Optimal Retirement Planning: Scenario Generation, Preferences, and Objectives

The global trend of shifting from defined benefit (DB) to defined contribution (DC) workplace pension plans is putting growing pressure on individuals to take more ownership in retirement planning and financial decision-making. The essence of the DB is the life-long income guarantee, which requires limited financial planning decisions to be made, either in the accumulation or decumulation phase. The DC on the other hand, is significantly more complex. The lump sum payment at retirement burdens individuals with the task of income generation, in the presence of challenges stemming from an uncertain future lifetime, economic conditions, and evolving consumption needs. The average retiree has limited competency to navigate these challenges, due to low financial literacy, lack of willpower, or deteriorating cognitive abilities with older ages. The high stake of these challenges calls for a normative solution to be proposed – a solution that considers the intricacy of risks, preferences, and normative objective formulations. The objective of this thesis is to explore such a solution. This thesis comprises three inter-related research directions: long-term economic scenario generators (ESGs), recursive preferences in life-cycle portfolio selection, and retirement objective formulation. A brief description of the subsequent chapters will now follow. The first chapter conducts a review of Wilkie’s ESG, with analysis restricted to series pertinent to retirement planning. Our main findings indicate that there exist challenges in modelling long-term economic series due to the presence of multiple structural shifts in the historical time series. Consequently, certain assumptions of stationarity are violated, and parameters are sensitive to the calibration period. A backtest based on 30-year out-ofsample data indicated that over that period the model had tended to overestimate inflation, underestimate total return on stocks, and performed relatively well for long-term interest rates. Additionally, Wilkie’s ESG can be under-representative of the risk in long-term stock investment, particularly in the tails. The second chapter provides an introductory discussion of Epstein-Zin preferences, which are adopted in the succeeding chapter as a normative preference model. The purpose is to first investigate the implied optimal behaviour and its plausibility. We pay particular attention to whether the output leads to plausible behaviour given the context of retirement planning. Specifically, analytical solutions for a simple consumption problem are derived, isolating the impact of relative risk aversion (RRA), elasticity of intertemporal substitution (EIS), time discounting, and risks stemming from mortality, investment, and inflation. We investigate three Epstein-Zin models employed in the literature, which differ in their treatment of mortality risk, and find that some lead to normatively implausible solutions. Importantly, we find that the EIS is not always monotone in its effect on consumption volatility over time, meaning that its interpretation can be ambiguous when considering an uncertain future lifetime. This has been misinterpreted in the literature to date. We also show that one particular Epstein-Zin specification is not necessarily a generalization of expected utility maximization under constant relative risk aversion, as many works wrongly