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A Stochastic Approach to Risk Management and Decision Making in Defined Benefit Pension Schemes

Published online by Cambridge University Press:  10 June 2011

S. Haberman ,
C. Day ,
D. Fogarty ,
M. Z. Khorasanee ,
M. McWhirter ,
N. Nash ,
B. Ngwira ,
I. D. Wright  and
Y. Yakoubov
S. Haberman
Affiliation:
Faculty of Actuarial Science & Statistics, Cass Business School, 106 Bunhill Row, London EC1Y 8TZ, U.K., Email:s.haberman@city.ac.uk
C. Day
Affiliation:
Watson Wyatt Partners, Watson House, London Road, Reigate, Surrey RH2 9PQ, U.K., Email: christopher.day@eu.watsonwyatt.com
D. Fogarty
Affiliation:
William M Mercer Ltd, Noble Lowndes House, PO Box 64, 5 Bedford Park, Croydon CR9 2ZT, U.K., Email: david.fogarty@uk.wmmercer.com
M. Z. Khorasanee
Affiliation:
Faculty of Actuarial Science & Statistics, Cass Business School, 106 Bunhill Row, London EC1Y 8TZ, U.K., Email: m.z.khorasanee@city.ac.uk
M. McWhirter
Affiliation:
Scottish Widows' Fund & Life Assurance Society, 15 Dalkeith Road, Edinburgh EH16 5BU, U.K., Email: martin.mcwhirter@scottishwidows.co.uk
N. Nash
Affiliation:
Aon Consulting, 40 Torphichen Street, Edinburgh EH3 8JB, U.K., Email: nicola.nash@aonconsulting.co.uk
B. Ngwira
Affiliation:
Faculty of Actuarial Science & Statistics, Cass Business School, 106 Bunhill Row, London EC1Y 8TZ, U.K., Email:b.ngwira@city.ac.uk
I. D. Wright
Affiliation:
Faculty of Actuarial Science & Statistics, Cass Business School, 106 Bunhill Row, London EC1Y 8TZ, U.K., Email:i.d.wright-1@city.ac.uk
Y. Yakoubov
Affiliation:
Aon Consulting, 15 Minories, London EC3N 1NJ, U.K., Email:yakoub.yakoubov@aonconsulting.co.uk
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Abstract

The trustees and sponsors of defined benefit schemes rely on the advice of the Scheme Actuary to make important decisions concerning the funding of the scheme, the investment of its assets, and the use of surplus assets to improve benefits. These decisions have to be made in the face of considerable uncertainty about financial and demographic factors that will affect the future experience of the scheme and its success in meeting various objectives.

The traditional actuarial valuation combined with actuarial judgement has played an important role in guiding decision making; but we argue that stochastic methods can add value in certain crucial areas, in particular the financial risk management of defined benefit schemes. Rather than dealing with risk by incorporating margins in the valuation basis, a stochastic approach allows the actuary to evaluate specific and quantifiable risk and performance measures for alternative funding and investment strategies.

This paper recommends a framework that, when combined with a suitable stochastic model, measures the risks inherent in contribution rate and asset allocation decisions, allowing better decisions to be made. In doing this, we suggest and apply various risk and performance measures that may be thought appropriate, although our intention is to illustrate their use rather than prescribe them as objective standards. The framework provides the means to explore the trade-offs involved in possible contribution and asset allocation decisions, and points to decision strategies expected to give improved outcomes for the same level of risk. A feature of the approach that marks it out from current asset/liability techniques is that it examines the funding and investment decisions together. It does not derive a contribution rate in the traditional way, but leaves this as free variable, in the same way that the investment decision is taken to be a free variable. Another distinctive feature of our framework is that it is based on projection rather than on valuation, involving stochastic simulation of the experience of the scheme over a time horizon reflecting the concerns of the trustees and the sponsoring employer.

The paper provides a case study (based on a model final salary pension scheme) showing the advantages of the framework, and goes on to explain how the results may practically be communicated to trustees and scheme sponsors.

Keywords

Defined Benefit Pension SchemesProjectionStochastic SimulationRisk and Performance MeasuresRisk ManagementDecision Making

Information

Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 9 , Issue 3 , 01 August 2003 , pp. 493 - 586
Copyright
Copyright © Institute and Faculty of Actuaries 2003

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References

Albrecht, P., Maurer, R. & Ruckpaul, U. (2001). The risk of stocks in the long run: unconditional vs conditional shortfall. Proceedings of 11th Annual International AFIR Colloquium, 1, 39–62.Google Scholar
Allais, M. (1953). Le comportement de l'homme rationnel devant le risque: critiques des postulats et axiomes de l'école Américaine. Econometrica, 21, 4, 503–546.CrossRefGoogle Scholar
Artzner, P., Delbaen, F., Eber, J.-M. & Heath, D. (1997). Thinking coherently. Risk, 10 (November), 68–71.Google Scholar
Artzner, P., Delbaen, F., Eber, J.-M. & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9, 203–228.Google Scholar
Bacinello, A.R. (1988). A stochastic simulation procedure for pension schemes. Insurance: Mathematics and Economics, 7, 153–161.Google Scholar
Begg, D., Fischer, S. & Dornbusch, R. (2000). Economics. (Sixth edition), McGraw-Hill, London.Google Scholar
Bertsekas, D.P. (1976). Dynamic programming and stochastic control. New York: Academic Press.Google Scholar
Black, F. & Jones, R. (1987). Simplifying portfolio insurance. Journal of Portfolio Management, fall, 48–51.Google Scholar
Boulier, J.-F., Trussant, E. & Florens, D. (1995). A dynamic model for pensions funds management. Proceedings of the 5th AFIR International Colloquium, Leuven, Belgium, 1, 361–384.Google Scholar
Bowers, N.L., Hickman, J.C. & Nesbitt, C.J. (1979). The dynamics of pension funding: contribution theory. Transactions of the Society of Actuaries 31, 93–122.Google Scholar
Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A. & Nesbitt, C.J. (1997). Actuarial Mathematics. Society of Actuaries.Google Scholar
Cairns, A.J.G. (1997). A comparison of optimal and dynamic control strategies for continuous-time pension fund models. Proceedings of the 7th AFIR International Colloquium, Cairns, Australia 1, 309–326.Google Scholar
Cairns, A.J.G. (2000). Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time. ASTIN Bulletin, 30, 19–55.Google Scholar
Cairns, A.J.G. (2000)a. A discussion of parameter and model uncertainty in insurance. Insurance: Mathematics and Economics, 27, 313–330.Google Scholar
Chapman, R.J., Gordon, T.J. & Speed, C.A. (2001). Pensions, funding and risk. British Actuarial Journal, 7, 605–662.Google Scholar
Chopra, V.K. & Ziemba, W.T. (1993). The effect of errors in means, variances and covariances on optimal portfolio choice. Journal of Portfolio Management, 19, 6–14.Google Scholar
Clarkson, R.S. & Plymen, J. (1988). Improving the performance of equity portfolios. Journal of the Institute of Actuaries, 115, 631–674, and Transactions of the Faculty of Actuaries, 41, 631–675, 730–750.CrossRefGoogle Scholar
Daykin, C.D., Pentikainen, T. & Pesonen, M. (1994). Practical risk theory for actuaries. Chapman and Hall, London.Google Scholar
Dowd, K. (1998). Beyond value at risk. John Wiley and Sons, Chichester.Google Scholar
Dufresne, D. (1988). Moments of pension contributions and fund levels when rates of return are random. Journal of the Institute of Actuaries, 115, 535–544.CrossRefGoogle Scholar
Exley, C.J., Mehta, S.J.B. & Smith, A.D. (1997). The financial theory of defined benefit pension schemes. British Actuarial Journal, 3, 835–996.CrossRefGoogle Scholar
Geoghegan, T.J., Clarkson, R.S., Feldman, K.S., Green, S.J., Kitts, A., Lavecky, P., Ross, J.M., Smith, W.J. & Toutounchi, A. (1992). Report on the Wilkie stochastic investment model. Journal of the Institute of Actuaries, 119, 173–212.Google Scholar
Haberman, S., Butt, Z. & Rickayzen, B.D. (2000). Multiple state models, simulation and insurer insolvency. Giornale dell' Istituto Italiano degli Attuari, 43, 83–109.Google Scholar
Haberman, S. & Vigna, E. (2002). Optimal investment strategies and risk measures in defined contribution pension schemes. Insurance: Mathematics and Economics, 31, 35–69.Google Scholar
Hairs, C.J., Belsham, D.J., Bryson, N.M., George, C.M., Hare, D.J.P., Smith, D.A. & Thompson, S. (2001). Fair valuation of liabilities. British Actuarial Journal, 8, 203–340.Google Scholar
Head, S.J., Adkins, D.R., Cairns, A.J.G., Corvesor, A.J., Cule, D.O., Exley, C.J., Johnson, I.S., Spain, J.G. & Wise, A.G. (2000). Pension fund valuations and market values. British Actuarial Journal, 6, 55–118.Google Scholar
Huber, P.P. (1998). A note on the jump-equilibrium model. British Actuarial Journal, 4, 615–636.Google Scholar
Kemp, M.H.D. (1996). Asset-liability modelling for pension funds. Presented to the Staple Inn Actuarial Society.Google Scholar
Khorasanee, M.Z. (1999). Actuarial modelling of defined contribution pension schemes. PhD thesis, City University, London.Google Scholar
Lee, E.M. (1986). An introduction to pension schemes. Faculty and Institute of Actuaries.Google Scholar
Lee, P.J. & Wilkie, A.D. (2000). A comparison of stochastic asset models. Presented to the Institute and Faculty of Actuaries Investment Conference.Google Scholar
Lintner, J. (1971). The aggregation of investors' diverse judgement and preferences in purely competitive security markets. Journal of Finance and Quantitative Analysis, 4, 347–450.Google Scholar
McGill, D.M., Brown, K.N., Haley, J.J. and Schieber, S.J. (1996). Fundamentals of private pensions. 7th Ed.Philadelphia, Pennsylvania: University of Pennsylvania Press.Google Scholar
Maurer, R. & Schlag, C. (2002). Money-back guarantees in individual pension accounts: evidence from the German pension reform. Centre for Financial Studies working paper No 2002/03. Johan Wolfgang Goethe-Universitat, Frankfurt am Main.Google Scholar
Modigliani, F. & Miller, M.H. (1958). The cost of capital, corporation finance and the theory of investment. American Economic Review, 48, 261–297.Google Scholar
Myners, P. (2001). Institutional investment in the United Kingdom: a review. HM Treasury website, www.hm-treasury.gov.ukGoogle Scholar
O'Regan, W.S & Weeder, J. (1988). A dissection of pension funding. Presented to the Staple Inn Actuarial Society.Google Scholar
Owadally, M.I. & Haberman, S. (1999) Pension fund dynamics and gains/losses due to random rates of investment return. North American Actuarial Journal, 3 (3), 105–117.CrossRefGoogle Scholar
Owadally, M.I. & Haberman, S. (2004). Efficient amortization of actuarial gains/losses and optimal funding in pension plans. North American Actuarial Journal, 8. (to appear)CrossRefGoogle Scholar
Ramsay, C.M. (1993). Percentile pension cost methods: a new approach to pension valuations. Transactions of the Society of Actuaries, 45, 351–415.Google Scholar
Shoemaker, P.J.H. (1980). Experiments on decisions under risk: the expected utility hypothesis. Nijhoff, Boston.Google Scholar
Siegmann, A.H. & Lucas, A. (1999). Continuous-time dynamic programming for ALM with risk averse loss functions. Proceedings of the 9th AFIR International Colloquium.Google Scholar
Sloman, J. (1999). Economics. Third edition. Prentice Hall.Google Scholar
Smith, A.D. (1996). How actuaries can use financial economics. British Actuarial Journal, 2, 1057–1193.CrossRefGoogle Scholar
Subject 304 Core Reading — Pensions and Other Benefits (2001). Faculty and Institute of Actuaries.Google Scholar
Treynor, J.L., Regan, P.J. & Priest, W.W. (1978). Pension claims and corporate assets. Financial Analysts Journal, May-June 1978, 84–88.Google Scholar
Trowbridge, C.L. & Farr, C.E. (1976). The theory and practice of pension funding. Homewood, Illinois: Richard D., Irwin.Google Scholar
Tversky, A. (1969). Intransitivity of preferences. Psychological Review, 76, 31–48.Google Scholar
Von Neumann, J. & Morgenstern, O. (1944). Theory of games and economic behaviour. Princeton University Press.Google Scholar
Wason, S. (2001). IAA solvency project: report of working party. Presented to the 11th Annual International AFIR Colloquium, Toronto.Google Scholar
Whitten, S.P. & Thomas, R.G. (1999). A non-linear stochastic model for actuarial use. British Actuarial Journal, 5, 919–953.Google Scholar
Wilkie, A.D. (1986). A stochastic investment model for actuarial use. Transactions of the Faculty of Actuaries, 39, 341–403.Google Scholar
Wilkie, A.D. (1995). More on a stochastic asset model for actuarial use. British Actuarial Journal, 1, 777–964.CrossRefGoogle Scholar
Wirch, J.L. & Hardy, M.R. (1999). A synthesis of risk measures for capital adequacy. Insurance: Mathematics and Economics, 25, 337–347.Google Scholar
Wise, A.J. (1984). The matching of assets to liabilities. Journal of the Institute of Actuaries, 111, 375–402.CrossRefGoogle Scholar
Yakoubov, Y., Teeger, M. & Duval, D.B. (1999). A stochastic investment model for asset and liability management. Presented to the Staple Inn Actuarial Society.Google Scholar