of the risk-return-trade-off, Financial Analysts Journal, 61, 34-44 (2005)
[12] Campbell, J. Y.; Viceira, L. M., Strategic Asset Allocation: Portfolio Choice for Long-Term Investors (2002), Oxford University Press: Oxford University Press Oxford
[13] Chang, S. C.; Tzeng, L. Y.; Miao, J. C., Pension funding incorporating downside risks, Insurance: Mathematics and Economics, 32, 217-228 (2003) · Zbl 1074.91547
[14] Cochrane, J. H., Asset Pricing (2005), Princeton University Press: Princeton University Press Princeton
[15] Detemple, J.; Rindisbacher, M., Dynamic asset liability management with tolerance for limited shortfalls, Insurance: Mathematics and Economics (2008) · Zbl 1152.91501
[16] DAV — Deutsche Aktuarsvereinigung, 2004. Herleitung der DAV-Sterbetafel 2004 R für Rentenversicherungen. Köln; DAV — Deutsche Aktuarsvereinigung, 2004. Herleitung der DAV-Sterbetafel 2004 R für Rentenversicherungen. Köln
[17] Dufresne, D., Moments of pension contributions and fund levels when rates of return are random, Journal of the Institute of Actuaries, 115, 535-544 (1988)
[18] Fama, E. F.; French, K. R., Business conditions and the expected returns on stocks and bonds, Journal of Financial Economics, 25, 23-49 (1989)
[19] Feldstein, M., Ranguelova, E., 2001. Individual risk in an investment-based social security system. NBER Working Paper 8074; Feldstein, M., Ranguelova, E., 2001. Individual risk in an investment-based social security system. NBER Working Paper 8074
[20] Haberman, S., Stochastic investment returns and contribution rate risk in a defined benefit pension scheme, Insurance: Mathematics and Economics, 19, 127-139 (1997) · Zbl 0901.90012
[21] Haberman, S., Risk in a defined benefit pension scheme, Singapore International Insurance and Actuarial Journal, 1, 93-103 (1997)
[22] Haberman, S.; Butt, Z.; Megaloudi, Ch., Contribution and solvency risk in a defined benefit pension scheme, Insurance: Mathematics and Economics, 27, 237-259 (2000) · Zbl 0994.91030
[23] Haberman, S.; Day, C.; Fogarty, D.; Khorasanee, M. Z.; Mcwhirter, M.; Nash, N.; Ngwira, B.; Wright, I. D.; Yakoubov, Y., A stochastic approach to risk management and decision making in defined benefit pension schemes, British Actuarial Journal, 9, 3, 493-618 (2003)
[24] Haberman, S.; Khorasanee, M. Z.; Ngwira, B.; Wright, I. D., Risk measurement and management of defined benefit pension schemes: A stochastic approach, IMA Journal of Management Mathematics, 14, 111-128 (2003) · Zbl 1106.91338
[25] Haberman, S.; Sung, J. H., Dynamic approaches to pension funding, Insurance: Mathematics and Economics, 15, 151-162 (1994) · Zbl 0818.62091
[26] Haberman, S.; Sung, J. H., Optimal pension funding dynamics over infinite control horizon when stochastic rates of return are stationary, Insurance: Mathematics and Economics, 36, 103-116 (2005) · Zbl 1111.91023
[27] Hainaut, D.; Devolder, P., Management of a pension fund under mortality and financial risks, Insurance: Mathematics and Economics, 41, 134-155 (2007) · Zbl 1119.91053
[28] Heubeck, K.; Rürup, B., Finanzierung der Altersversorgung des öffentlichen Dienstes (2000), Peter Lang Verlag: Peter Lang Verlag Frankfurt
[29] Hoevenaars, R. P.; Molenaar, R. D.; Schotman, P. C.; Steenkamp, T. B., Strategic asset allocation with liabilities: Beyond stocks and bonds, Journal of Economic Dynamics and Control (2008) · Zbl 1181.91097
[30] Hoevenaars, R. P.; Molenaar, R. D.; Steenkamp, T. B., Simulation for the long run, (Scherer, B., Asset Liability Management Tools (2003), Risk Books: Risk Books London), 177-210
[31] Hustead, E. C.; Mitchell, O. S., Public sector pension plans, (Mitchell, O. S.; Hustead, E. C., Pensions in the Public Sector (2001), University of Pennsylvania Press: University of Pennsylvania Press Philadelphia), 3-10
[32] Josa-Fombellida, R.; Rincón-Zapatero, J. P., Optimal investment decisions with a liability: The case of defined benefit pension plans, Insurance: Mathematics and Economics, 39, 81-98 (2006) · Zbl 1147.91341
[33] Lee, E. M., An Introduction to Pension Schemes (1986), Institute and Faculty of Actuaries: Institute and Faculty of Actuaries London, UK
[34] Maurer, R.; Mitchell, O. S.; Rogalla, R., The victory of hope over Angst? Funding, asset allocation, and risk taking in German public sector pension reform, (Broeders, D.; Eijffinger, S.; Houben, A., Frontiers in Pension Finance (2008), Edward Elgar: Edward Elgar Cheltenham), 51-79
[35] Maurer, R., Mitchell, O.S., Rogalla, R., 2008b. Reforming German civil servant pensions: Funding policy, investment strategy, and intertemporal risk budgeting. PRC Working Paper, 2008-09; Maurer, R., Mitchell, O.S., Rogalla, R., 2008b. Reforming German civil servant pensions: Funding policy, investment strategy, and intertemporal risk budgeting. PRC Working Paper, 2008-09
[36] McGill, D. M.; Brown, K. N.; Haley, J. J.; Schieber, S. J., Fundamentals of Private Pensions (2005), Oxford University Press: Oxford University Press Oxford
[37] Mitchell, O. S.; Mccarthy, D.; Wisniewski, S. C.; Zorn, P., Developments in state and local pension plans, (Mitchell, O. S.; Hustead, E. C., Pensions in the Public Sector (2001), University of Pennsylvania Press: University of Pennsylvania Press Philadelphia), 11-40
[38] Ngwira, B.; Gerrard, R., Stochastic pension fund control in the presence of Poisson jumps, Insurance: Mathematics and Economics, 40, 283-292 (2007) · Zbl 1120.60063
[39] Novy-Marx, R., Rauh, J.D., 2008. The intergenerational transfer of public pension promises. Working Paper. http://ssrn.com/abstract=1156477; Novy-Marx, R., Rauh, J.D., 2008. The intergenerational transfer of public pension promises. Working Paper. http://ssrn.com/abstract=1156477
[40] Owadally, M. I.; Haberman, S., Pension fund dynamics and gains/losses due to random rates of investment return, North American Actuarial Journal, 3, 3, 105-117 (1999) · Zbl 1082.62543
[41] Owadally, M. I.; Haberman, S., Efficient amortization of actuarial gains/losses and optimal funding in pension plans, North American Actuarial Journal, 8, 1, 21-36 (2004) · Zbl 1085.62509
[42] PBGC. Pension benefit guaranty corporation, 2008. PBGC Announces New Investment Policy. Washington, D.C.: PBGC. http://www.pbgc.gov/media/news-archive/news-releases/2008/pr08-19.html; PBGC. Pension benefit guaranty corporation, 2008. PBGC Announces New Investment Policy. Washington, D.C.: PBGC. http://www.pbgc.gov/media/news-archive/news-releases/2008/pr08-19.html
[43] Rockafellar, R. T.; Uryasev, S., Conditional value-at-risk for general loss distributions, Journal of Banking and Finance, 26, 1443-1471 (2002)
[44] Winklevoss, H. E., Pension Mathematics with Numerical Illustrations (1993), University of Pennsylvania Press: University of Pennsylvania Press Philadelphia
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.