Pension Fund Risk Management: Actuarial and Financial Modeling

摘要

PrefaceudINTEGRATED RISK MANAGEMENTudIN PENSION FUNDSudMarco Micocci, Greg N. Gregoriou, and Giovanni B. MasalaudThe world of pension funds is facing a period of extreme changes. Countries around the world have experienced unexpected increases in life expectancy and fertility rates, changing accounting rules, contribution reductions, low financial returns, and abnormal volatility of markets. All these elements have led to a fall in funded systems and to an increase in the dependency ratios in many countries. U.K. and U.S. pension funds, which have traditionally had relatively high equity allocations, have been hit hard. Many public pay-as-you-go (PAYGO) systems in Europe are reducing their “generosity” with new calculation rules pointing toward the reduction of the substitution ratios of workers. Europe is moving toward a risk-based approach also for the regulation and the control of the technical risk of funded pension schemes.udRisk management is becoming highly complex both in public pension funds and in private pension plans, requiring the expertise of different specialists who are not frequently disposable in the professional market. The world is quite rich with skilled investment managers but their comprehension of the demographic and of the actuarial face of pension risk is often inadequate. On the other hand, you have many specialized actuaries who are able to perform very sophisticated calculations and forecasts of pension liabilities but who are not able to fully understand the coexistence (or integration) of financial and actuarial risks. Also, the international accounting standards introduce new actuarial and financial elements in the balance sheet of the firms that may affect the corporate dividend and its investment policy. In other words, little is being said about the integration of actuarial and financial risks in the risk management of pension funds.udWe believe the chapters in this book highlight and shed new light on the current state of pension fund risk management and provide the reader new technical tools to face pension risk from an integrated point of view.udThe exclusive new research for this book can assist pension fund executives, risk management departments, consultancy firms, and academic researchers to hopefully get a clearer picture of the integration of risks in the pension world. The chapters in this book are written by well-known academics and professionals worldwide who have published numerous journal articles and book chapters. The book is divided into four parts—udPart I: Financial Risk Management; Part II: Technical Risk Management;udPart III: Regulation and Solvency Topics; and Part IV: InternationaludExperience in Pension Fund Risk Management.udIn Part I, Chapter 1 focuses on the correct measurement of risk in pension funds. The author formalizes an intuitive concept of investment risk in providing for pensions, taking it as a measure of the financial impact when the actual investment experience differs from the expected.udInvestment risk can be explicitly measured and, through a series of case studies, the author estimates the investment risk associated with different investment strategies in different markets over the twentieth century.udHe shows that within a broad range, the relative investment risk associated with different strategies is not particularly sensitive to how the pension objective is framed. The investment risk associated with equity investment can be of the same order of magnitude as bond investment if the bond duration mismatches those of the targeted pension. He suggests that failure to explicitly measure investment risk entails that pension portfolios might not be optimally structured, holding the possibility that investment risks could be reduced without reducing the expected pension proceeds.udIn Chapter 2, the authors scrutinize the fund dynamics under a performance- oriented arrangement (i.e., bonus fees and downside penalty), whereby a stochastic control is formulated to further characterize the defined contribution (DC) pension schemes. A five-fund separation theorem is derived to characterize its optimal strategy. When performance oriented arrangement is taken into account, the fund managers tend to increase the holdings in risky assets. Hence, an incentive program has to be carefully implemented in order to balance the risk and the reward in DC pension fund management.udChapter 3 proposes an attribution model for monitoring the performance and the risk of a defined benefit (DB) pension fund. The model is based on a liability benchmark that reflects the risk and return characteristics of the liabilities. As a result, the attribution model focuses the attention of the portfolio managers on creating a portfolio that replicates liabilities. The attribution model allocates differences in return between the actual portfolio and the benchmark portfolio to decisions relative to the benchmark portfolio. In addition, the model decomposes risks according to the same structure by using a measure of downside risk.udChapter 4 investigates an optimal investment problem faced by a DC pension fund manager under inflationary risk. It is assumed that a representative member of a DC pension plan contributes a fixed share of his salary to the pension fund during the time horizon. The pension contributions are invested continuously in a risk-free bond, an index bond, and a stock. The objective is to maximize the expected utility of terminal value of the pension fund. By solving this investment problem, the author presents a way to deal with the optimization problem, in case of an (positive) endowment (or contribution), using the martingale method.udChapter 5 deals with the study of a pension plan from the point of view of dynamic optimization. Th is subject is currently widely discussed in the literature. The optimal management of an aggregated type of DB pension fund, which is common in the employment system, is analyzed by a mean–variance portfolio selection problem. The main novelty is that the risk-free market interest rate is a time-dependent function and the benefits are stochastic.udIn Chapter 6, the author highlights the fact that a pension fund is a complex system. Asset and liability management (ALM) models of pension fund problems incorporate, among others, stochasticity, liquidity control, population dynamics, and decision delays to better forecast and foresee solvency in the long term. In order to model uncertainties or to enable multicriteria analyses, many methods are considered and analyzed to obtain a dynamic asset and liability management approach.udIn Chapter 7, the authors investigate the optimal asset allocation of U.S. pension funds by taking into account the funds’ liabilities. Besides the traditional inputs, such as expected returns and the covariance matrix, the uncertainty of expected returns plays a crucial role in creating robust portfolios that are less sensitive to small changes in inputs. The authors illustrate this with an example of a pension fund that decides on investing in emerging market equities. udChapter 8 explains that most pension funds already manage the different risks they face, but usually from a “single stakeholder” pension fund perspective, typically expressed in, e.g., the risk of funding shortfall. The many different stakeholders in pension funds, such as the employees, retirees, and sponsors, all bear different risks, but there is oft en hardly any insight in the objective market value of these risks. In addition, there is usually no explicit compensation agreement for those who bear the risks.udTherefore, a technique that identifies and values these stakeholders’ risks has many useful applications in pension fund management.udChapter 9 focuses on value-at-risk (VaR). VaR has become a popular risk measure of financial risk and is also used for regulatory capital requirement purposes in banking and insurance sectors. The VaR methodology has been developed mainly for banks to control their short-term market risk. Although, VaR is already widespread in financial industry, this method has yet to become a standard tool for pension funds. However, just as any other financial institution, pension funds recognize the importanceudof measuring their financial risks. The aim of this chapter is to specifyconditions under which VaR could be a good measure of long-termmarket risk.udChapter 10 examines the effects of taxation, risk sharing between theemployer and employees, and default insurance on the asset allocation ofDB pension schemes. These three factors can have a powerful effect on theoptimal asset allocation of a fund. The authors show that the three factorshave the potential to create confl ict between the employer and the employees,particularly when the employer is not subject to taxation.udIn Part II, Chapter 11 is devoted to examining how uncertainty regarding future mortality and life expectancy outcomes, i.e., longevity risk, affects employer-provided DB private pension plan liabilities. The author argues that to assess uncertainty and associated risks adequately, a stochastic approach to model mortality and life expectancy is preferable because it allows one to attach probabilities to different forecasts. In this regard, the chapter provides the results of estimating the Lee–Carter model for several OECD countries. Furthermore, it conveys the uncertainty surrounding future mortality and life expectancy outcomes by means of Monte-Carlo simulations of the Lee–Carter model. In order to assess the impact of longevity risk on employer-provided DB pension plans, the author examines the different approaches that private pension plans follow in practice when incorporating longevity risks in their actuarial calculations.udChapter 12 analyzes the pension plan of a firm that offers wage-based lump sum payments by death, retirement, or dismissal by the employer, but no payment is made by the employer when the employee resigns. An actuarial risk model for funding severance payment liabilities is formulated and studied. The yearly aggregate lump sum payments are supposed to follow a classical collective model of risk theory with compound distributions. The final wealth at an arbitrary time is described explicitly including formulas for the mean and the variance. Annual initial level premiums required for “dismissal funding” are determined and useful gamma approximations for confidence intervals of the wealth are proposed. A specific numerical example illustrates the non-negligible probability of a bankruptcy in case the employee structure of a “dismissal plan” is not well balanced.udChapter 13 starts from the fact that retirement is being remade owing to the confluence of demographic, economic, and policy factors. The authors empirically investigate major influences on the retirement behavior of older U.S. workers from 1992 through 2004 using survey data from the Health and Retirement Study. Their analysis builds on the large empirical literature on retirement, in particular, by examining how market booms and busts affect the likelihood and timing of retirement, an issue that will be of growing importance given the ongoing shift from traditional DB pensions to 401(k)s. They comprehensively model all major sources of health insurance coverage and identify their varying impacts, and also reveal the significant policy-driven retirement differences across cohorts that are attributable to the changes in social security full-retirement age. These fundamental retirement changes need to be taken into account when we design corporate and public retirement programs. udChapter 14 deals with a study on occupational pension insurance for Germany—a country where Pillar II pension schemes are (still) widely based on a book reserve system. The insurance of occupational pension schemes is provided for by the Pensions-Sicherungs-Verein Versicherungsverein auf Gegenseitigkeit (PSVaG), which is the German counterpart to the U.S. PBGC. Th is study investigates potential adverse selection and moral hazard problems originating from the introduction of reduced premiums for funded pensions and assesses whether the risk-adjusted risk premiums, as introduced by the U.K. Pension Protection Fund, can be a means to mitigate these problems.udChapter 15 describes the longevity risk securitization in pension schemes, focusing mainly on longevity bonds and survivor swaps. The authors analyze the evaluation of these mortality-linked securities in an incomplete market using a risk-neutral pricing approach. A Poisson Lee– Carter model is adopted to represent the mortality trend. The chapter concludes with an empirical application on Italian annuity market data. udIn Part III, Chapter 16 highlights that the international trend toward adopting a “fair value” approach to pension accounting has transpired the risks involved in promises of DB pensions. The hunt is on for ways to remove or limit the employers’ risk exposures to financial statements volatility. Th is chapter examines the U.K. firms’ risk management of their pension fund asset allocation over a period when the new U.K. pension GAAP (FRS 17) became effective. The findings suggest that firms manage their pension risk exposure in order to minimize cash contribution risks associated with the adoption of “fair value”–based pension accounting rules, consistent with a risk off setting explanation.udChapter 17 develops and tests a theory of competition among pressure groups over political influence in the context of confl icting U.K. standards concerning the factors affecting the recent development of pension fund accountability rules. The chapter models both sources of pressure affecting the accountability relationship as well as how those factors combined to influence U.K. pension fund managers’ discretion over the adoption and retention of disclosure regulations. The author finds that auditors and pension management groups exerted most political pressure, which translated to political influence during the extended adoption period. The findings are mostly consistent with a capture or private interest perspective on pension accounting regulation.udChapter 18 reviews three useful instruments—notional defined-contribution accounts (NDCs), the actuarial balance (AB), and automatic balance mechanisms (ABMs)—derived from actuarial analysis methodology that can be applied to the public management of PAYGO systems to improve their fairness, transparency, and solvency. The authors suggest that these tools are not simply theoretical concepts but, in some countries, an already legislated response to the growing social demand for transparency in the area of public finance management as well as the desire to set the pension system firmly on the road to long-term financial solvency.udIn Chapter 19, the authors review the risk-based solvency regime for pension funds in the Netherlands. The supervision of pension funds aims to ensure that institutions are always able to meet their commitments to the beneficiaries. In addition, the pension fund must be legally separated from the employer offering the pension arrangement. Furthermore, the marked-to-market value of the assets must be at least equal to the marked-to-market value of the liabilities at all times (full funding prerequisite).udRisk-based solvency requirements are intended as a buffer to absorb the risks from unexpected changes in the value of assets and liabilities. Finally, a key element of the Dutch regulatory approach is the continuity analysis for assessing the pension fund’s solvency in the long run.udIn Chapter 20, the author addresses the fact that the global financial crisis of 2008 highlighted the importance of shielding pension participants from market volatility. Th is policy concern is of general relevance due to the global shift from DB to DC as main mechanisms for financing retirement income. Policy options being debated in the aft ermath of the crisis include, but are not necessarily limited to, the following: (1) the introduction of lifetime minimum return guarantees, (2) the review of default investment options, and (3) the outright reversal to PAYGO earning–related pensions. Th is chapter reviews the performance during the crisis of countries that already rely on mandatory DC plans. The author suggestsudthat important welfare gains can be achieved by requiring the introduction of liability-driven default investment products based on a modified version of the target date funds commonly available in the retail industry for retirement wealth. Such products would reconnect the accumulation with the decumulation phase, improve the hedging of annuitization risk, but avoid the introduction of liabilities for plan managers.udIn Part IV, Chapter 21 highlights the DB pension freezes in large healthy firms such as Verizon and IBM, as well as terminations of plans in the struggling steel and airline industries that cannot be viewed as riskfree from the employee’s perspective. The authors develop an empirical dynamic programming framework to investigate household saving decisions in a simple life cycle model with DB pensions subject to the risk of being frozen. The model incorporates important sources of uncertainty facing households, including asset returns, employment, wages, and mortality, as well as pension freezes.udChapter 22 is referred to as the Italian experience. In Italy, social security contributions of Italian employees finance a two-pillar system: public and private pensions that are both calculated in a DC scheme (funded for the private pension and unfunded for the public one). In addition to this, a large number of workers have also termination indemnities at the end of their active service. The authors aim to answer the following questions. Are the different flows of contributions coherent with the aim of minimizing the pension risk of the workers? Given the actual percentages of contributions, is the asset allocation of private pension funds optimal? What percentages would optimize the pension risk management of the workers (considering public pension, private pension, and termination indemnities)?udChapter 24 examines the Greek experience in limiting the opportunity of investments of pension funds in foreign assets. In fact, suffering from inefficient funding, the current imbalance of the Greek social security system, to some extent, was the result of the restrictive investment constraints in the period 1958–2000 that directed reserves to low-yielding deposits with the Bank of Greece with little or no exposure to market yields or the stock market. As shown in the 43 year analysis, these investment restrictions incurred a significant economic opportunity loss both in terms of inferior returns as well as lower risks.udChapter 25 examines the effect of a company’s unfunded pension liabilities on its stock market valuation. Using a sample of UK FTSE350 firms with DB pension schemes, the authors find that although unfunded pension liabilities reduce the market value of the firm, the coefficient estimates indicate a less than one-for-one effect. Moreover, there is no evidence of significantly negative subsequent abnormal returns for highly underfunded schemes. These results suggest that shareholders do take into consideration the unfunded pension liabilities when valuing the firm, but do not fully incorporate all available information.udChapter 26 focuses on the selection of an appropriate style model to explain the returns of Spanish balanced pension plans as well as on the analysis of the relevance of these strategic allocations on portfolio performance. Results suggest similar findings than those obtained in previous studies, providing evidence that asset allocations explains about 90% of portfolio returns over time, more than 40% of the variation of returns among plans, and about 100% of total returns.