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Determining the optimal investment strategy according to the loss attitude in defined contribution pension plans

Year 2023, Volume: 16 Issue: 2, 39 - 56, 31.12.2023

Abstract

In recent years, as in the rest of the world, the transition from defined benefit pension plans to defined contribution pension plans has become quite common in our country as well. Because the investment risk is on the participant, it is very important to determine the optimal investment strategy in defined contribution pension plans. Studies that determine the optimal investment strategy in defined contribution pension plans generally use the classical approach of maximizing expected utility. However, maximizing expected utility does not reflect the real world well, especially when the individual is loss-averse. Besides, most investors are actually loss-averse. Therefore, it is crucial to determine the optimal investment strategy for loss-averse individuals in defined contribution pension plans. Another method based on minimizing the difference between the target fund and the actual fund size is to determine the optimal investment strategy by minimizing the discounted sum of cost functions defined as the square of the difference between the target fund size and the actual fund size, by specifying end-of-period target fund size and interim fund targets. In this study, the results obtained for loss-averse individuals are compared with the results obtained from the model using the cost function. Dynamic programming methods are used in both models to determine the optimal investment strategy. When the results obtained in both models were examined, it was observed that the results were very close to each other. The optimal investment strategy is to use the entire fund in a risky investment asset at the beginning of the accumulation period, to decrease the ratio of the fund used in the risk-free investment asset in the later years of the accumulation period, to increase the ratio used in the risk-free investment asset, and to use a large part of the fund in the risk-free investment asset at the end of the accumulation period. Furthermore, it is observed that a loss-averse individual follows a more conservative investment strategy over a longer period, taking less risk.

References

  • [1] Blake, D., Annuities in Pension Plans, In Commentary at World Bank Annuities Workshop, 7-8 June, United Kingdom, 1999, p. 7.
  • [2] Aitken, W. H., A Problem-Solving Approach to Pension Funding and Valuation, Actex Publications, 1996.
  • [3] Samuelson, P. A., Lifetime Portfolio Selection by Dynamic Stochastic Programming, The Review of Economics and Statistics, (1969) 239.
  • [4] Merton, R. C., Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case, The Review Of Economics And Statistics, (1969) 247.
  • [5] Merton, R. C., Optimum Consumption and Portfolio Rules in a Continuous-Time Model, Journal of Economic Theory, 3(4) (1971) 373.
  • [6] Bodie, Z., Merton, R. C. and Samuelson, W. F., Labor Supply Flexibility and Portfolio Choice in a Life Cycle Model, Journal of Economic Dynamics and Control, 16(3-4) (1992) 427.
  • [7] Cairns, A. J. G., An Introduction to Stochastic Pension Fund Management, Working Paper 9607, Pensions Institute, 1996.
  • [8] Owadally, M. I., The Dynamics and Control of Pension Funding, Doctoral Dissertation, City University, London, 1998.
  • [9] Vigna, E. and Haberman, S., Optimal Investment Strategy for Defined Contribution Pension Schemes, Insurance: Mathematics and Economics, 28(2) (2001) 233.
  • [10] Blake, D., Cairns, A. J. and Dowd, K., Pensionmetrics: Stochastic Pension Plan Design and Value-At-Risk During The Accumulation Phase, Insurance: Mathematics and Economics, 29(2) (2001) 187.
  • [11] Haberman, S. and Vigna, E., Optimal Investment Strategies and Risk Measures in Defined Contribution Pension Schemes, Insurance: Mathematics and Economics, 31(1) (2002) 35.
  • [12] Gerrard, R., Haberman, S. and Vigna, E., Optimal Investment Choices Post-Retirement in a Defined Contribution Pension Scheme, Insurance: Mathematics and Economics, 35(2) (2004) 321.
  • [13] Cairns, A. J., Blake, D. and Dowd, K., Stochastic Lifestyling: Optimal Dynamic Asset Allocation for Defined Contribution Pension Plans, Journal of Economic Dynamics and Control, 30(5) (2006) 843.
  • [14] Battocchio, P., Menoncin, F. and Scaillet, O., Optimal Asset Allocation for Pension Funds Under Mortality Risk During The Accumulation and Decumulation Phases, Annals of Operations Research, 152(1) (2007) 141.
  • [15] Yang, S. S. and Huang, H. C., The Impact of Longevity Risk on the Optimal Contribution Rate and Asset Allocation for Defined Contribution Pension Plans, The Geneva Papers on Risk and Insurance Issues and Practice, 34(4) (2009) 660.
  • [16] Blake, D., Wright, D. and Zhang, Y., Age-Dependent Investing: Optimal Funding and Investment Strategies in Defined Contribution Pension Plans When Members Are Rational Life Cycle Financial Planners, Journal of Economic Dynamics and Control, 38 (2014) 105.
  • [17] Chen, A., Haberman, S. and Thomas, S., Optimal Decumulation Strategies During Retirement with Deferred Annuities, Available at SSRN 2911959, 2017. [18] Rabin, M. and Thaler, R. H., Anomalies: Risk Aversion, The Journal of Economic Perspectives, 15(1) (2001) 219.
  • [19] Kahneman, D. and Tversky, A., Prospect Theory: An Analysis of Decision under Risk, Econometrica, 47 (1979) 263.
  • [20] Berkelaar, A. B., Kouwenberg, R. and Post, T., Optimal Portfolio Choice Under Loss Aversion. Review of Economics and Statistics, 86(4) (2004) 973.
  • [21] Gomes, F. J., Portfolio Choice and Trading Volume with Loss‐Averse Investors, The Journal of Business, 78(2) (2005) 675.
  • [22] Blake, D., Wright, D. and Zhang, Y., Target-Driven Investing: Optimal Investment Strategies in Defined Contribution Pension Plans Under Loss Aversion, Journal of Economic Dynamics and Control, 37(1) (2013) 195.
  • [23] M. I. Owadally, S. Haberman, D. G. Hernández, 2013, A Savings Plan with Targeted Contributions, The Journal of Risk and Insurance, 80(4), 975-1000.
  • [24] H. K. Sezen, 2007, Yöneylem Araştırması, 2. Baskı, Ekin Basım Yayın Dağıtım, Bursa.
  • [25] R. Bellman, 1957, Dynamic Programming, Princeton University Press, New Jersey.
  • [26] Tversky, A. and Kahneman, D., Advances in Prospect Theory: Cumulative Representation of Uncertainty, Journal of Risk and uncertainty, 5(4) (1992) 297.
  • [27] Kırkağaç, M., Gençtürk, Y. (2016). Bireysel emeklilik planlarında hedef fon büyüklüğüne ulaşmak için değişken katkı ve optimal yatırım stratejisi. İstatistikçiler Dergisi: İstatistik ve Aktüerya, 9(2), 54-65.

Katkısı belirli emeklilik planlarında kayıp tutumuna göre optimal yatırım stratejisinin belirlenmesi

Year 2023, Volume: 16 Issue: 2, 39 - 56, 31.12.2023

Abstract

Dünyada olduğu gibi ülkemizde de son yıllarda faydası belirli emeklilik planlarından katkısı belirli emeklilik planlarına geçiş oldukça yaygınlaşmıştır. Katkısı belirli emeklilik planlarında yatırım riski katılımcı üzerinde olduğu için optimal yatırım stratejisinin belirlenmesi oldukça önemlidir. Katkısı belirli emeklilik planlarında optimal yatırım stratejisinin belirlendiği çalışmalarda genellikle, klasik bir yaklaşım olan beklenen faydanın maksimizasyonu kullanılmıştır. Fakat beklenen faydanın maksimizasyonu gerçek dünyayı, özellikle birey kayıptan kaçınan bir birey olduğunda iyi yansıtmamaktadır. Bununla birlikte, yatırımcıların çoğu da aslında kayıptan kaçınan bireylerdir. Bu nedenle katkısı belirli emeklilik planlarında optimal yatırım stratejisinin kayıptan kaçınan bireyler için belirlenmesi oldukça önemlidir. Hedeflenen fon ile gerçekleşen fon büyüklüğü arasındaki farkın minimizasyonuna dayanan bir diğer yöntem ise, dönem sonu hedef fon büyüklüğü ve ara dönem fon hedeflerini belirleyerek, hedeflenen fon büyüklüğü ile gerçekleşen fon büyüklüğü arasındaki farkın karesi olarak tanımlanan maliyet fonksiyonlarının iskontolu toplamını minimize edecek şekilde optimal yatırım stratejisinin belirlenmesidir. Bu çalışmada kayıptan kaçınan bireyler için elde edilen sonuçlar, maliyet fonksiyonunun kullanıldığı modelden elde edilen sonuçlar ile karşılaştırmalı olarak elde edilmiştir. Optimal yatırım stratejisi belirlenirken her iki modelde de dinamik programlama yöntemi kullanılmıştır. Her iki modelde elde sonuçlar incelendiğinde ise sonuçların birbirine çok yakın gerçekleştiği görülmüştür. Optimal yatırım stratejisi birikim döneminin başında fonun tamamının riskli yatırım aracında değerlendirilmesi, birikim döneminin ilerleyen yaşlarında fonun riskli yatırım aracında değerlendirilen oranının azaltılarak, risksiz yatırım aracında değerlendirilen oranının artırılması, birikim döneminin sonunda ise fonun büyük bir kısmının risksiz yatırım aracında değerlendirilmesi biçimindedir. Bununla birlikte kayıptan kaçınan bireyin daha uzun bir süre, daha az risk alarak daha tutucu bir yatırım stratejisi izlediği görülmektedir.

Ethical Statement

Bu yayın “Katkısı Belirli Emeklilik Planlarında Optimal Stratejilerin Belirlenmesi” isimli doktora tezinden üretilmiştir

References

  • [1] Blake, D., Annuities in Pension Plans, In Commentary at World Bank Annuities Workshop, 7-8 June, United Kingdom, 1999, p. 7.
  • [2] Aitken, W. H., A Problem-Solving Approach to Pension Funding and Valuation, Actex Publications, 1996.
  • [3] Samuelson, P. A., Lifetime Portfolio Selection by Dynamic Stochastic Programming, The Review of Economics and Statistics, (1969) 239.
  • [4] Merton, R. C., Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case, The Review Of Economics And Statistics, (1969) 247.
  • [5] Merton, R. C., Optimum Consumption and Portfolio Rules in a Continuous-Time Model, Journal of Economic Theory, 3(4) (1971) 373.
  • [6] Bodie, Z., Merton, R. C. and Samuelson, W. F., Labor Supply Flexibility and Portfolio Choice in a Life Cycle Model, Journal of Economic Dynamics and Control, 16(3-4) (1992) 427.
  • [7] Cairns, A. J. G., An Introduction to Stochastic Pension Fund Management, Working Paper 9607, Pensions Institute, 1996.
  • [8] Owadally, M. I., The Dynamics and Control of Pension Funding, Doctoral Dissertation, City University, London, 1998.
  • [9] Vigna, E. and Haberman, S., Optimal Investment Strategy for Defined Contribution Pension Schemes, Insurance: Mathematics and Economics, 28(2) (2001) 233.
  • [10] Blake, D., Cairns, A. J. and Dowd, K., Pensionmetrics: Stochastic Pension Plan Design and Value-At-Risk During The Accumulation Phase, Insurance: Mathematics and Economics, 29(2) (2001) 187.
  • [11] Haberman, S. and Vigna, E., Optimal Investment Strategies and Risk Measures in Defined Contribution Pension Schemes, Insurance: Mathematics and Economics, 31(1) (2002) 35.
  • [12] Gerrard, R., Haberman, S. and Vigna, E., Optimal Investment Choices Post-Retirement in a Defined Contribution Pension Scheme, Insurance: Mathematics and Economics, 35(2) (2004) 321.
  • [13] Cairns, A. J., Blake, D. and Dowd, K., Stochastic Lifestyling: Optimal Dynamic Asset Allocation for Defined Contribution Pension Plans, Journal of Economic Dynamics and Control, 30(5) (2006) 843.
  • [14] Battocchio, P., Menoncin, F. and Scaillet, O., Optimal Asset Allocation for Pension Funds Under Mortality Risk During The Accumulation and Decumulation Phases, Annals of Operations Research, 152(1) (2007) 141.
  • [15] Yang, S. S. and Huang, H. C., The Impact of Longevity Risk on the Optimal Contribution Rate and Asset Allocation for Defined Contribution Pension Plans, The Geneva Papers on Risk and Insurance Issues and Practice, 34(4) (2009) 660.
  • [16] Blake, D., Wright, D. and Zhang, Y., Age-Dependent Investing: Optimal Funding and Investment Strategies in Defined Contribution Pension Plans When Members Are Rational Life Cycle Financial Planners, Journal of Economic Dynamics and Control, 38 (2014) 105.
  • [17] Chen, A., Haberman, S. and Thomas, S., Optimal Decumulation Strategies During Retirement with Deferred Annuities, Available at SSRN 2911959, 2017. [18] Rabin, M. and Thaler, R. H., Anomalies: Risk Aversion, The Journal of Economic Perspectives, 15(1) (2001) 219.
  • [19] Kahneman, D. and Tversky, A., Prospect Theory: An Analysis of Decision under Risk, Econometrica, 47 (1979) 263.
  • [20] Berkelaar, A. B., Kouwenberg, R. and Post, T., Optimal Portfolio Choice Under Loss Aversion. Review of Economics and Statistics, 86(4) (2004) 973.
  • [21] Gomes, F. J., Portfolio Choice and Trading Volume with Loss‐Averse Investors, The Journal of Business, 78(2) (2005) 675.
  • [22] Blake, D., Wright, D. and Zhang, Y., Target-Driven Investing: Optimal Investment Strategies in Defined Contribution Pension Plans Under Loss Aversion, Journal of Economic Dynamics and Control, 37(1) (2013) 195.
  • [23] M. I. Owadally, S. Haberman, D. G. Hernández, 2013, A Savings Plan with Targeted Contributions, The Journal of Risk and Insurance, 80(4), 975-1000.
  • [24] H. K. Sezen, 2007, Yöneylem Araştırması, 2. Baskı, Ekin Basım Yayın Dağıtım, Bursa.
  • [25] R. Bellman, 1957, Dynamic Programming, Princeton University Press, New Jersey.
  • [26] Tversky, A. and Kahneman, D., Advances in Prospect Theory: Cumulative Representation of Uncertainty, Journal of Risk and uncertainty, 5(4) (1992) 297.
  • [27] Kırkağaç, M., Gençtürk, Y. (2016). Bireysel emeklilik planlarında hedef fon büyüklüğüne ulaşmak için değişken katkı ve optimal yatırım stratejisi. İstatistikçiler Dergisi: İstatistik ve Aktüerya, 9(2), 54-65.
There are 26 citations in total.

Details

Primary Language Turkish
Subjects Risk Analysis, Operation, Statistics (Other)
Journal Section Articles
Authors

Murat Kırkağaç 0000-0002-2703-8768

Yasemin Saykan 0000-0002-8916-8509

Early Pub Date December 29, 2023
Publication Date December 31, 2023
Published in Issue Year 2023 Volume: 16 Issue: 2

Cite

IEEE M. Kırkağaç and Y. Saykan, “Katkısı belirli emeklilik planlarında kayıp tutumuna göre optimal yatırım stratejisinin belirlenmesi”, JSSA, vol. 16, no. 2, pp. 39–56, 2023.