A new way of looking at the risk in defined benefit pension plans

The portability feature of a defined contribution (DC) pension greatly reduces the risk to the accumulation of pension wealth. Conversely, defined benefit (DB) pensions have a variety of default risks that decrease the expected value of DB pension wealth. This paper examines those risks. Accrual of DB pension wealth is characterized in terms of purchases of risky bonds. Changing jobs triggers default on these bonds. Simulations are presented to show the potential loss in pension wealth from default. In addition, a methodology used to price corporate bonds is applied to generate estimates of the implied risk premiums of DB pension bonds over comparable riskless bonds.     

Pension Portfolio Choice and Peer Envy

I examine the effect of envy on the portfolio allocation of workers in a defined contribution (DC) pension plan. If a worker’s DC plan performs better than his co‐worker’s, he may gloat; on the other hand, if his DC plan performs worse, he may feel envy. I model anticipated envy when workers make portfolio allocations, and find that in equilibrium, workers will mimic their co‐worker’s allocation to eliminate the disutility from envy. This portfolio allocation is riskier than that of a worker who does not exhibit envy.     

Valuation of Contingent Pension Liabilities and Guarantees Under Sponsor Default Risk

This article analyzes the relationship between a pension fund with contingently indexed defined benefit liabilities and its sponsor, using contingent claims analysis. As pension funds generally choose to run a mismatch risk, future surpluses and deficits will occur. Surpluses are divided between beneficiaries and sponsor through contingent indexation of the benefits and refunding. Covering a deficit at the pension fund level is a function of the sponsor's financial ability to do so. This article suggests that this system creates an asymmetric allocation of the residual risk between sponsor and beneficiaries. The optimal investment policy for the pension fund in this context can be found by reverse engineering option valuation formulas. The main conclusion is that sponsor default risk negatively impacts the optimum risk profile and thereby the market value of contingent pension liabilities.     

Florida's Pension Election: From DB to DC and Back

During the year 2002, the State of Florida's 600,000 public employees were given the choice of converting their traditional defined benefit (DB) pension plan into an individual‐account defined contribution (DC) plan with full control over asset allocation and investment decisions. To mitigate some of the risk and uncertainty in the decision, the State granted each employee electing the DC plan an additional option to switch back (i.e., change their mind once) at any point prior to retirement. This option has been labeled the 2nd election by the State and the cost of reentry is fixed at the accumulated benefit obligation of their pension entitlement, which is the present value of the life annuity. Our article presents some original analytic insights relating to the optimal time and financial value of this unique 2nd election. Although our model is deterministic in nature, we believe that it provides a number of intuitive insights that are quite robust. Our results can be contrasted with Lachance, Mitchell, and Smetters (2003) . We estimate that the increase in retirement wealth that arises from having the 2nd election is equivalent to at most 30 percent in future value, and only when utilized optimally. Furthermore, for most State employees above the age of 45, the 2nd election has little economic value because the DB plan dominates the DC plan from day one. Of course, it remains to be seen what percent of Florida's 600,000 employees will elect to behave rationally with their newfound pension autonomy.     

The appropriateness of default investment options in defined contribution plans: Australian evidence

For participants in defined contribution (DC) plans who refrain from exercising investment choice, plan contributions are invested following the default investment option of their respective plans. Since default investment options of different plans vary widely in terms of their benchmark asset allocation, the most important determinant of investment performance, participants enrolled in these options face significantly different wealth outcomes at retirement. This paper simulates the terminal wealth outcomes under different static asset allocation strategies to evaluate their relative appeal as default investment choice in DC plans. We find that strategies with low or moderate allocation to stocks are consistently outperformed in terms of upside potential of exceeding the participant's wealth accumulation target at retirement as well as downside risk of falling below that target outcome by aggressive strategies whose allocation to stocks approach 100%. The risk of extremely adverse wealth outcomes for plan participants also does not appear to be very sensitive to asset allocation. Our evidence suggests the appropriateness of strategies heavily tilted towards stocks to be nominated as default investment options in DC plans unless plan providers emphasize predictability of wealth outcomes over adequacy of retirement wealth.     

Management of Portfolio Depletion Risk through Optimal Life Cycle Asset Allocation

Members of defined contribution (DC) pension plans must take on additional responsibilities for their investments, compared to participants in defined benefit (DB) pension plans. The transition from DB to DC plans means that more employees are faced with these responsibilities. We explore the extent to which DC plan members can follow financial strategies that have a high chance of resulting in a retirement scenario that is fairly close to that provided by DB plans. Retirees in DC plans typically must fund spending from accumulated savings. This leads to the risk of depleting these savings, that is, portfolio depletion risk. We analyze the management of this risk through life cycle optimal dynamic asset allocation, including the accumulation and decumulation phases. We pose the asset allocation strategy as an optimal stochastic control problem. Several objective functions are tested and compared. We focus on the risk of portfolio depletion at the terminal date, using such measures as conditional value at risk (CVAR) and probability of ruin. A secondary consideration is the median terminal portfolio value. The control problem is solved using a Hamilton-Jacobi-Bellman formulation, based on a parametric model of the financial market. Monte Carlo simulations that use the optimal controls are presented to evaluate the performance metrics. These simulations are based on both the parametric model and bootstrap resampling of 91 years of historical data. The resampling tests suggest that target-based approaches that seek to establish a safety margin of wealth at the end of the decumulation period appear to be superior to strategies that directly attempt to minimize risk measures such as the probability of portfolio depletion or CVAR. The target-based approaches result in a reasonably close approximation to the retirement spending available in a DB plan. There is a small risk of depleting the retiree’s funds, but there is also a good chance of accumulating a buffer that can be used to manage unplanned longevity risk or left as a bequest.     

The Impact of DC Pension Systems on Population Dynamics

Abstract

This study investigates the risk inherent in defined contribution (DC) pension plans on an individual and aggregate basis, based on U.S. data. Our aim is to gain insight into the consequences of a DC pension scheme becoming the predominant pillar of retirement income for an entire society. Using the stochastic simulated output of a DC flexible age-of-retirement model, we first determine the optimal investment strategies. We then examine the demographic retirement dynamics of an entire population of DC pension plan participants.

We observe that even for the most risk-averse plan members there is a high level of uncertainty in an individual’s age at retirement. At the aggregate population level, we find that this uncertainty does not get dampened to any great extent by a diversification effect. Instead, the central role played by the market in determining retirement dates results in significant variation in the dependency ratio (the ratio of retirees to workers) over time. In addition, an attempt to ameliorate the outcome by introducing additional realistic features in the DC population modeling did little to dampen this volatility, which suggests that countries dominated by DC schemes of this type may, over time, be exposed to significant risk in the size of its labor force.     

Optimal Control of DC Pension Plan Management under Two Incentive Schemes

Since the late 1990s, a performance fee arrangement has been approved as a managerial incentive in direction contribution (DC) pension plan management to motivate managers. However, the fact that managers may take undue risk for the larger performance fees and thus reduce members’ utility has been a subject of debate. As such, this study investigates the optimal risk-taking policies of DC pension fund managers under both the single management fee scheme and a mixed scheme with a lower management fee, as well as an additional performance fee. The analytical solutions are derived by using the duality method and concavification techniques in a singular optimization problem. The results show the complex risk-taking structures of fund managers and recognize the win-win situation of implementing performance-based incentives in DC pension plan management. Under the setting of geometric Brownian motion asset price dynamics and constant relative risk aversion utility, the optimal risk investment proportion shows a peak-valley pattern under the mixed scheme. Further, the manager gambles for gain when fund wealth is low and time to maturity is short. As opposed to the existing literature, this study found that the risk-taking policy is more conservative when fund wealth is relatively large. Furthermore, the utilities of the manager and members could both be improved by appropriately choosing the performance fee rate.     

Defined Benefit or Defined Contribution? A Study of Pension Choices

We solve an empirically parameterized life‐cycle model of consumption and pension choices to show how expected earnings growth and risk affect the benefits of final‐salary defined benefit (DB) pension plans, relative to pension plans that are defined contribution (DC) in nature. We use micro data on the pension choices of individuals to provide evidence consistent with the model predictions: (1) individuals who expect a higher growth rate of earnings are more likely to choose DB final‐salary schemes, and (2) individuals who face a higher variance of persistent income shocks are less likely to choose DB final‐salary schemes. We control for cohort and age fixed effects in the empirical analysis.     

Allocating Shareholder Capital to Pension Plans

This article discusses the corporate challenge of providing retirement income to employees while limiting the costs and risks of pension plans to the companies themselves by addressing five main questions:

• ? What are the major issues and challenges surrounding pensions? Although the pension shortfalls have been the focus of attention, the author argues that the more serious concern is the risk stemming from the mismatch between pension assets and pension liabilities— that is, the funding of debt‐like liabilities with equity‐heavy asset portfolios.
• ? To what extent do the equity market and equity prices reflect the shortfall in value and the mismatch in risk? While the author describes some evidence of the market's ability to capture pension risk, analysts' P/E multiples and management's assessments of cost of capital may still be distorted by failure to take full account of the risks associated with pension assets.
• ? How should management analyze and formulate strategic solutions? Without offering specific solutions, the author presents a framework for analyzing the problem from a strategic perspective that can be used in formulating a company's pension policy. In particular, the article recommends that companies take an integrated perspective that views pension assets and liabilities as parts of the corporate balance sheet, and the pension asset allocation decision as a critical aspect of a corporate‐wide enterprise risk management program.
• ? If a company chooses to make a major change in its pension policy, such as a partial or complete immunization accomplished by substituting bonds for stocks, how would you communicate the new policy to the rating agencies and investors?
• ? What are the major issues to be thinking about when contemplating a change from a DB plan to a defined contribution, or DC, plan? The author argues that DC plans without some corporate oversight or responsibility for results are not a long‐term solution.

     

Optimal Gradual Annuitization: Quantifying the Costs of Switching to Annuities

We compute the optimal dynamic annuitization and asset allocation policy for a retiree with Epstein–Zin preferences, uncertain investment horizon, potential bequest motives, and pre‐existing pension income. In our setting the retiree can decide each year how much he consumes and how much he invests in stocks, bonds, and life annuities, while the prior literature mostly considered restricted so‐called deterministic or stochastic switching strategies. We show that postponing the annuity purchase is no longer optimal in the gradual annuitization (GA) case since investors are able to attain the optimal mix between liquid assets (stocks and bonds) and illiquid life annuities each year. In order to assess potential utility losses, we benchmark various restricted annuitization strategies against the unrestricted GA strategy.     

An Economic Approach to Capital Allocation

This article starts with primitive assumptions on preferences and risk. It then derives prices consistent with a social optimum within an insurance company and the consumer‐level capital allocation implied therein. The allocation “adds up” to the total capital of the firm (a result echoing findings in the congestion pricing literature—where optimal tolls exactly cover the rental cost of the highway). The allocation follows each consumer's share of recoveries in states of insurer default, weighted by the severity of the default in terms of welfare impact. However, the article argues that an economic approach technically restricts only the capital allocated to marginal units of coverage: inframarginal units could in principle receive different allocations.     

Modeling a Dynamic Portfolio for Pension Plans in Emerging Markets With Myopic and Nonmyopic Behavior

ABSTRACT

We introduce a dynamic formulation for the problem of portfolio selection of pension funds in the absence of a risk-free asset. In emerging markets, a risk-free asset might be unavailable, and the approaches commonly used may no longer be suitable. We use a parametric approach to combine dynamic programming and Monte Carlo simulation to gain additional flexibility. This approach is general in the sense that optimal asset allocation is tractable for all HARA utility functions in the absence of a risk-free asset. The traditional case composed of several risky assets and one risk-free asset is compared to a case in which the risk-free asset is unavailable.     

西方养老金最优化管理研究综述

养老金管理作为保险精算、金融数学的重要研究内容得到了广泛关注,特别是老龄化严重或正趋于老龄化的国家,更应重视养老金的管理。基于对DB型养老金、DC型养老金及其相关问题的现有研究成果进行系统梳理,分析讨论了西方养老金最优化管理的发展历史、研究现状及存在的问题,并据此提出未来可能的研究方向,希望能对相关研究者和保险企业提供...     

Asset–liability modelling and pension schemes: the application of robust optimization to USS

This paper uses a novel numerical optimization technique – robust optimization – that is well suited to solving the asset–liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximize the Sharpe ratio. We disaggregate pension liabilities into three components – active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme's projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes–Stein and Black–Litterman models as well as the actual USS investment decisions. Over a 144-month out-of-sample period, robust optimization is superior to the four benchmarks across 20 performance criteria and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks.     

The Pension Protection Fund*

We develop a model of the Pension Protection Fund (PPF), a defined benefit pension guarantee system for the UK, based on an analogy between pension liabilities and corporate debt obligations. We show that the PPF is likely to face many years of low claims interspersed irregularly with periods of very large claims. There is a significant chance that these claims will be so large that the PPF will default on its liabilities, leaving the government with no option but to bail it out. The cause of this problem is the double impact of a fall in equity prices on the PPF: it makes sponsor firms more likely to default and it makes defaulted plans more likely to be underfunded. We use our model to derive a fair premium for PPF insurance under different circumstances, to estimate the extent of cross‐subsidies in the PPF between strong and weak sponsors, and to show that risk‐rated premiums are unlikely to have a substantial effect on either the size or the lumpiness of claims. We argue that for the PPF to operate effectively, it should be introduced in tandem with strong minimum funding requirements and a lower level of benefit guarantee than at present.     

Pension Contributions and Firm Performance: Evidence from Frozen Defined Benefit Plans

We study the impact of freezing defined benefit (DB) pension plans and replacing them with defined contribution (DC) plans on liquidity, financial leverage, investment, and market value of a sample of firms over 2001‐2008. We find evidence that the pension freeze tends to attenuate the drain on corporate liquidity and relieve the pressure to borrow to pay for mandatory contributions (MCs) associated with underfunded DB plans. Although investors seem to favor the pension freeze as evidenced by positive announcement abnormal stock returns, there is little reliable evidence that the freeze increases investment efficiency and long‐term stock performance.     

The optimal asset allocation of the main types of pension funds: a unified framework

The existing literature deals with the optimal investment strategy of defined benefit (DB) or defined contribution (DC) pension plans. This article’s objective is to compare the optimal policies of different types of pension plans. This is done by first defining an original framework, which is based on the distinction between the nature of the guarantee—which can be internal or external—offered by or to a pension fund. This framework allows to establish links between optimization programs of DC, DB and targeted money purchase schemes. The case of an internal guarantee appears as a standard portfolio insurer’s problem. The second kind of guarantee, not analyzed in the literature yet with regard to the resulting optimal policy, is characterized by the existence of an option in the final wealth definition. Four funds are present in the internal guarantee optimal allocation: the speculative component, the preference independent guarantee- and contribution-hedge terms and the preference dependent state variable-hedge fund. The external guarantee program, solved with an original method using the principles of standard options theory, yields an optimal policy incorporating the delta of the option embodied in the final wealth definition. The conclusion is that the resulting optimal portfolio policy becomes riskier.

Investor Tax Heterogeneity and Ex-Dividend Day Trading Volume

We propose that ex‐dividend day excess volume is motivated by tax heterogeneity among investors, and thus is increasing in investor tax heterogeneity. Institutional ownership is our measure of heterogeneity. Since investor heterogeneity is a concave function of institutional ownership, we hypothesize that ex‐day volume is a concave function of institutional ownership. Cross‐sectional tests support the tax‐motivated trading hypothesis. Additional tests, using trade size and pension ownership as proxies for institutional trades, yield similar results. We contribute to the literature by considering the interaction between payout policy and ownership structure in explaining the cross‐sectional variation in ex‐day volume.