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Assisting Defined-Benefit Pension Plans
Abstract
The defined-benefit pension system poses substantial, long-term risks for the U.S. economy. We describe a flexible asset-liability management (ALM) system for pension planning. The primary goals are to improve the performance and survivability of the pension trust. We first employ a stochastic program for enhancing investment strategies in light of company and other goals and pension risk constraints. The results are linked with a policy simulator for further analysis. We illustrate the concepts via two disparate real-world companies. The first is a slowly growing auto company, and the second a pro. table pharmaceutical enterprise. We show that a stochastic program can help in the process of discovering sound policy rules. The ALM system has been employed extensively throughout the world by a large global actuarial firm.
... The suitability of multistage approach to deal with ALM problems has been proved in multiple works during the last decades. Mulvey et al. (2006) suggested a multiperiod model to increase the understanding of risk and reward in a long-term horizon framework for pension plans and other long-term investors, see also (Mulvey et al. 2007(Mulvey et al. , 2008. Comprehensive collections are in Ziemba and Mulvey (1998) and Zenios and Ziemba (2006), Zenios and Ziemba (2007). ...
This paper considers an extension of the common asset universe of a pension fund to investment certificates. Investment certificates are a class of structured products particularly interesting for their special payoff structures and they are acquiring relevancy in the worldwide markets. In fact, some subclasses of certificates offer loss protection and show high liquidity and, thus, they can be very appreciated by pension fund managers. We consider the problem of a pension fund manager who has to implement an Asset and Liability Management model trying to achieve a long-term sustainability. Therefore, we formulate a multi-stage stochastic programming problem adopting a discrete scenario tree and a multi-objective function. We propose a technique to price highly structured products such as investment certificates on a discrete scenario tree. Finally, we solve the investment problem considering some investment certificate types both in term of payoff structure and protection level, and we test whether they are preferred or not to standard hedging contract such as put options. Moreover, we test the inclusion of first-order and second-order stochastic dominance constraints on multiple stages with respect to a benchmark portfolio. Numerical results show that the portfolio composition reacts to the inclusion of the stochastic dominance constraints, and that the optimal portfolio is efficiently able to reach several targets such as liquidity, returns, sponsor's extraordinary contribution and funding gap.
... Given the nature of complexity, we use multi-stage stochastic programming (MSP) to solve the valuation problem (Birge and Louveaux, 1997). MSP is a well-established approach for decision making under uncertainty especially in application areas such as finance and energy (Mulvey et al., 2008;Gassmann and Ziemba, 2013). ...
Traditional take-or-pay contracts have been used to mitigate risks in energy supply chains for decades. More recently, the downstream segment of the natural gas industry has increased capital expenditure on storage facilities in order to enhance supply flexibility and minimize operational risks. In this paper, we study the enhanced value of a take-or-pay gas contract from a buyer’s perspective in the presence of spot market trading and local storage capability. We use a multistage stochastic program via a computationally efficient split-variable formulation and solve this procurement problem to delineate the impact of various key managerial levers on the design, valuation and usage of a take-or-pay contract. Among these, the net convenience yield, storage cost and take-or-pay contract terms are identified as being the most important. Further, we numerically show the subadditivity of values for take-or-pay and storage options. Practically relevant managerial insights are generated to assist decision makers in energy supply chains, where price and demand uncertainties are abundant.
... Contrary to (9), formula (11) suggests a simple financial hedging strategy of taking the initial wealth, e.g., of £10,000, of the original investment strategy and multiplying it by the probability, under the risk-neutral measure, of staying within the lower and upper bounds. This is easy to understand and will minimize the operational risk of misunderstanding and, perhaps, The simplicity of the mathematical hedging of this paper makes our strategy less blackbox-like and more intuitive internally in the company than, for example, strategies based on stochastic programming, which, nevertheless, can be extremely powerful and useful for pensions; see Geyer and Ziemba (2008) for a good example of dynamic stochastic programming of defined contribution schemes as considered in this paper, and also Mulvey et al. (2008) for an example in defined benefit schemes. We refer to Kraft and Munk (2011) for an intelligent life-cycle modelling of household needs that optimize consumer needs, which, nevertheless, seems to fail the simple communication requirement. ...
The paper shows how to reform the platform of pension products so that pension savers, professional financial advisors, actuaries and investment experts intuitively understand the underlying financial risk of the optimal investment profile. It is also pointed out that an excellent optimal investment strategy can destroy the future expected utility of a pension saver if the financial communication is wrong. It is shown that a simple system with an upper and a lower bound, originally inspired by Merton (2014), which can be executed easily using fintech, can replace complicated power utility optimization for the pension saver so that everyone can exactly understand the amount of financial risk taken. The paper focuses on investing money as a lump sum because being able to communicate the associated financial risk can serve as the first step towards communicating more complex pension saving structures.
... (2) 5 They include models for dynamic asset allocation (Hibiki, 2006;Mulvey and Vladimirou, 1992), personal financial planning (Berger and Mulvey, 1998;Consiglio et al., 2007;Dempster and Medova, 2011), defined-benefits and defined-contributions pension plans (Hilli et al., 2007;Mulvey et al., 2008;Ziemba, 2016), insurance with or without minimum guarantees (Carinõ and Ziemba, 1998;Consiglio et al., 2006;Mulvey et al., 2000), mortgage portfolio management (Zenios et al., 1998), corporate bonds (Jobst et al., 2006), and for asset and liability management of large institutions (Mulvey and Ziemba, 1998;Zenios and Ziemba, 2007). Stochastic programming also found applications in pricing derivative securities in incomplete markets (King, 2002;King et al., 2005), including the pricing of sovereign contingent debt (Consiglio and Zenios, 2018). ...
... (2) 5 They include models for dynamic asset allocation (Hibiki, 2006;Mulvey and Vladimirou, 1992), personal financial planning (Berger and Mulvey, 1998;Consiglio et al., 2007;Dempster and Medova, 2011), defined-benefits and defined-contributions pension plans (Hilli et al., 2007;Mulvey et al., 2008;Ziemba, 2016), insurance with or without minimum guarantees (Carinõ and Ziemba, 1998;Consiglio et al., 2006;Mulvey et al., 2000), mortgage portfolio management (Zenios et al., 1998), corporate bonds (Jobst et al., 2006), and for asset and liability management of large institutions (Mulvey and Ziemba, 1998;Zenios and Ziemba, 2007). Stochastic programming also found applications in pricing derivative securities in incomplete markets (King, 2002;King et al., 2005), including the pricing of sovereign contingent debt (Consiglio and Zenios, 2018). ...
The mix of instruments used to finance a sovereign is a key determinant of debt sustainability through its effect on funding costs and risks. We extend standard debt sustainability analysis to incorporate debt-financing decisions in the presence of macroeconomic, financial, and fiscal risks. We optimize the maturity of debt instruments to trade off borrowing costs with refinancing risk. Risk is quantified with a coherent measure of tail risk of financing needs, conditional Flow-at-Risk. A constraint on the pace of reduction of debt stocks is also imposed, and we model the effect of debt stocks on the yield curve through endogenous risk and term premia. On a simulated economy, we show that the cost-risk and flow-stock trade-offs embedded in issuance decisions are key determinants of the evolution of debt dynamics and are economically significant. Comparing three alternative optimizing strategies and some simple fixed-issuance rules, we also draw lessons on when and why optimizing matters the most. This depends on the risk tolerance level, the size, cost, and maturity of legacy debt, and the sensitivity of interest rates to debt. Our model quantifies thresholds for the minimum level of refinancing risks and the maximum pace of debt reduction that a sovereign could reach given its economic fundamentals. Going beyond those thresholds is only feasible through adjustments of gross financing needs, and an extension of the model identifies hot spots for these adjustments, computing their minimum size and optimal timing. Our findings inform policy decisions concerning official sector borrowing and public finance, with a focus not only on minimizing interest payments but also on managing refinancing risks and debt dynamics.
... Nevertheless, in Mulvey et al. (2006) the authors suggest again a multiperiod model to increase the understanding of risk and reward in a long-term horizon framework for pension plans and other long-term investors, see also Mulvey et al. (2007Mulvey et al. ( , 2008. Comprehensive collections are in Ziemba and Mulvey (1998) andZenios andZiemba (2006, 2007). ...
The main goal of a pension fund manager is sustainability. We propose an Asset and Liability Management model structured as a multi-stage stochastic programming problem adopting a discrete scenario tree and a multi-objective function. Among other constraints, we consider the second-order stochastic dominance with respect to a benchmark portfolio. To protect the pension fund from shocks, we test the inclusion of hedge financial contracts in the form of put options and, moreover, we stress the portfolio introducing a new scenario tree contamination technique, namely the nodal contamination. Numerical results show that we can efficiently manage the pension fund satisfying several targets such as liquidity, returns, sponsor's extraordinary contribution and funding gap. Moreover, we test the sensitivity with respect to put option strikes and to the stochastic dominance constraints. Finally, we demonstrate the effect of the scenario tree contamination.
... Milestone models, among others, are: the Russell-Yasuda Kasai Model (see Cariño et al. 1994Cariño et al. , 1998bCariño and Ziemba 1998a), the InnoALM model for multistage managing of a pension fund (see Ziemba 2008, Ziemba 2006), and the CALM model for long-term pension fund planning (see Consigli and Dempster 1998b, a). More recently, Mulvey et al. 2006 suggests a multiperiod model to increase the understanding of the risks and rewards in a long-term horizon framework for pension plans and other long-term investors (see also Mulvey et al. 2007Mulvey et al. , 2008). An innovative formulation of the ALM problem is proposed in Consigli et al. (2011), Consigli and di Tria (2012) and in Consigli and Moriggia (2014). ...
We address the problem of a private pension plan sponsor who has to find the best pension funds for its members. Starting from a descriptive analysis of the pension plan members we identify a set of representative subscribers. Then, the optimal allocation for each representative will become a pension fund of the pension plan. For each representative, we propose a multistage stochastic program (MSP) which includes a multi-criteria objective function. The optimal choice is the portfolio allocation that minimizes the average value at risk deviation of the final wealth and satisfies a wealth target in the final stage and other constraints regarding pension plan regulations. Stochasticity arises from the investor’s salary process and from asset returns. Numerical results show the optimal dynamic portfolios with respect to the investor’s preferences and then the best pension funds the sponsor might offer.
... Ziemba (2009) show several optimization problems to find optimal portfolios, using SP. Mulvey et al (2008) design investment strategies and policy rules with SP to define benefit pension plans. For more applications of SP in asset allocation, see Ziemba and Vickson (2014), Maranas et al (1997) and Hilli et al (2007). ...
Long-term investments such as Private Equity (PE), present timing differences in cash inflows and outflows. When allocations in PE are not planned correctly, investors can suffer liquidity problems when paying for unexpected commitments. We present a multistage stochastic optimization model that includes PE assets as free cash flows projects. This model can determine PE allocations, in relation to public equity, under different market settings. Using a factor-based model to construct public and private equity markets, the major findings are: Liquidity problems can be avoided by planning PE allocations in advance and according to market conditions. Our tool reduces commitments taken for more volatile PE market or when investor target is lower. For target returns above 20 per cent, PE allocations enhance portfolio annual returns from 2 to 3 per cent (no volatility increase) only if PE net present value volatility is below 15 per cent. Beyond this point, higher returns comes with more risk. When PE investments are less correlated with public equity, the latter threshold extends to 45 per cent. PE allocation weight changes in time and according to its age. For favorable market conditions and high investors' appetite, PE investment value can be greater than the entire wealth at some time periods. Leverage option for PE investments decreases performance, even in low PE volatility market. Potential PE gains are offset by debt interest payments and risk becomes higher.
... ALM models have been implemented in numerous pension and insurance studies (Dert (1995), Peskin (1997), Boender, et al. (1998, Ryan and Fabozzi (2003), Hilli et al. (2003), Olson (2005), and Mulvey, et al. (2008)). In these models, there are three basic ingredients: a system for generating future scenarios, a set of rules for significant decisions at each time period, and an algorithm for selecting the best set of decisions. ...
... We do this by attempting to replicate the managers final payoff using an optimal static portfolio including options. Our approach to ALM problems is based on multi-stage stochastic optimization ; see for example Mulvey et al. [11] for an introduction to ALM problems and Dempster et al. 2002 [5] for a general and complete description of the stochastic optimization approach. See Grinold and Kahn [6] for a discussion of active portfolio management with risk controls, or Scherer [17] for a treatment of option replicating strategies such as portfolio insurance. ...
We propose to measure the value added by periodic portfolio rebalancing in actively managed strategies. Using Monte-Carlo simula-tion and dynamic stochastic programming we simulate the pay-off of an actively managed strategy. We seek to replicate this pay-off using a static investment based on the same Monte-Carlo scenarios and the same investment timeframe, but including in the static portfolio some deriva-tive strategies not available to the active manager. We contend that the allocation to the derivative strategies quantifies the value added by ac-tive management. We then test the sensitivity of the solution to various parameters of the problem.
... Risk measures applied to pension fund ALM are, for instance, VaR constraints (Dert [8]), CVaR constraints (Bogentoft et al. [4]), and integrated chance constraints (Klein Haneveld et al. [19]). Country-specific requirements are modeled for, for instance, Austria (Geyer and Ziemba [14]), the Czech Republic (Dupačová and Polívka [11]), Finland (Hilli et al. [16]), the Netherlands (Drijver [9] and [20]), and US (Mulvey at al. [26]). Insights on the generation of good scenarios specifically for pension fund ALM can be found in Hilli et al. [16], Kouwenberg [22], and Pflug et al. [27]. ...
Indexation (correction for inflation) of defined benefit pension rights is an important topic in the current pension debate fostered by the ageing of populations. In the Netherlands, pension funds need to formulate policies concerning indexation. We show how indexation decisions can be modeled adequately in multistage recourse ALM models, which can be used for supporting the policy making. Moreover, for a stylized pension fund we analyze the working of these indexation decisions in a numerical experiment.
... Yale, Harvard, Princeton, and Stanford Universities) and other leading institutional investors have achieved 15-20 + % annual returns over the past decade by shifting a large proportion of their capital to private investments. In contrast, especially since 2000, numerous pension trusts have fallen behind, with many funding ratios dropping to the 75-80% range [6]. ...
This article discusses the role of nontraditional assets in constructing a portfolio for long-term investors. Alternative investments can provide novel patterns of returns and increase diversification benefits. In turn, investors can apply leverage in conjunction with wide diversification to improve their risk-adjusted performance. The concepts are illustrated via popular categories of alternative investments. We focus on long-term investors who are able to rebalance their portfolios on a regular basis. Careful risk management is critical in this domain.
... For example, in a defined-benefit pension plan, the cost of maintaining the plan can be evaluated as the expected discounted value of contribution. The risk measurement can be probability of making a large contribution, likelihood of a bankruptcy over the planning period, or related worst-case events (Mulvey et al., 2008). Various metrics apply to returns and risks over multiple periods, such as measuring risk as a function of a related probability distribution. ...
Investment and risk control are becoming increasingly important for financial institutions. Asset allocation provides a fundamental investing principle to manage the risk and return trade-off in financial markets. This article proposes a general formulation of a first approximation of multiperiod asset allocation modeling for institutions that invest to meet the target payment structures of a long-term liability. By addressing the shortcomings of both single-period models and the single-point forecast of the mean variance approach, this article derives explicit formulae for optimal asset allocations, taking into account possible future realizations in a multiperiod discrete time model. Copyright (c) The Journal of Risk and Insurance, 2010.
... Next, we evaluate the DEO strategies under the asset-liability management context. ALM models have been implemented in numerous pension and insurance studies (Dert (1995), Peskin (1997), Boender, et al. (1998, Ryan and Fabozzi (2003), Hilli et al. (2003), Olson (2005), and Mulvey, et al. (2008)). In these models, there are three basic ingredients: a system for generating future scenarios, a set of rules for significant decisions at each time period, and an algorithm for selecting the best set of decisions. ...
Many large corporate and public pension trusts remain underfunded since the 2001–2002 recessionary periods. These plans are challenged by global demographic trends and the recent slowing economic conditions. We show that a special overlay strategy can improve performance and reduce risks by adding duration to the portfolio. The approach combines elements of liability-driven investing and asset liability management. Versions of the strategy are evaluated via historical data. In addition, the strategy is tested with a widely employed, forward-looking economic projection system.
The area of finance has been relatively immune to the ML technology, except for a few exceptions such as high-frequency trading and credit scoring for loans. Significant financial decisions are made with reference to formal decision models. The first, and most famous, example is the Markowitz portfolio model. This model has been endlessly enhanced. Institutional investors build structured asset allocation and asset-liability management models for a variety of reasons, including the desire to improve performance and others, such as satisfying governance procedures. Regulators may charge institutional investors with imprudence if there is no formal analysis of their portfolio selection decisions and large losses occur. Due to the levels of uncertainties and time-lags in strategic decisions, it can be difficult to evaluate the quality of the recommendations, thus complicating the search for ML breakthroughs. Recall the need for measurements of correctness in supervised learning.
Introduction Integrated Corporate/Pension Planning Model Assisting the Defined Benefit Pension System Conclusions
In many countries, there is a concern about demographic trends associated with providing adequate pensions to retired work-ers. For example, the workforce in Japan is expected to shrink from 84 million to 74 million, while the number of retirees will increase from 26 million to 36 million by 2030. In Europe, the population aged 65 years and older, as a ratio of the working-age population, will increase from 25 per cent in 2008 to 53 per cent in 2060. Given these headwinds, companies who sponsor pension trusts will benefit from improving their investment performance.
We optimize the asset allocation, consumption and bequest decisions of a couple with an uncertain lifetime. The asset menu consists of zero coupon bonds and pure endowments with different maturities, whole life annuities and stocks. The pure endowments pay either fixed or variable benefits, and, similarly to the whole life annuities, are contingent on either a single or a joint lifetime. We model the stock returns and the parameters for the term structure with a vector autoregressive model, thus considering time-varying investment opportunities. To find the optimal solution we use a multi-stage stochastic programming approach, which allows for including complex surrender charges on pure endowments and annuities, as well as transaction costs on stocks and bonds. Our findings indicate that despite high surrender charges, households should invest in a wide combination of life contingent products with different maturities and underlying financial risk.
The paper investigates the importance of inflation-linked annuities in retirement planning. Given nominal, inflation-linked, and variable annuities, as well as bonds and stocks, we search for optimal consumption and investment decisions under two different objective functions: (1) maximization of expected utility of real consumption, and (2) minimization of expected deviations from an inflation-adjusted target. When optimizing the objective, we allow for rebalancing the portfolio during retirement by buying additional annuities and by trading bonds and stocks. To find the optimal solution, we apply a multi-stage stochastic programming approach. Our findings indicate that independently of the considered objective function, real annuities are a crucial asset in every portfolio. In addition, without investing in real annuities, the retiree has to rebalance the portfolio more frequently, and still obtains a lower and more volatile real consumption.
Following the recession of the early 2000s, defined benefit corporate pension plans faced dramatic funding challenges. They had barely recovered before the recession of 2008 to 2009 sent funding ratios tumbling once again. Many plan sponsors must now make larger contributions than they originally budgeted, in order to bring their plans back to full funding. This article aims to deepen the current discussion of risk reduction in the context of defined benefit plans It investigates two key issues. First, its authors analyze the effect of non-normality of asset returns on a defined benefit pension plan's liabilities. They argue that analytical frameworks that assume normality can lead to an underestimation of downside risk, a concern with regard to contributions. Second, the authors develop a multi-dimensional risk-management framework for managing contribution risk.
The paper provides some guidelines to individuals with defined contribution (DC) pension plans on how to manage pension savings both before and after retirement. We argue that decisions regarding investment, annuity payments, and the size of death sum should not only depend on the individual’s age (or time left to retirement), nor should they solely depend on the risk preferences, but should also capture: (1) economical characteristics—such as current value on the pension savings account, expected pension contributions (mandatory and voluntary), and expected income after retirement (e.g. retirement state pension), and (2) personal characteristics—such as risk aversion, lifetime expectancy, preferable payout profile, bequest motive, and preferences on portfolio composition. Specifically, the decisions are optimal under the expected CRRA utility function and are subject to the constraints characterizing the individual. The problem is solved via a model that combines two optimization approaches: stochastic optimal control and multi-stage stochastic programming. The first method is common in financial and actuarial literature, but produces theoretical results. However, the latter, which is characteristic for operations research, has practical applications. We present the operations research methods which have potential to stimulate new thinking and add to actuarial practice.
Commodity investments have gained considerable interest over the past decade. For traditionally diversied investors, an allocation to a fund that invests exclusively in commodity markets oers not only a hedge against ination, but also eective diversication due to its low correlation with traditional asset classes. Over the long run, commodity investment funds show equity-like returns, but are accompanied by lower volatility and shortfall risk.
Over the next several decades, traditional corporate and government pension plans will encounter increasingly severe problems
in many countries. Contributing factors include underfunding status, demographic trends, low savings rates, and inefficient
investment/saving strategies. This chapter takes up the last point, showing that a systematic forward-looking asset–liability
management model can improve performance across many reward and risk measures. The model takes the form of a multi-stage stochastic
program. We approximate the stochastic program via a set of state-dependent policy rules. A duration-enhancing overlay rule
improves performance during economic contractions. The methodology is evaluated via historical backtests and a highly flexible,
forward-looking financial planning tool.
KeywordsAsset and liability management-Financial optimization-Pension plans-Risk management-Asset allocation-Surplus optimization
We discuss integrated chance constraints in their role of sh ort-term risk constraints in a strategic ALM model for Dutch pension funds. The problem is set up as a multistage recourse model, with special attention for modeling the guidelines proposed by the regulating authority for Dutch pension funds. The paper concludes with a numerical illustration of the importance of such short-term risk constraints.
Frank Russell Company and The Yasuda Fire and Marine Insurance Co., Ltd., developed an asset/liability management model using multistage stochastic programming. It determines an optimal investment strategy that incorporates a multiperiod approach and enables the decision makers to define risks in tangible operational terms. It also handles the complex regulations imposed by Japanese insurance laws and practices. The most important goal is to produce a high-income return to pay annual interest on savings-type insurance policies without sacrificing the goal of maximizing the long-term wealth of the firm. During the first two years of use, fiscal 1991 and 1992, the investment strategy devised by the model yielded extra income of 42 basis points (8.7 billion Yen or US$79 million).
We have seen in recent years a significant growth in investment products aimed at investors who are worried about downside potential in the financial markets. One response is a dynamic stochastic optimization model for managing products with nominal or real guarantees. An optimal dynamic portfolio allocation strategy combined with risk management allows an institution to provide the best possible portfolio returns commensurate with clients' risk aversion. Implementation of such an investment strategy is illustrated using real market data and backtested through 1999-2004.
This paper studies formal optimal decision approaches for a multi-period Asset/Liability Management model for a pension fund. As a risk measure we use Conditional Value-at-Risk (CVaR), which is the weighted average of the Value-at-Risk (VaR) and the losses exceed-ing VaR. The model is based on sample-path simulation of the fund liabilities and returns of ¯nancial instruments included in the portfolio. The same optimal decisions are made for groups of sample-paths which exhibit similar performance characteristics. Since allocation proportions depend on time, these techniques are more °exible than more standard allocation procedures such as \constant proportions." Optimization is conducted using linear program-ming. However, compared to traditional stochastic programming algorithms for which the problem dimension increases exponentially in the number of time stages, our approach ex-hibits a linear growth of the dimension. Therefore, this approach allows for the solution of problems with very large numbers of instruments and scenarios.
In models of decision making under uncertainty we often are faced with the problem of representing the uncertainties in a form suitable for quantitative models. If the uncertainties are expressed in terms of multivariate continuous distributions, or a discrete distribution with far too many outcomes, we normally face two possibilities: either creating a decision model with internal sampling, or trying to find a simple discrete approximation of the given distribution that serves as input to the model. This paper presents a method based on nonlinear programming that can be used to generate a limited number of discrete outcomes that satisfy specified statistical properties. Users are free to specify any statistical properties they find relevant, and the method can handle inconsistencies in the specifications. The basic idea is to minimize some measure of distance between the statistical properties of the generated outcomes and the specified properties. We illustrate the method by single- and multiple-period problems. The results are encouraging in that a limited number of generated outcomes indeed have statistical properties that are close to or equal to the specifications. We discuss how to verify that the relevant statistical properties are captured in these specifications, and argue that what are the relevant properties, will be problem dependent.
For a given public or private pension plan benefit structure and for a given funding level, a plan sponsor may want to choose an investment strategy to minimize the present value of future contributions to the plan. This goal is consistent with the way most sponsors make decisions on investment projects generally and in the interests of the plan participants. Kerwin comment on accuracy of abstract and editor's response (September/October 2008). Mehrling and Mindlin comment on accuracy of abstract and editor's response (May/June 2009).
Towers Perrin-Tillinghast employs a stochastic asset-and-liability management system for helping its pension plan and insurance clients understand the risks and opportunities related to capital market investments and other major decisions. The system has three major components: (1) a stochastic scenario generator (CAP:Link); (2) a nonlinear optimization simulation model (OPT:Link); and (3) a flexible liability- and financial-reporting module (FIN:Link). Each part improves over existing technology as compared with traditional actuarial approaches. The integrated investment system links asset risks to liabilities so that company goals are best achieved. For example, US WEST saved $450 to $1,000 million in opportunity costs in its pension plan by following the advice of the asset-and-liability system.
The Towers Perrin company applies integrative asset-liability planning to the problem of pension management. The planning system depends upon a stochastic economic projection model - called CAP:Link - for generating economic factors and asset returns via a set of representative scenarios. Each scenario depicts a coherent set of outcomes. The projections span a long-run horizon - 10 to 40 years. Risks and rewards for alternative investment strategies are determined via dynamic asset and liability allocation over the scenarios. The approach has been implemented in 12 countries in Europe, North America, and Asia.
Corporate management views a defined benefit pension plan as a trust for the employees and manages the fund almost as if it were a defined contribution plan with a guaranteed floor specified by the benefit formula. In order to minimize the cost to the sponsor of providing the minimum benefit guarantee, there is a strong incentive to hedge the accumulated benefit obligation (ABO) by investing in fixed income securities with a matching duration -- that is, to immunize it. The incentive to immunize the ABO is strongest when the plan is fully funded. If the plan is overfunded, it makes sense to invest in equities and pursue a kind of portfolio insurance strategy known as contingent immunization. If the plan is very underfunded and the sponsor is in financial distress, it may be optimal to exploit the put provided by PBGC insurance through a high-risk investment strategy. Tax, regulatory, and other considerations have in the past created strong incentives to overfund the pension plan. Recent changes in accounting rules and tax law are likely to reinforce the use of fixed income immunization strategies and reduce pension fund investment in equities. While useful for estimating a firm's future cash flow, the projected benefit method is misleading in the conduct of pension fund investment policy. The PBO is not an appropriate measure of the benefits that the employer has guaranteed and therefore not a target to be hedged by pension fund investment policy. The failure of pension funds to show any significant interest in inflation -protected investment products such as CPI -linked bonds is clear evidence that they do not view their liabilities as indexed for inflation. Investing in equities provides pension funds with higher expected returns, but does not offer an effective hedge against inflation risk.
A stock-bonus plan with a provision to permit diversification can come close to replicating the classic default risks in defined-benefit pension plans. The diversification formula is a function of a worker's service in the company and the particular features of the defined benefit (DB) plan that are being reproduced. The diversifiable stock-bonus (DSB) plan still gives workers a stake in the financial performance of the company, but the diversification formula eliminates the extreme downside of a traditional stock-bonus plan, namely, the possibility that workers could lose up to all of their retirement accounts after long years of service. Because the DSB plan imposes about the same default risks on workers as a DB plan, workers' compensation levels with a DSB plan need not be any higher than in a traditional pension plan.
The paper argues that the market significantly overvalues firms with severely underfunded pension plans. These companies earn lower stock returns than firms with healthier pension plans for at least 5 years after the first emergence of the underfunding. The low returns are not explained by risk, price momentum, earnings momentum, or accruals. Further, the evidence suggests that investors do not anticipate the impact of the pension liability on future earnings, and they are surprised when the negative implications of underfunding ultimately materialize. Finally, underfunded firms have poor operating performance, and they earn low returns, although they are value companies.
The US economy is arguably following an unsustainable trajectory. The main indicators of this are a large current account deficit, a large federal budget deficit and trend-wise increasing costs of Social Security and Medicare. In this chapter, we will discuss these observations and to what extent the financial and economic crisis may have changed the outlook. Before this, we need to define what we mean by sustainability. An often used definition of sustainability is that the inter-temporal budget restriction is satisfied.
: We develop a framework for analyzing the capital allocation and capital structure decisions facing financial institutions such as banks. Our model incorporates two key features: i) value-maximizing banks have a well-founded concern with risk management; and ii) not all the risks they face can be frictionlessly hedged in the capital market. This approach allows us to show how bank-level risk management considerations should factor into the pricing of those risks that cannot be easily hedged. We examine several applications, including: the evaluation of proprietary trading operations; and the pricing of unhedgeable derivatives portfolios. I. Introduction One of the fundamental roles of banks and other financial intermediaries is to invest in illiquid financial assets--assets which, because of their information-intensive nature, cannot be frictionlessly traded in the capital markets. The standard example of such an illiquid asset is a loan to a small or medium-sized company. A m...
Stochastic programming is a powerful modelling paradigm for asset and liability management problems. It incorporates in a common framework multiple correlated sources of risk for both the asset and liability side, takes a long time horizon perspective, accommodates different levels of risk aversion and allows for dynamic portfolio rebalancing while satisfying operational or regulatory restrictions and policy requirements. This chapter introduces stochastic programming models for broad classes of asset and liability management problems, describes procedures for generating the requisite event trees, discusses the validity of model results for illustrative applications, compares stochastic programming with alternative modelling approaches, and hinges upon solution techniques and computational issues.
Risk management and a unified theory of the firm
- R Jarrow
Statement before the Subcommittee on Select Revenue Measures, Committee on Ways and Means. United States House of Representatives
- S A Kandarian