Pension Plan Members Research Articles

Policy Forum: Pensions, Retirement Incentives, and the Role of Inflation

This article describes the role of wage and price inflation for the retirement plans and well-being of registered pension plan members. The federal Public Service Pension Plan is used as an example to illustrate how wage and price inflation can be accounted for in pension design. Alternative scenarios illustrate the importance of pension plan provisions for the standard of living afforded retirees as well as incentives to delay retirement and continue working at older ages.

Optimal investment strategy for the DC pension plan based on jump diffusion model and S-shaped utility

In this paper, we study the optimal investment strategy for a defined contribution pension plan under the jump diffusion model and S-shaped utility. We assume that pension plan members can invest their pension fund in the financial market consisting of a risk-free asset and a risk asset whose price process follows a jump diffusion process. The goal of pension plan managers is to maximize the expected utility of the real terminal wealth under the jump diffusion model and S-shaped utility. We apply Lagrange dual method, concavification technique and martingale method to derive the closed-form expressions of the optimal wealth process and the optimal investment strategy. Finally, we also try to use some numerical analysis to explain the impacts of model parameters on the optimal terminal wealth value and trading strategy.

Socioeconomic differentials in mortality: implications on index-based longevity hedges

In this paper, we address the mortality modeling needs for pension plan sponsors who wish to use index-based solutions to mitigate their longevity risk exposures. Specifically, we propose the three-way Li-Lee (TWLL) model, which enforces a certain extent of coherence between the population to which the index-based hedging instrument is linked and the population of pension plan members, and at the same time incorporates the empirical fact that mortality improvement rates of different socioeconomic subgroups in the pension plan are persistently different. We further develop a delta longevity hedging strategy that is compatible with the TWLL model. With the aid of real mortality data, we demonstrate that if persistent socioeconomic differentials in mortality improvement rates exist but are not considered in an index-based longevity hedge, the performance of the hedge could be compromised, and the extent of underperformance would depend on the distributions of pension plan members and pension amounts across different socioeconomic subgroups. This problem can be alleviated if the longevity hedge is calibrated on the basis of the TWLL model.

Asset allocation for a DC pension plan with learning about stock return predictability

<p style='text-indent:20px;'>This paper investigates an optimal investment problem for a defined contribution pension plan member who receives a stochastic salary, and considers inflation risk and stock return predictability. The member aims to maximize the expected power utility from her terminal real wealth by investing her pension account wealth in a financial market consisting of a risk-free asset, an inflation-indexed bond and a stock. The expected excess return on the stock can be predicted by both an observable predictor and an unobservable predictor, and the member has to estimate the unobservable predictor by learning the history information. By using the filtering techniques and dynamic programming approach, the closed-form optimal investment strategy and the corresponding value function are derived. Finally, with the help of numerical analysis, we explore the impact of model parameters on the optimal investment strategy, and analyze the welfare benefits from leaning and using inflation-indexed bond to hedge the stock return predictors.</p>

Public pension reform and the 49th parallel: Lessons from Canada for the U.S.

AbstractPublic employee pension systems around the world show remarkable diversity in design and execution. Among these, the U.S. defined benefit public pension system has drawn increased attention because of questions about the long‐term sustainability of many of the underlying pension funds – as well as concerns of equity between pension plan members, retirees, taxpayers, bondholders, and users of public services. The Covid‐19 pandemic introduced new fissures in state and local government finances, heightening the need to bolster long‐term public pension fund robustness. As an alternative model, the Canadian public pension system is widely respected. This was not foreordained. The authors trace difficult decisions undertaken in Canada in the 1980s and 1990s along with essential descriptive features of the Canadian Model. Using a novel primary dataset, the authors benchmark the 25 largest U.S. plans against their ten largest Canadian peers, exploring key issues in a paired analysis. The authors extract fundamental lessons from the Canadian experience, proposing a roadmap for reform of the U.S. public pension system. They argue that long‐term pension sustainability, once politically prioritized, must be built on equity and discipline in plan design, funding, and amortization of existing deficits. They emphasize the importance of legal framework, particularly joint sponsorship, alongside enhanced governance and unified legislation. They also draw lessons from the Canadian experience with respect to enhanced investment organizations and investment strategies.

Public Pension Reform and the 49th Parallel: Lessons from Canada for the U.S.

Public employee pension systems around the world show remarkable diversity in design and execution. Among these, the U.S. defined benefit public pension system has drawn increased attention because of questions about the long-term sustainability of many of the underlying pension funds – as well as concerns of equity between pension plan members, retirees, taxpayers, bondholders, and users of public services. The Covid-19 pandemic introduced new fissures in state and local government finances, heightening the need to bolster long-term public pension fund robustness. As an alternative model, the Canadian public pension system is widely respected. This was not foreordained. The authors trace difficult decisions undertaken in Canada in the 1980s and 1990s along with essential descriptive features of the Canadian Model. Using a novel primary dataset, the authors benchmark the 25 largest U.S. plans against their ten largest Canadian peers, exploring key issues in a paired analysis. The authors extract fundamental lessons from the Canadian experience, proposing a roadmap for reform of the U.S. public pension system. They argue that long-term pension sustainability, once politically prioritized, most be built on equity and discipline in plan design, funding, and amortization of existing deficits. They emphasize the importance of legal framework, particularly joint sponsorship, alongside enhanced governance and unified legislation. They also draw lessons from the Canadian experience with respect to enhanced investment organizations and investment strategies.

DETERMINISTIC INVESTMENT STRATEGY IN A DC PENSION PLAN WITH INFLATION RISK UNDER MEAN-VARIANCE CRITERION

This paper studies an optimal deterministic investment problem for a DC pension plan member with inflation risk. We describe the price processes of the inflation-indexed bond and the stock by a continuous diffusion process and a jump diffusion process with random parameters, respectively. The contribution rate linked to the income of the DC plan member is assumed to be a non-Markovian adapted process. Under the mean-variance criterion, we use Malliavin calculus to derive a characterization for the optimal deterministic investment strategy. In some special cases, we obtain the explicit expressions for the optimal deterministic strategies.

On Application of Matlab on Efficient Portfolio Management for a Pension Plan in the Presence of Uneven Distributions of Accumulated Wealth

In this paper, we solved the problem encountered by a pension plan member whose portfolio is made up of one risk free asset and three risky assets for the optimal investment plan with return clause and uneven distributions of the remaining accumulated wealth. Using mean variance utility function as our objective function, we formulate our problem as a continuous-time mean–variance stochastic optimal control problem. Next, we used the variational inequalities methods to transform our problem into Markovian time inconsistent stochastic control, to determine the optimal investment plan and the efficient frontier of the plan member. Using mat lab software, we obtain numerical simulations of the optimal investment plan with respect to time and compare our results with an existing result.

Robust portfolio choice for a DC pension plan with inflation risk and mean-reverting risk premium under ambiguity

This paper investigates a robust optimal portfolio choice problem for a defined contribution (DC) pension plan member. The member worries about model ambiguity and aims to seek robust optimal investment strategies. Specifically, the member has a stochastic salary, considers inflation risk and invests her pension account wealth into a financial market consisting of a risk-free asset, an inflation-indexed bond and a stock whose expected return rate follows a mean-reverting process. By using the dynamic programming approach, the robust optimal investment strategy and the corresponding value function are explicitly derived, and subsequently a verification theorem is provided. Furthermore, two special cases of our portfolio model are discussed. Finally, a numerical example is presented to reveal economic implications of our theoretical results and to illustrate the effects of the model parameters on the robust optimal investment strategy. We find that ambiguity about the dynamics of the inflation-indexed bond price and the stock price and expected return rate has different influences on the robust optimal investment strategy, and that neglecting ambiguity will always lead to utility loss.

On the Effect of Inflation and Impact of Hedging on Pension Wealth Generation Strategies under the Geometric Brownian Motion Model

This work investigates the effect of Inflation and the impact of hedging on the optimal investment strategies for a prospective investor in a DC pension scheme, using inflation-indexed bond and inflation-linked stock. The model used here permits the plan member to make a defined contribution, as provided in the Nigerian Pension Reform Act of 2004. The pension plan member is allowed to invest in risk-free asset (cash), and two risky assets (i.e., the inflation-indexed bond and inflation-linked stock). A stochastic differential equation of the pension wealth that takes into account certain agreed proportions of the plan member’s salary, paid as contribution towards the pension fund, is constructed and presented. The Hamilton-Jacobi-Bellman (H-J-B) equation, Legendre transformation, and dual theory are used to obtain the explicit solution of the optimal investment strategies for CRRA utility function. Our investigation reveals that the inflation have significant negative effect on wealth investment strategies, particularly, the RRA(w) is not constant with the investment strategy, since the inflation parameters and coefficient of CRRA utility function have insignificant input on the investment strategies, and also the inflation-indexed bond and inflation-linked stock has a positive damping effect (hedging) on the severe effect of inflation.

Mean-variance investment strategy with proportional transaction costs and withdrawal process for a defined contribution pension scheme

In this paper, we consider an extension of the Markowitz portfolio and investment problem in which transaction costs are incurred; contributions and withdrawals are made by the pension plan members (PPMs) in the investment portfolio. The transaction costs are modelled as a proportion of the value of risky assets transacted. The aims of this paper are to: a) minimise the investment risks; b) minimise the contribution risks and simultaneously maximise amount of contributions; c) strategically minimise the amount of withdrawal by the PPMs. The optimal portfolio, contributions and withdrawal processes, with proportional transaction costs were obtained. Some numerical results are also presented in this paper.

Mean-variance investment strategy with proportional transaction costs and withdrawal process for a defined contribution pension scheme

In this paper, we consider an extension of the Markowitz portfolio and investment problem in which transaction costs are incurred; contributions and withdrawals are made by the pension plan members (PPMs) in the investment portfolio. The transaction costs are modelled as a proportion of the value of risky assets transacted. The aims of this paper are to: a) minimise the investment risks; b) minimise the contribution risks and simultaneously maximise amount of contributions; c) strategically minimise the amount of withdrawal by the PPMs. The optimal portfolio, contributions and withdrawal processes, with proportional transaction costs were obtained. Some numerical results are also presented in this paper.

On the Modified Optimal Investment Strategy for Annuity Contracts under the Constant Elasticity of Variance (CEV) Model

In this work, the optimal pension wealth investment strategy during the decumulation phase, in a defined contribution (DC) pension scheme is constructed. The pension plan member is allowed to invest in a risk free and a risky asset, under the constant elasticity of variance (CEV) model. The explicit solution of the constant relative risk aversion (CRRA) and constant absolute risk aversion (CARA) utility functions are obtained, using Legendre transform, dual theory, and change of variable methods. It is established herein that the elastic parameter, β, say, must not necessarily be equal to one (β ≠ 1). A theorem is constructed and proved on the wealth investment strategy. Observations and significant results are made and obtained, respectively in the comparison of our various utility functions and some previous results in literature.

Factors Affecting the Development of Voluntary Pension Schemes in CEE Countries: A Panel Data Analysis

AbstractThe study provides some quantitative information on voluntary pension plans in 10 CEE countries obtained from various local sources. The comparative analysis shows that there is a considerable variation in this group in terms of participation and contributions to the voluntary pension plans. In addition, this study empirically examines several factors that can possibly affect the development of voluntary pensions: income per capita and poverty rate, income inequality, replacement rate from the pension system, education attainment, interest rate and demographic burden. It uses a panel regression framework for the period of 2006–2014. The results reveal that, in the case of participation in voluntary pension plans, only income level per capita is associated with a greater number of pension plan members. As far as contributions are concerned, education seems to be the most important determinant of additional pension savings. Other factors do not seem to explain well both of the studied variables reflecting the development of voluntary pension schemes. However, as individual fixed effects are proven to be significant in the estimated models, one could conclude that country-specific characteristics play a significant role in explaining the development of voluntary pension schemes. They can be referred to the design and parametric settings of the non-mandatory pension system.

Optimal Surplus and Minimum Benefits for a Defined Contribution Pension Plan: a Mean-variance Approach

In this paper, we study a mean-variance portfolio selection problem, optimal surplus, minimum pension benefits (MPB) and consumption plan of a defined contribution pension scheme. The problem is formulated as a tri-objective stochastic problem of mean-variance techniques. The problem is solved using dynamic programming approach. The aim of the fund manager is to maximize pension plan member’s (PPM) expected MPB and expected surplus, and at the same time minimize the consumption and portfolio risks. We find the efficient frontier to be nonlinear and parabolic in shape. We further show that the optimal portfolio depend linearly on consumption plan and linearly on MPB. The aggregate optimal pension benefits accrued to a plan member at retirement and life-time consumption of the plan member are obtained. Some numerical illustration of our results were determined.

Engagement with Retirement Savings: It Is a Matter of Trust

People who engage with their retirement savings are more likely to opt out of unsuitable defaults. We use cluster analysis of matched survey and administrative data to identify groups of pension plan members that are alike in their attitudes toward retirement saving. We find that engaged and disengaged members segregate into groups based on their interest and trust. Group membership in turn helps predict plan engagement, as proxied by nondefault choices. Specifically, engagement is stronger among interested groups. Trust, however, has a more complex relationship with engagement, particularly as it interacts with interest. While members with low interest and high trust are less likely to engage (e.g., by not checking plan performance), less trusting members engage more (e.g., by actively choosing asset allocations). As interest and trust successfully determine group membership, and ultimately engagement, pension plan providers should address members' diverse needs and circumstances with personalized approaches.

OPTIMAL INVESTMENT AND OPTIMAL ADDITIONAL VOLUNTARY CONTRIBUTION RATE OF A DC PENSION FUND IN A JUMP-DIFFUSION ENVIRONMENT

This paper considers an optimal investment and an optimal additional contribution rate of a pension plan member (PPM) who faces both diffusion and jump risks in a defined contribution (DC) pension plan. We put into consideration three background risks which include interest rate, investment and salary risks. The stock prices, interest rate and salary process of a PPM are allowed to follow a jump-diffusion process. A PPM is expected to make two kind of contributions: compulsory and additional voluntary contributions. The compulsory one is a fixed proportion of a PPM's salary and the additional one is voluntary which is time and interest rate dependent. The aims of the investor is to determine the optimal investment and optimal contribution rate in a jump-diffusion environment. In order to obtain the optimal investment and optimal contribution rate, the resulting wealth process was transformed into Hamilton–Jacobi–Bellman equation by the method of dynamic programming. As a result, the optimal investment and optimal contribution rate of a PPM were obtained. Furthermore, some empirical analyses were conducted and results obtained. We found that the optimal investment ultimately depend on stocks diffusion and jump risks, interest rate and salary risks, optimal contribution rate and the salary process. The contribution rate of a PPM was found to depend on the investment strategies, salary process and interest rate risks, salary and its growth rate and CRRA coefficient. We also found that the contribution rate depends inversely on the salary process of a PPM over time.

Equilibrium Investment Strategy for a DC Plan With Partial Information and Mean–Variance Criterion

This paper studies a mean–variance portfolio selection problem with partial information for a defined-contribution (DC) pension scheme. We assume that the DC pension plan member can only observe the price of the risky asset but not the appreciation rate of it in the financial market. Moreover, inflation risk and salary risk are taken into account in our model. First, by virtue of the filtering theory, we transform the partially observable mean–variance portfolio selection problem to a completely observable one. Then, to look for an equilibrium investment strategy, we formulate and tackle the mean–variance problem within a game theoretic framework. By solving an extended Hamilton–Jacobi–Bellman (HJB) system of equations, closed-form expressions of the equilibrium investment strategy and corresponding equilibrium value function with partial information are derived for the DC pension plan. In addition, some numerical illustrations are provided to show the effects of parameters on the derived equilibrium investment strategies and the efficient frontier.

Optimal pension fund management in a jump–diffusion environment: Theoretical and empirical studies

This paper considers a theoretical and an empirical study of an optimal pension fund in an inflation environment in which the consumption–portfolio selection problem of an investor who faces both diffusion and jump risks was analyzed. Since the time horizon of a pension fund management is relatively long, we put into consideration four background risks which include inflation, interest rate, investment and income risks. A pension plan member (PPM) is expected to contribute continuously a time-consistent proportion of his income into the scheme. These contributions are invested into a market that is characterized by multiple risk-free assets (which include riskless bonds and bank deposit accounts), stocks and index bonds. The risky assets (stocks and index bonds), interest rates and income process are assumed to follow a jump–diffusion process. Real wealth for the plan member is considered. The resulting Hamilton–Jacobi–Bellman equation was solved using dynamic programming approach. From which, the optimal consumption and optimal investments with jump risks were obtained. Empirical data were collected from Nigeria Stock Exchange; National Bureau of Statistics, Nigeria; and Bursary Department, University of Benin, Nigeria. The analyses of the data were carried out using SPSS package in order to obtain the needed information for the parameters in our derived models. The resulting models for optimal portfolio and consumption were solved using MatLab and Mathematica software. We found that inflation, interest rate and income risks have significant influence on the investor’s portfolio values in the risky assets. We also found that as the risk averse coefficient increases, consumption increases and vice versa. Furthermore, we found that an increase in income can lead to an increase in the portfolio risks and vice versa.

Asset allocation under loss aversion and minimum performance constraint in a DC pension plan with inflation risk

In this paper we investigate an optimal investment strategy for a defined-contribution (DC) pension plan member who is loss averse, pays close attention to inflation and longevity risks and requires a minimum performance at retirement. The member aims to maximize the expected S-shaped utility from the terminal wealth exceeding the minimum performance by investing her wealth in a financial market consisting of an indexed bond, a stock and a risk-free asset. We derive the optimal investment strategy in closed-form using the martingale approach. Our theoretical and numerical results reveal that the wealth proportion invested in each risky asset has a V-shaped pattern in the reference point level, while it always increases in the rising lifespan; with a positive correlation between salary and inflation risks, the presence of salary decreases the member’s investment in risky assets; the minimum performance helps to hedge the longevity risk by increasing her investment in risky assets.