Extending Life Cycle Models of Optimal Portfolio Choice

Extending Life Cycle Models of Optimal Portfolio Choice
Author:
Publisher:
Total Pages: 31
Release: 2009
Genre: Portfolio management
ISBN:

This paper derives optimal life cycle portfolio asset allocations as well as annuity purchases trajectories for a consumer who can select her hours of work and also her retirement age. Using a realistically-calibrated model with stochastic mortality and uncertain labor income, we extend the investment universe to include not only stocks and bonds, but also survival-contingent payout annuities. We show that making labor supply endogenous raises older peoples' equity share; substantially increases work effort by the young; and markedly enhances lifetime welfare. Also, introducing annuities leads to earlier retirement and higher participation by the elderly in financial markets. Finally, if we allow for an age-dependent leisure preference parameter, this fits well with observed evidence in that it generates lower work hours and smaller equity holdings at older ages as well as sensible retirement age patterns.

Optimal Portfolio Choice with Health-Contingent Income Products

Optimal Portfolio Choice with Health-Contingent Income Products
Author: Shang Wu
Publisher:
Total Pages: 41
Release: 2016
Genre:
ISBN:

Whereas there is ample evidence that life-contingent income products (life annuities) have the potential to improve individual welfare, combining them with health-contingent income products (resulting in so-called life care annuities) would serve to further increase welfare for individuals who are exposed to uncertain out-of-pocket healthcare expenditure later in life. We develop a life-cycle model of annuitization, consumption, and investment decisions for a single retired individual who faces stochastic capital market returns, uncertain health status, differential mortality risks, and uncertain out-of-pocket healthcare expenditure with cost of dying. Using the calibrated model, we show that individuals who are eligible to purchase life care annuities instead of standard life annuities increase their level of annuitization by around 12 percentage points. Health status at retirement affects the extent to which the insurance feature and the pricing advantage of life care annuities contribute to this increment, with end-of-life healthcare expenditure being of particular importance. Also, life care annuities allow individuals to consume more throughout their retirement and to invest a higher proportion of their liquid wealth in the risky asset. They are willing to pay a loading up to 21% for having access to life care annuities.

Optimal Retirement Planning

Optimal Retirement Planning
Author: Saisai Zhang
Publisher:
Total Pages: 254
Release: 2018
Genre: Finance, Personal
ISBN:

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-of-sample 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 claim. The third chapter investigates the normative validity of the optimal consumption and investment strategies of a discrete-time Epstein-Zin utility maximizing DC retiree who wishes to benefit from stock investment, longevity insurance, and inflation protection. A comparison of three Epstein-Zin specifications is conducted. We use a combination of qualitative and quantitative criteria to evaluate the adequacy of the optimal consumption profile, with special attention paid to the downside risk at extreme old ages. We find that it remains optimal to fully annuitize, but agents with high relative risk aversion hold precautionary savings, the level of which is impacted by the EIS and the preference specification. As discussed in the preceding chapter, the interpretation of EIS on consumption volatility is found to be ambiguous. Investigations of the optimal consumption profile reveal that agents are exposed to relatively high levels of downside risk in the long run. This is partially attributed to a time discounting factor less than 1, which implicitly (and contradictorily) assumes myopia in normative decision-making. An investigation of zero time discounting is conducted, with downside risk found be to significantly reduced in the long run. The fourth chapter focuses on retirement objective formulation. This chapter is motivated by the unsatisfactory normative solutions found in the preceding chapter under mathematically convenient objective functions. In order to develop more actionable prescriptive solutions, we seek to holistically explore actual retirement decision-making. To this end, we conduct a survey study of 1,000 Canadian (pre-)retirees age 50 to 80, on topics of retirement consumption, wealth, income, risk perception, decision making, and planning objectives. Additionally, we investigate the descriptive validity of the expected lifetime discounted utility maximization framework in predicting optimal planning behaviours. Overall, there is overwhelming evidence of heterogeneity in wealth, income, concerns, and objectives. We find a prevalence of low retirement assets, a severe underestimation of survival probabilities to an extreme old age of 95, and a strong aversion toward life annuities. Pre-retirees appear to have reasonable expectations regarding income and assets in retirement, with the median retiree relying heavily on public pension sources. (Pre-)retirees are primarily concerned with liquidity needs, consumption smoothing, inflation, and longevity in retirement, and are least concerned with bequests. We elicited risk and time preferences, and found an average RRA parameter between 1.74 to 2.48 for pre-retirees and 2.48 to 3.74 for retirees, and a median subjective time discount factor of 0.997. A study of decision-making under risky scenarios reveals dramatic differences between the actual and implied choices under the expected utility maximization framework. Particularly, in the presence of inflation risk, agents lack the understanding of the long-term cumulative impact of inflation on the cost of living. In the presence of investment risk, the upside gain drives decision-making, and the presence of minimum income protection effectively provided by public pension income induces more risk-taking behaviour. The last chapter concludes the thesis, and proposes general directions for future work in retirement planning research.

Investing Retirement Wealth

Investing Retirement Wealth
Author: John Y. Campbell
Publisher:
Total Pages: 49
Release: 2010
Genre:
ISBN:

If household portfolios are constrained by borrowing and short-sales restrictions asset markets, then alternative retirement savings systems may affect household welfare by relaxing these constraints. This paper uses a calibrated partial-equilibrium model of optimal life-cycle portfolio choice to explore the empirical relevance of these issues. In a benchmark case, we find ex-ante welfare gains equivalent to a 3.7% increase in consumption from the investment of half of retirement wealth in the equity market. The main channel through which these gains are realized is that the higher average return on equities permits a lower Social Security tax rate on younger households, which helps households smooth their consumption over the life cycle. There is a smaller welfare gain of 0.5% of consumption when Social Security tax rates are held constant. We also find that realistic heterogeneity of risk aversion and labor income risk can strongly affect optimal portfolio choice over the life cycle, which provides one argument for a privatized Social Security system with an element of personal portfolio choice.

Strategic Financial Planning Over the Lifecycle

Strategic Financial Planning Over the Lifecycle
Author: Narat Charupat
Publisher: Cambridge University Press
Total Pages: 383
Release: 2012-05-28
Genre: Business & Economics
ISBN: 0521764564

This is a final-year college level textbook on personal finance, jointly written by business school and mathematics professors. It is aimed at a wide audience of people who are interested in wealth management from a more rigorous perspective. It may be used in both personal applications and professional classrooms.

Life Insurance and Pension Contracts I

Life Insurance and Pension Contracts I
Author: Knut K. Aase
Publisher:
Total Pages: 52
Release: 2014
Genre:
ISBN:

We analyze optimal consumption in the life cycle model by introducing life and pension insurance contracts. The model contains a credit market with biometric risk, and market risk via risky securities. This idealized framework enables us to clarify important aspects life insurance and pension contracts. We find optimal pension plans and life insurance contracts where the benefits are state dependent. We compare these solutions both to the ones of standard actuarial theory, and to policies offered in practice. Implications of this include what role the insurance industry may play to improve welfare. The relationship between substitution of consumption and risk aversion is highlighted in the presence of a consumption puzzle. One problem related portfolio choice is discussed - the horizon problem. Finally, we present some comments on longevity risk and cohort risk.

Optimal Consumption and Life Insurance Under Shortfall Aversion and a Drawdown Constraint

Optimal Consumption and Life Insurance Under Shortfall Aversion and a Drawdown Constraint
Author: Xun Li
Publisher:
Total Pages: 0
Release: 2022
Genre:
ISBN:

This paper studies a life-cycle optimal portfolio-consumption problem when the consumption performance is measured by a shortfall aversion preference subjecting to an additional drawdown constraint on consumption rate. Meanwhile, the agent also dynamically chooses her life insurance premium to maximize the expected bequest at the death time. By using dynamic programming arguments and the dual transform, we solve the HJB variational inequality explicitly in a piecewise form across different regions and derive some thresholds of the wealth variable for the piecewise optimal feedback controls. Taking advantage of our analytical results, we are able to numerically illustrate some quantitative impacts on optimal consumption and life insurance by model parameters and discuss their financial implications.