Defined Benefit Pension Funds Research Articles

Liability-driven investment for pension funds: stochastic optimization with real assets

Using a multi-stage stochastic programming method, we suggest an optimal liability-driven investment (LDI) strategy for a closed defined-benefit pension fund including real assets. The objective is to jointly optimize contribution, funding ratio, and buyout cost, subject to a constraint on downside risk in terms of expected shortfall of assets relative to liabilities. Over a 10-year planning horizon, the optimal LDI strategy with a key-rate duration-matching bond portfolio outperforms the corresponding strategy with a duration-convexity matching bond portfolio as well as a strategy with an aggregate bond index-tracking portfolio. When real assets are introduced, the optimal LDI strategy includes significant investment in infrastructure and real estate, illiquidity notwithstanding. Nevertheless, delays in sales of real assets induced by illiquidity can increase downside risk.

Solvency and performance persistence of defined benefit private and public pension plans

PurposeThis study aims to examine the solvency and performance persistence of defined benefit private and public pension plans (DBPPs) in the Republic of Congo.Design/methodology/approachThe authors use the 2 × 2 contingency table approach and the time product ratio (TPR)-based cross-product ratio (CPR) on data covering ten years from 2011 to 2020, with variable funded ratios and excess returns, to determine the solvency and performance persistence of defined benefit pension plans.FindingsThe authors document a lack of solvency and performance persistence in DBPP funds. They conclude that the solvency and performance of DBPP funds are not repetitive. The previous year's private and public defined benefit pension funds’ results do not repeat in the current year. Hence, the current solvency and performance of defined benefit pension funds are not good predictors of future funds' solvency and performance.Originality/valueTo the best of the authors’ knowledge, this study is the first to combine solvency and performance to examine the persistence of defined benefit pension plans in sub-Saharan Africa.

Assessing the Efficiency of Defined Benefit Private and Public Pension Plans using Data Envelopment Analysis Adjusted Estimator

This study uses data envelopment analysis (DEA) adjusted estimator to assess the efficiency of defined benefit private and public pension plans in the Republic of Congo. We also incorporate the industry fund in the assessment. The authors apply constant return to scale (CRS) adjusted estimator input and output orientation. In input orientation, we intellectualize efficiency as the ability of defined benefit pension funds to reduce costs, whereas assets remain constant. In output orientation, we conceive efficiency as raising the return on investment in existing contribution, administrative, and investment cost capacities. CRS-adjusted scores depict that the defined benefit private pension fund is on the efficient frontier regarding its input and output. The defined benefit public and industry pension funds are off the efficient frontier. Hence the private sector ranked first, is more efficient than the public sector, ranked third. The industry sector is less efficient compared to the private sector but more efficient than the public sector. As far as efficiency studies are concerned, this study is the first in sub-Saharan Africa to use the DEA-adjusted estimator to assess the efficiency of defined benefit pension funds.

Optimal chance-constrained pension fund management through dynamic stochastic control

We apply a dynamic stochastic control (DSC) approach based on an open-loop linear feedback policy to a classical asset-liability management problem as the one faced by a defined-benefit pension fund (PF) manager. We assume a PF manager seeking an optimal investment policy under random market returns and liability costs as well as stochastic PF members’ survival rates. The objective function is formulated as a risk-reward trade-off function resulting in a quadratic programming problem. The proposed methodology combines a stochastic control approach, due to Primbs and Sung (IEEE Trans Autom Control 54(2):221–230, 2009), with a chance constraint on the PF funding ratio (FR) and it is applied for the first time to this class of long-term financial planning problems characterized by stochastic asset and liabilities. Thanks to the DSC formulation, we preserve the underlying risk factors continuous distributions and avoid any state space discretization as is typically the case in multistage stochastic programs (MSP). By distinguishing between a long-term PF liability projection horizon and a shorter investment horizon for the FR control, we avoid the curse-of-dimensionality, in-sample instability and approximation errors that typically characterize MSP formulations. Through an extended computational study, we present in- and out-of-sample results which allows us to validate the proposed methodology. The collected evidences confirm the potential of this approach when applied to a stylized but sufficiently realistic long-term PF problem.

Defined benefit pension de-risking strategy: determinants of pension buy-ins

ABSTRACT Many firms have sought to de-risk their pension provision by closing or freezing their defined benefit (DB) pension plans. This shifts future pension risk onto employees, but it does not de-risk the firm’s existing obligations. Pension buy-ins and buy-outs, which are a form of insurance, have become an established option for de-risking such obligations in several developed economies. This paper investigates the influence on pension buy-in transactions of the degree of risk associated with a firm’s DB pension obligations and, because of the substantial costs involved, the sponsor firm’s financial position. We employ hand-collected data between 2007 and 2017 to examine how pension fund and firm financial characteristics are related to both the occurrence and timing of buy-ins. Using probit analysis of UK FTSE 350 firms and a wide range of robustness checks, the findings show that firms that sponsor riskier DB pension funds, associated with higher investment risk and longer investment horizon, are more likely to engage in a pension buy-in transaction. We also find evidence that firms with greater financial slack are more likely to engage in buy-ins. Survival analysis reveals that those characteristics also tend to be significant influences upon the timing of buy-in transactions. Our study contributes to the literature on risk management in general and the literature on pension de-risking in particular, and it paves the way for research on pension buy-ins and buy-outs in other countries. Implications for firms with DB pension obligations and the insurance companies that offer pension buy-ins are identified.

What determines the asset allocation of defined benefit pension funds?

ABSTRACT The asset allocation decision is one of the most important decisions made by defined benefit pension schemes, with a major effect on the scheme contribution rate, funding ratio and financial position of the sponsoring company. We investigate the determinants of the equity allocation of UK pension funds using a panel of 1,304 observations on 125 companies that were members of the FTSE 100 over the 2003–2019 period. We find that seven variables have a significant effect on the allocation between equities and bonds – maturity (as measured by the effective duration of scheme liabilities), default risk, leverage of the sponsor, size of the sponsor (or the scheme), whether the scheme is closed to future contributions, whether the scheme has significant overseas liabilities, and a time trend. Our sensitivity analysis finds that the biggest effects on the asset allocation come from scheme maturity, the scheme’s funding ratio and a time trend.

Stochastic modeling of assets and liabilities with mortality risk

ABSTRACT This paper describes a general approach for the stochastic modeling of assets returns and liability cash-flows of a typical pensions insurer. On the asset side, we model the investment returns on equities and various classes of fixed-income instruments including short- and long-maturity fixed-rate bonds as well as index-linked and corporate bonds. On the liability side, the risks are driven by future mortality developments as well as price and wage inflation. All the risk factors are modeled as a multivariate stochastic process that captures the dynamics and the dependencies across different risk factors. The model is easy to interpret and to calibrate to both historical data and to forecasts or expert views concerning the future. This feature is particularly useful in unprecedented circumstances like pandemics when historical data alone does not give a reasonable description of the future. The simple structure of the model allows for efficient computations. The construction of a million scenarios takes only a few minutes on a personal computer. The approach is illustrated with an asset-liability analysis of a defined benefit pension fund, pre- and post-COVID-19.

Liability-Driven Investment for Pension Funds: Stochastic Optimization with Real Assets

Using a multi-stage stochastic programming method, we suggest an optimal liability-driven investment (LDI) strategy for a closed defined-benefit pension fund including real assets. The objective is to minimize or stabilize contributions, funding ratio, buyout cost, and expected shortfall. Over a 10-year planning horizon, the optimal LDI strategy with a key-rate duration-matching bond portfolio outperforms one with a duration-convexity matching bond portfolio or an aggregate bond index-tracking portfolio in terms of the objective measures. When real assets are introduced, the optimal LDI strategy includes significant investment in infrastructure and real estate, illiquidity notwithstanding. Nevertheless, delays in sales of real assets induced by illiquidity can increase downside risk.

What Determines the Asset Allocation of UK Defined Benefit Pension Funds?

The asset allocation decision is one of the most important decisions made by defined benefit pension schemes, with a major effect on the scheme contribution rate, funding ratio and financial position of the sponsoring company. We investigate the determinants of the equity allocation of UK pension funds using a panel of 1,304 observations on 125 companies that were members of the FTSE 100 over the 2003-2019 period. We find that seven variables have a significant effect on the allocation between equities and bonds – maturity (as measured by the effective duration of scheme liabilities), default risk, leverage of the sponsor, size of the sponsor (or the scheme), whether the scheme is closed to future contributions, whether the scheme has significant overseas liabilities, and a time trend. Our sensitivity analysis finds that the biggest effects on the asset allocation come from scheme maturity, the scheme’s funding ratio and a time trend.

An Analysis of Connecticut's Public Employee Retirement Plans

The state of Connecticut runs six defined benefit pension funds for its employees, which in the aggregate are among the most poorly funded retirement plans in the country and place increasing fiscal burdens on the state budget. We use a computer model to simulate the finances of these plans, demonstrating how sensitive the plans’ funded ratios and unfunded liabilities are to changes in assumed future investment returns. Future investment returns that are well within the reasonable distribution of outcomes could produce substantially greater unfunded liabilities than even those that currently are reported. This exercise demonstrates the need for greater attention to uncertain investment returns in government analyses and financial disclosures regarding public employee pensions plans.

Estimating the effect of active management and private equity for defined benefit pension funds

We conduct a returns-based Sharpe (1988, 1992) style analysis of U.S. corporate defined benefit pension plans. The returns for corporate pension funds are reported only once per year, limiting the degrees of freedom for a returns-based style analysis. To address this problem, we introduce a “Search” method that systematically tests all possible combinations of a limited number of factors (market indices) to find the set with the highest explanatory power of historical returns. We find that pension funds exhibit significant exposure to private equity, much more so then balanced funds. We provide a new approach to measuring the relative contributions of policy and active management by using squared partial correlation coefficients to control for market movements. We find that pension funds show more active management compared to balanced funds.

PENSION FUND RESTORATION POLICY IN GENERAL EQUILIBRIUM

When the financial positions of pension funds worsen, regulations prescribe that pension funds reduce the gap between their assets (invested contributions) and their liabilities (accumulated pension promises). This paper quantifies the business cycle effects and distributional implications of various types of restoration policies. We extend a canonical New-Keynesian model with a tractable demographic structure and, as a novelty, a flexible pension fund framework. Fund participants accumulate inflation-indexed or non-indexed benefits and funding adequacy is restored by revaluing previously accumulated pension wealth (Defined Contribution (DC)) or changing the pension fund contribution rate on labor income (Defined Benefit (DB)). Economies with DC pension funds respond similarly to adverse capital quality shocks as economies without pension funds. DB pension funds, however, distort labor supply decisions and exacerbate economic fluctuations. While DB pension funds achieve intergenerational risk-sharing, welfare analyses indicate that the negative effects of the induced distortions are sizeable.

Management Strategies for the Defined Benefit Pension Fund Under Stochastic Framework

In this article, we analyze the optimal contributions and investment strategies problem for a defined benefit pension fund. The pension fund manager allocates the capital in riskless and risky assets and the dynamics of the risky asset price follows the Hull and White stochastic volatility model. The choice of the Hull and White model is due to its mean-reverting property. The stochastic dynamic programing principle is used to derive the Hamilton-Jacob-Bellman (HJB) equation. Due to the complications of the HJB when finding the closed form solution, we use the Legendre transform and dual theory to transform the primary problem into a dual one. Furthermore, we obtain the closed form solutions for optimal strategies for the logarithm utility functions by variable transformation technique. Finally, a numerical example is conducted to analyze the effects of parameters in the model and provide some economic implications. To conclude, the Hull and White stochastic volatility model shown to have a substantial impact on the optimal investment strategies and thus can be exploited appropriately to improve the final wealth of the pension fund.

Risk Budgeting and Longevity Insurance: Strategies for Sustainable Defined Benefit Pension Funds

Today, many defined benefit pension funds across the world are closing in response to twelve years of intense market volatility and dramatic increases in life expectancy. To the casual observer, it must seem as though the risk of maintaining a defined benefit pension fund has contributed to its rapid decline. Certainly, a defined benefit pension is a very significant promise for the plan sponsor, who has pledged to pay the plan participants for as long as they live and no matter what happens to the assets. The key question today is whether the defined benefit plans that remain open and accruing benefits for employees can be sustained. In fact, a sustainability model may be emerging in the best practices of a few pension plans. These plans generally have three things in common: 1. They have engaged in a rigorous risk budgeting process, involving an analysis of their risk, an estimation of the potential losses in their pension funds and a decision regarding how much they can afford to lose. 2. They have dramatically reduced their asset risk in an effort to keep pension losses within the risk budget and they may have two-thirds or more of their assets invested in a low volatility strategy such as fixed income or total return. 3. They have a strategy for longevity risk, which may involve longevity insurance to ensure that the quantum of their liability is known and knowable so that funding and investing activities can be carried out with certainty as to the ultimate liability. While these strategies may seem less exciting than using risky assets to reach for high returns, they are rooted in the premise that investing in equities, private equity, commodities, property and other risky assets actually involves risk and to the extent that those strategies expose the plan sponsor to more risk than the sponsor can afford, too much risk is likely to lead to the closure of the pension fund and the elimination of the defined benefit from the employees' future retirement security. Perhaps risk budgeting and disciplined risk management, combined with new techniques to insure longevity risk can be used to sustain more pension funds and safeguard the health of the plan sponsors.

Heterogeneity effects on the management of retirement fund

ABSTRACTThis article studies the importance of plan members’ heterogeneity to the management of defined benefit (DB) pension fund. We propose a new multi-member model of DB pension fund that allows for heterogeneity in plan members’ retirement ages, salary growths and other characteristics. We first solve analytically for optimal management strategy and show that the sponsor’s supplementary contribution and the fund’s allocation in risky assets are determined by the cross-product between the fund’s expected retirement liabilities and some heterogeneity-adjusted discount factors. We then demonstrate that the presence of heterogeneity can have a significant influence on the optimal management strategy and that a management decision made while ignoring heterogeneity will be suboptimal. The knowledge of desirable and undesirable effects of heterogeneity that we uncover in this article also provides implications to the grouping of fund members. Introducing a presence of young member whose salary is positively correlated with the risky asset and avoid stacking members with negative correlations will all help the management.

Behavioral biases and retirement assets allocation of corporate pension plans

PurposeThe purpose of this paper is to investigate the existence of behavioral biases, disposition effect and house money effect in investment decisions of defined benefit pension funds. It investigates the determinants of portfolios by examining whether pensions display risk seeking or risk aversion behavior in reaction to prior gains and losses.Design/methodology/approachThe first research question is to examine the impact of prior period’s return and αs on existing portfolio allocation in equity, debt, real estate and other assets. In order to test this relationship, four separate regressions are estimated using the pooled data. Regression helps in examining the relationship between prior gains with current allocation in four categories of assets of varying degrees of riskiness (stocks, debt, real estate and other assets). In order to investigate the second research question on whether pension funds increase (decrease) their investments in risky (safer) assets due to prior gains and αs, the four variables representing the changes in portfolio allocation for each asset class over one period are employed. These changes in allocation are regressed against the prior year’s actual return, expected return, αs and a set of control variables.FindingsThe results suggest significant negative (positive) relationship between prior positive returns and αs with portfolio allocation in risky (safer) assets. Also, there is an increased (decreased) investment in safer (risky) assets following prior period’s positive returns and αs. The findings confirm the existence of disposition effect, while there is no evidence of house money effect.Originality/valueThe portfolio allocation of pension plans provides unique setting to investigate the relevance of behavioral finance and examine the role of psychological biases on risk taking. This study attempts to contribute to the literature by empirically investigating whether the tenets of behavioral finance are relevant in defined benefit pension fund’s portfolio allocation decisions. Specifically, it focuses on the determinants of portfolio choices by directly investigating pension funds’ reaction to prior period’s actual as well as risk adjusted return (or αs – the difference between the actual and expected return).

The Influence of Pension Scheme Maturity on Investment Strategies of Pension Funds in Kenya

The longevity risk borne by members of defined contribution pension schemes and the funding risk borne by sponsors of defined benefit pension funds have shifted attention to the investment strategies employed by pension funds. We use secondary data from 206 occupational retirement benefits schemes in Kenya, to examine the influence of pension scheme maturity on investment strategies. We then triangulate the results using focused group discussions with industry experts. Results from the regression models indicate that scheme maturity does not influence the investment strategies of occupation schemes in Kenya contrary to life cycle theory. The Retirement Benefits Authority and trustees of retirement benefits schemes in Kenya are advised to offer members’ investment choices coupled with education to enable them make decisions to reduce their exposure to risky assets as they age.

Pension Fund Restoration Policy in General Equilibrium

When the financial positions of pension funds worsen, regulations prescribe that pension funds reduce the gap between their assets (invested contributions) and their liabilities (accumulated pension promises). This paper quantifies the business cycle effects and distributional implications of various types of restoration policies. We extend a canonical New-Keynesian model with a tractable demographic structure and, as a novelty, a flexible pension fund framework. Fund participants accumulate real or nominal benefits and funding adequacy is restored by revaluing previously accumulated pension wealth (Defined Contribution) or changing the pension fund contribution rate on labour income (Defined Benefit). Generally, economies with Defined Contribution pension funds respond similarly to adverse capital quality shocks as economies without pension funds. Defined Benefit pension funds, however, distort labour supply decisions and exacerbate economic fluctuations. Retirees prefer Defined Benefit over Defined Contribution funds in case they face deficits, while the current and future working population prefers the opposite.

Nexus Between Pension Fund Size, Design and Investment Strategy: A Review of Occupational Retirement Benefits Schemes in Kenya

The funding risk borne by sponsors of defined benefit pension funds and the residual risk borne by members of defined contribution pension funds have necessitated focus on the investment strategies employed by pension funds. We use secondary data from 206 pension funds in Kenya, to determine the nexus between the investment strategy, size and design. We then validate the results using focused group discussions with industry experts. Results from the regression models indicate that larger schemes adopted a riskier investment strategies compared to their smaller counterparts. However, the investment strategies are not informed by the fund designs. Trustees of retirement benefit schemes are therefore advised to focus their investment strategies to avoid exposing the residual claimants to excessive risk.

ALM models based on second order stochastic dominance

We propose asset and liability management models in which the risk of underfunding is modelled based on the concept of stochastic dominance. Investment decisions are taken such that the distribution of the funding ratio, that is, the ratio of asset to liabilities, is non-dominated with respect to second order stochastic dominance. In addition, the funding ratio distribution is close in an optimal sense to a user-specified target distribution. Interesting results are obtained when the target distribution is degenerate; in this case, we can obtain equivalent risk minimisation models, with risk defined as expected shortfall or as worst case loss. As an application, we consider the financial planning problem of a defined benefit pension fund in Saudi Arabia.