Do pension buyouts help or hurt employees (retirees)?

This article compares expected pension default losses of employees and retirees before and after pension buyouts. The comparisons are made using a stochastic model calibrated with market data. The analysis shows that the lower protection level provided by the State Guarantee Association relative to that of the Pension Benefit Guaranty Corporation (PBGC) is a critical factor that explains the welfare reduction, or equivalently, larger expected pension default losses, of most retirees who become annuity holders in the buyouts. The analysis also shows that the employee welfare, or equivalently expected pension default gains or losses, depends on the continued PBGC protection and, critically, their employers' postbuyout default risk and pension funding status. Moreover, these employee welfare changes are quite different for the corporations included in this analysis. Our results suggest that welfare improvements depend on the PBGC and state insurance regulators' cooperation in protecting pension participants and supervising buyout insurers.     

Parameter risk in time-series mortality forecasts

The projection of mortality rates is an essential part of valuing liabilities in life insurance portfolios and pension schemes. An important tool for risk management and solvency purposes is a stochastic projection model. We show that ARIMA models can be better representations of mortality time-series than simple random-walk models. We also consider the issue of parameter risk in time-series models from the point of view of an insurer using them for regulatory risk reporting – formulae are given for decomposing overall risk into undiversifiable trend risk (parameter uncertainty) and diversifiable volatility. Particular attention is given to the contrasts in how academic researchers might view these models and how insurance regulators and practitioners in life offices might use them. Using a bootstrap method we find that, while certain kinds of parameter risk are negligible, others are too material to ignore. We also find that an objective model selection criterion, such as goodness of fit to past data, can result in the selection of a model with unstable parameter values. While this aspect of the model is superficially undesirable, it also leads to slightly higher capital requirements and thus makes the model of keen interest to regulators. Our conclusions have relevance to insurers using value-at-risk capital assessments in the European Union under Solvency II, but also territories using conditional tail expectations such as Australia, Canada and Switzerland.     

Smoothing Mechanisms in Defined Benefit Pension Accounting Standards: A Simulation Study*

The accounting for defined benefit (DB) pension plans is complex and varies significantly across jurisdictions despite recent international convergence efforts. Pension costs are significant, and many worry that unfavorable accounting treatment could lead companies to terminate DB plans, a result that would have important social implications. A key difference in accounting standards relates to whether and how the effects of fluctuations in market and demographic variables on reported pension cost are “smoothed". Critics argue that smoothing mechanisms lead to incomprehensible accounting information and induce managers to make dysfunctional decisions. Furthermore, the effectiveness of these mechanisms may vary. We use simulated data to test the volatility, representational faithfulness, and predictive ability of pension accounting numbers under Canadian, British, and international standards (IFRS). We find that smoothed pension expense is less volatile, more predictive of future expense, and more closely associated with contemporaneous funding than is “unsmoothed” pension expense. The corridor method and market‐related value approaches allowed under Canadian GAAP have virtually no smoothing effect incremental to the amortization of actuarial gains and losses. The pension accrual or deferred asset is highly correlated with the pension plan deficit/surplus. Our findings complement existing, primarily archival, pension accounting research and could provide guidance to standard‐setters.     

Iterated VaR or CTE measures: A false good idea?

The purpose of this paper is twofold. Firstly, we consider different risk measures in order to determine the solvency capital requirement of a pension fund. Secondly, we illustrate the impact of the time horizon of long-term guarantee products on these capital. We consider a financial market modelled by a common Black–Scholes–Merton model. We neglect the mortality and underwriting risks by assuming that the pension fund is fully hedged against these risks, which allows us to keep understandable and tractable formulæ (the longevity risk will be a part of future researches). A portfolio is built in this market according to different strategies and the pension fund offers a fixed guaranteed rate on a certain time horizon. We begin with well-known static risk measures (value at risk and conditional tail expectation measures) and then we consider their natural dynamic generalization. In order to be time consistent, we consider their iterated versions by a backward iterations scheme. Within the dynamic setting, we show that solvency capital can be expensive and that attention must be paid to the safety level considered.     

Downside Risk Management of a Defined Benefit Plan Considering Longevity Basis Risk

To control downside risk of a defined benefit pension plan arising from unexpected mortality improvements and severe market turbulence, this article proposes an optimization model by imposing two conditional value at risk constraints to control tail risks of pension funding status and total pension costs. With this setup, we further examine two longevity risk hedging strategies subject to basis risk. While the existing literature suggests that the excess-risk hedging strategy is more attractive than the ground-up hedging strategy as the latter is more capital intensive and expensive, our numerical examples show that the excess-risk hedging strategy is much more vulnerable to longevity basis risk, which limits its applications for pension longevity risk management. Hence, our findings provide important insight on the effect of basis risk on longevity hedging strategies.     

Rentenversicherung, Bev?lkerungsentwicklung und Kapitalmarktrendite – Eine Simulationsrechnung

How can the pension schemes be sustainably financed? This is an important issue particularly with regard to the demographic changes in many industrialized countries but also in other emerging economies such as China and India. In this paper, we use a macroeconomic model of overlapping generations to analyze the impacts of the demographic changes as well as the interactions between pension system, bond and stock markets. Furthermore, we examine how the pension system influences the distribution of wealth, consumption and saving within generations. We found out that an aging population will cause a drastic decline. Moreover, we examined which impacts on individuals?? welfare demographic changes can have for an existing pay-as-you-go pension scheme. An increase of pension age combined with a decrease of the contributions seems to be the best policy. On the other hand, increases in contributions as a result of demographic changes show the highest welfare losses.     

The Tail Probability of Discounted Sums of Pareto-like Losses in Insurance

In an insurance context, the discounted sum of losses within a finite or infinite time period can be described as a randomly weighted sum of a sequence of independent random variables. These independent random variables represent the amounts of losses in successive development years, while the weights represent the stochastic discount factors. In this paper, we investigate the problem of approximating the tail probability of this weighted sum in the case when the losses have Pareto-like distributions and the discount factors are mutually dependent. We also give some simulation results.     

The smoothing of pension expenses: a panel analysis

The main purpose of this paper is to utilize recent developments in panel data techniques to evaluate whether the smoothing of pension expenses is neutral in its long-term effect on reported earnings. Adopting a long-term perspective, the empirical analysis also identifies sources of potential deviations. Results suggest that the current smoothing mechanism tends to induce significant biases in the recognized pension expenses. For a majority of the sample firms, the tendency is to overstate the sponsoring firms’ earnings in the long run. To a large extent, such biases reflect the combination of both ineffective amortization of the deferred gains and losses and questionable latitude in pension rate discretions.     

The effect of regulation on optimal corporate pension risk

We study firms' pension prefunding and portfolio allocation choices in a model in which firms trade off the need to compensate workers for the financial risk in their pension benefit against the cost advantage that may be gained by exploiting underpriced pension insurance. In the absence of pension insurance, the firm minimizes costs by rendering promised benefits free of risk to workers, who are assumed to be unable to hedge firm-specific risk. Various forms of government intervention, such as benefit guarantees, can alter this outcome dramatically by providing the firm with an incentive to shift risk to other parties. In this case, we find that the firm's decisions depend on, among other influences, the degree of insurance mispricing, the amount of guaranteed benefits, the stringency of minimum funding requirements, and the costs of financial distress.     

How suboptimal are linear sharing rules?

The objective of this paper is to analyze criteria for portfolio choice when two investors are forced to invest in a common portfolio and share the proceeds by a linear sharing rule. A similar situation with many investors is typical for defined contribution pension schemes. The restriction implies two sources of suboptimal investment decisions as seen from each of the two investors individually. One is the suboptimal choice of portfolio, the other is the forced linear sharing rule. We measure the combined consequence for each investor by their respective loss in wealth equivalent. We show that significant losses can arise when investors are diverse in their risk attitude. We also show that an investor with a low degree of risk aversion, like the logarithmic or the square root investor, often applied in portfolio choice models, can either inflict or be subject to severe losses when being forced to participate in such a common investment pool.     

Financial Crises and Recapitalizations

We develop a dynamic stochastic general equilibrium model with financial frictions on both financial intermediaries and goods‐producing firms. Since financial intermediaries are highly leveraged, we show that the welfare gains from their recapitalization in response to large but rare net worth losses are as large as those from eliminating typical business cycle fluctuations. We also find that these gains are increasing in the size of the net worth loss, are larger when recapitalization funds are raised from the household rather than the real sector, and can be larger when lower idiosyncratic risk leads to higher leverage.     

Pension Valuation Under Uncertainties: Implementation of a Stochastic and Dynamic Monitoring System

Financial soundness and funding stability are two critical issues in pension fund management. First, we construct a generalized stochastic model to monitor the solvency risk and cash flow dynamics of the defined benefit pension plan. A semi‐Markov process proposed by Dominicis et al. (1991) and Janssen and Manca (1997) is employed in structuring the transition pattern of the plan's population, and the economic‐based factors are generated through plausible stochastic processes. Modifications according to classification and movements of the plan member and the plan's turnover pattern are also employed to improve its practical usefulness. Then the actuarial valuations, cash flow analyses, and workforce projection are performed and investigated. Second, we explicitly formulate the plan dynamics and implement the proposed mechanism into a risk management framework for pension management. By employing the stochastic and dynamic approach, the cost factors can be monitored throughout the valuation process. Third, we outline the procedure of implementing the proposed methodology into a monitoring system. Finally, the Taiwan Public Employees Retirement System is simplified to illustrate techniques in achieving risk management goals.     

Performance measurement of pension strategies: a case study of Danish life cycle products

The Danish pension markets of life cycle products have expanded considerably since its introduction in the beginning of the millennium. The market is maturing and pensioners have the choice between a wide area of different products. It is therefore about time that financial insurance technology is developed to guide the performance measurement of available products. In this paper we develop a simple first version of such a method and we investigate life cycle products recommended on the web of the four biggest commercial Danish pension companies on one day in February 2007. All considered products are outperformed by trivial benchmark products with constant stock proportion over time. Our approach is the following: for each life cycle product we first find a trivial benchmark product with the same long-term risk and then we compare the long-term return of the two equivalent products. We primarily consider value at risk and tail value at risk as risk measures, but we also include a study where the fair value of an interest guarantee is used as risk measure. We consider both long-term mean returns and long-term median returns. We hope that our new method will be regarded as a first step towards a scientifically based ranking of the quality of pension products.     

The dynamics of operational loss clustering

This paper investigates the characteristics of the operational loss data formation mechanism that takes place between the date of discovery of a new operational risk event and the final settlement date on which all losses are materialized. The first loss that characterizes the initial impact of a new operational risk event frequently triggers a sequence of related losses. Then, losses generated by the same event are not independent and follow a predictable scheme and the frequency of secondary losses is not homogeneous: both are functions of the initial loss amount and time. We model the arrival intensity and loss severities with a shot-noise stochastic process and derive its key properties. We then discuss implications of our model for the estimation of the regulatory capital charge for operational risk. In an empirical analysis, we find strong evidence of a shot-noise behavior in operational losses using the data of a major US commercial bank.     

New Salary Functions for Pension Valuations

Abstract

This paper investigates salary functions as used in the valuation of pension plans. Pension actuaries as well as researchers in actuarial science may find many of the ideas in this article useful. The main conclusion of this paper is that salary functions, as derived from the parametric models, yield gains and losses that can be quite small and, in some cases, less variable than nonparametric methods. This paper starts by defining the salary function as an accumulation function based on inflation and merit. Next, we investigate traditional estimation methods in the context of this definition. We then present a parametric age-based model for the salary function and compare it with a parametric service-based model. Finally, we apply real pension plan data to derive age-and service-based salary functions and, through the use of two funding methods, investigate how these salary functions affect salary gains and losses.     

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.     

Human Survival at Older Ages and the Implications for Longevity Bond Pricing

Abstract

Governments are concerned about the future of pension plans, for which increasing longevity is judged to be an important risk to their future viability. We focus on human survival at age 65, the starting age point for many pension products. Using a simple model, we link basic measures of life expectancy to the shape of the human survival function and consider its various forms. The model is then used as the basis for investigating actual survival in England and Wales. We find that life expectancy is increasing at a faster rate than at any time in history, with no evidence of this trend slowing or any upper age limit. With interest growing in the use of longevity bonds as a way to transfer longevity risks from pension providers to the capital markets, we seek to understand how longevity drift affects pension liabilities based on mortality rates at the point of annuitization, versus what actually happens as a cohort ages. The main findings are that longevity bonds are an effective hedge against longevity risk; however, it is not only the oldest old that are driving risk, but also more 65-year-olds reaching less extreme ages such as 80. In addition, we find that the possibility of future inflation and interest rates could be as an important a risk to annuities as longevity itself.     

The Poisson Log-Bilinear Lee-Carter Model

Abstract

Life insurance companies deal with two fundamental types of risks when issuing annuity contracts: financial risk and demographic risk. Recent work on the latter has focused on modeling the trend in mortality as a stochastic process. A popular method for modeling death rates is the Lee-Carter model. This methodology has become widely used, and various extensions and modifications have been proposed to obtain a broader interpretation and to capture the main features of the dynamics of mortality rates. In order to improve the measurement of uncertainty in survival probability estimates, in particular for older ages, the paper proposes an extension based on simulation procedures and on the bootstrap methodology. It aims to obtain more reliable and accurate mortality projections, based on the idea of obtaining an acceptable accuracy of the estimate by means of variance reducing techniques. In this way the forecasting procedure becomes more efficient. The longevity question constitutes a critical element in the solvency appraisal of pension annuities. The demographic models used for the cash flow distributions in a portfolio impact on the mathematical reserve and surplus calculations and affect the risk management choices for a pension plan. The paper extends the investigation of the impact of survival uncertainty for life annuity portfolios and for a guaranteed annuity option in the case where interest rates are stochastic. In a framework in which insurance companies need to use internal models for risk management purposes and for determining their solvency capital requirement, the authors consider the surplus value, calculated as the ratio between the market value of the projected assets to that of the liabilities, as a meaningful measure of the company’s financial position, expressing the degree to which the liabilities are covered by the assets.     

Pension Funding Regulations and Actuarial Gains and Losses

With pervasive pension funding deficits, Korean firms have been under pressure to improve their funding levels. We examine whether firms have incentives to set obligation‐decreasing pension assumptions when they have large pension deficits (pension obligations in excess of plan assets) and when they make insufficient contributions to external pension funds. We find that firms report larger actuarial gains (or smaller actuarial losses) associated with the remeasurement of pension liabilities when their pension funding ratio (the ratio of the fair value of plan assets to defined benefit obligations) is lower and when contributions to plan assets relative to pension service costs are smaller. Next, upon the introduction of a minimum pension funding guideline, we find that the effect of the funding ratio and contributions to pension funds on actuarial gains and losses is more pronounced for firms whose funding ratios are slightly below the minimum funding ratio than it is for firms whose funding ratios exceed or fall short of the minimum by a large margin. Our results indicate that firms opportunistically exercise discretion regarding corporate pension accounting under International Financial Reporting Standards to comply with pension funding regulations, thereby reducing perceived pension deficits.