Forecasting Danish Pension Savings Through Stochastic Non-linear Modeling

Nicholas Domanyi Fribert & Mathias Duelund Hansen

Student thesis: Master thesis


How does an inclusion of a stochastic lifecycle income model impact individuals’ pension plans in Denmark? The master’s thesis will answer this question by modeling pension forecasts. The need for such assessment has shown persistent growth in recent years due to the shift in risk. It is now born by the individual rather than the pension funds. The paper begins with an introduction to the Danish pension system and a presentation of the new common investment assumptions connected with pension forecasting. Other studies find the new investment assumptions decrease expected coverage ratios and it seems more important than ever to build a reliable model to forecast pension savings. In the master’s thesis, pension savings are forecasted for three stereotypical individuals within three riskprofiles. To evaluate changes to the model, a baseline case is created which reflects the current forecasting model. The baseline case reveals high coverage ratios in all scenarios. However, the baseline case relies on an unrealistic static income pattern. To improve the model, an implementation of a stochastic lifecycle income model is made. Through analyses, the lifecycle income model is found to have a hump-shaped pattern that can be expressed by a cubic equation. The model implies the average income increases to a factor 1.80 at age 52 and decreases by 7% at retirement. By adding more accurate and sophisticated income assumptions, our analysis shows how coverage ratios decrease relative to the baseline case. As a consequence of volatile income patterns, the standard deviation of the wealth and pension distributions increase. Furthermore, the more comprehensive model concludes on several aspects of pension forecasting. Through a sensitivity analysis, changes in contribution rates are shown to have a lower impact on total annual pension than changes in real returns. Thus, the effect of compounded interest seems to outperform the effect of contributions. Additionally, the hump-shaped income causes the effect of retiring 5-years before the official age to be significantly worse than postponing pension contributions five years. To put the findings into perspective, the master’s thesis discusses the political proposal of early retirement. Conclusively, the answer lies in a personal expectation to future consumption. If a hump-shaped income pattern is assumed, the average low-income individual will have to decrease consumption habits by up to 30 % if retiring five years before the age of 72. The decrease in consumption must be increased with higher income, and it must be expected a high-income individual should contribute to a private pension saving if early retirement is desired.

EducationsMSc in Finance and Investments, (Graduate Programme) Final Thesis
Publication date2019
Number of pages102
SupervisorsHenrik Ramlau-Hansen