Optimal Retirement Savings Under Uncertainty: A Monte Carlo Analysis of Lifecycle Portfolios and Value-at-Risk Metrics

Abstract

This thesis investigates how life-cycle based investment strategies perform within the Danish market-rate pension system, where individuals increasingly bear the financial risk of retirement. The study models thousands of stochastic life trajectories using a Monte Carlo framework that combines the Heston model for equity returns and the Vasicek model for interest rates, thereby realistically reflecting long-term market uncertainty. The key objective is to evaluate how fixed pension contribution levels and varying risk profiles impact both the expected and worst-case replacement rate—defined as retirement income relative to final salary. A central analytical tool is Value-at-Risk, which is used not to estimate the probability of falling below a target, but to identify the lower tail of possible outcomes, thereby highlighting how poorly a given strategy can perform under adverse market conditions. This allows for a nuanced assessment of downside risk across income groups. Due to unresolved errors in the simulation code, no numerical results were produced, and the subsequent analysis is therefore based solely on the theoretical structure of the model. The findings reveal that low-income individuals are less exposed to downside financial risk due to the stabilizing role of the public pension, which is means-tested and largely independent of capital market outcomes. This buffering effect means they can, in many cases, tolerate higher investment risk. In contrast, middle- and high-income earners rely more heavily on private pension savings to reach their retirement goals, making them more vulnerable to poor investment returns. The thesis concludes that tailored life-cycle strategies—sensitive to market dynamics, income level, and public pension interactions—can significantly improve the likelihood of achieving satisfactory pension outcomes. These strategies offer a robust framework for goal-based pension planning in an increasingly individualized and uncertain financial environment.