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Article Excerpt
This paper describes the financial planning model InnoALM we developed at Innovest for the Austrian pension fund of the electronics firm Siemens. The model uses a multiperiod stochastic linear programming framework with a flexible number of time periods of varying length. Uncertainty is modeled using multiperiod discrete probability scenarios for random return and other model parameters. The correlations across asset classes, of bonds, stocks, cash, and other financial instruments, are state dependent using multiple correlation matrices that correspond to differing market conditions. This feature allows InnoALM to anticipate and react to severe as well as normal market conditions. Austrian pension law and policy considerations can be modeled as constraints in the optimization. The concave risk-averse preference function is to maximize the expected present value of terminal wealth at the specified horizon net of expected discounted convex (piecewise-linear) penalty costs for wealth and benchmark targets in each decision period. InnoALM has a user interface that provides visualization of key model outputs, the effect of input changes, growing pension benefits from increased deterministic wealth target violations, stochastic benchmark targets, security reserves, policy changes, etc. The solution process using the IBM OSL stochastic programming code is fast enough to generate virtually online decisions and results and allows for easy interaction of the user with the model to improve pension fund performance. The model has been used since 2000 for Siemens Austria, Siemens worldwide, and to evaluate possible pension fund regulation changes in Austria.
Subject classifications: scenarios; correlation matrices; pension fund planning; stochastic linear programming. Area of review: OR Practice.
History: Received July 2003; revisions received January 2006, August 2006, January 2007, March 2007; accepted March 2007.
Introduction
The Siemens pension fund, established in 1998, is the largest corporate pension plan in Austria. More than 15,000 employees and 5,000 pensioners are members of the pension plan, with 510 million euro in assets under management as of December 1999. Innovest Finanzdien-stleistungs AG, founded in 1998, is the investment manager of the Siemens pension plan and other institutional investors, with more than 7 billion euro in assets under management. The pension fund asset-liability management model InnoALM has been in use at Innovest since 2000. Meanwhile, it has become the only consistently implemented and fully integrated proprietary tool for assessing pension allocation issues within Siemens AG worldwide.
Several factors led Innovest to develop InnoALM, primarily the realization that changing demographics are creating a much higher ratio of retirees to workforce. Furthermore, the asset allocation constraints imposed by Austrian pension law are relaxed if a pension fund is using advanced modeling tools and proves adequate risk management capability. This makes it paramount that the pension plan be managed using systematic asset-liability management models as a tool in the decision-making process. A promising way to approach this was a multi-period stochastic linear programming model.
InnoALM is one of the first implemented models to fully exploit the power of the multiperiod stochastic programming optimization approach in a European pension fund. The mathematical aspects of such models applied to asset-liability management are documented in Ziemba and Mulvey (1998), Gondzio and Kouwenberg (2001), and Wallace and Ziemba (2005). While following to some extent the work on the Russell-Yasuda insurance company planning models (Carino et al. 1994, 1998; Carino and Ziemba 1998), the application to European pension funds is new, and this model has new features such as state-dependent correlation matrices, fat-tailed asset return distributions, and output not in previous models. Zenios (1999) surveys large-scale asset-liability applications to bond and fixed-income portfolio management. Gondzio and Kouwenberg (2001) solved Dutch pension fund asset-liability management problems with millions of scenarios, constraints, and variables. Publicly available codes to solve large stochastic programming problems are detailed in Wallace and Ziemba (2005).
What is crucial are models that represent well the situation at hand, are user friendly, and provide the essential information quickly to those who need to make sound pension fund asset-liability decisions. The multiperiod stochastic programming approach includes more of the essential elements of the real problem faced by the pension plan than alternative approaches such as static mean-variance analysis (see, e.g., Sharpe and Tint 1990), continuous-time modeling (see, e.g., Campbell and Viceira 2002 and Rudolf and Ziemba 2004), shortfall risk minimization (see, e.g., Leibowitz and Henriksson 1988), and other approaches (see, e.g., Ziemba and Mulvey 1998). Key elements that make InnoALM superior to other models are the flexibility to formulate constraints and targets in combination with a broad and deep array of scenario-specific results. This allows Innovest to investigate path-dependent behavior of assets and liabilities as well as scenario-based risk assessment. Some of these aspects are illustrated in the application presented in [section]4.
InnoALM implements state-dependent correlation across asset classes, as asked for in discussions by Lo (1999) and Merton (2000). This feature allows the model to react to extreme events and to plan in advance to do so. Models that assume constant correlation matrices make a conceptual error that is one of the major factors appearing in most of the financial trading disasters of the 1990s and beyond, such as Orange County in 1994, Barrings in 1995, Niederhoffer in 1997 and 2006, Long Term Capital Management in 1998, the Tiger and Soros Hedge Funds in 2000, and Amarath in 2006. When funds are nondiversified and overleveraged, a plausible but low-probability extreme scenario can lead to a financial disaster. Consideration of the state-dependent correlations in advance should lead to portfolios that can react better to an extreme scenario and still produce good results when other, more probable scenarios occur. This feature is documented in the application presented in [section]4.
The paper briefly discusses the pension fund situation in Austria and Europe in [section]1. Section 2 develops the stochastic programming model formulation. Section 3 discusses the scenario generation and statistical inputs available for use in the model. Section 4 presents an illustrative application, using an example of a model formulation with five decision periods and four asset classes in various circumstances, including the difficult market conditions faced in 2000-2003. Section 5 provides conclusions and final remarks.
1. The Pension Fund Situation in Austria and Europe
The world's populations are aging rapidly. By 2030 there will be roughly a doubling from about 20% to about 40% of those 65 and older, the retiree group, compared to those 15-64, the worker group, in most countries of the world (see Bos 1994 or Roseveare et al. 1996). This demographic effect will have a major impact on public and private pension plans in Europe and across the world. European Union state pensions (usually labeled as Pillar 1) account for about 88% of total pension costs. While pay-as-you-go plans, where the contributions of current workers support current pensioners similar to U.S. social security, are the most threatened by aging populations, defined contribution plans are also at risk. Without changes, the pension payouts will grow from 10% of GDP in 1997 to over 15% of GDP in 2030 for many EU countries. Contribution rates must be raised significantly to enable the public social security system to cope. Reforms of the public pension systems will be necessary, together with an effective environment for Pillar 2 (company pensions) and Pillar 3 (private pension systems).
This paper describes a model for the effective operation Pillar 2 private pension funds in Austria. These funds usually work on a funded basis, where the pension benefits depend on an employment contract or the pursuit of a particular profession. Schemes are administered by private institutions, and benefits are not guaranteed by the state. Normally, contributions to such systems are made by the employer and, on an optional basis for additional benefits, by employees. Defined contribution plans (DCP), such as the Siemens pension plan for Austria, have fixed contributions, but the pensions are not fixed and the payout depends on the capital accumulation of the plan. Defined benefit plans (DBP) have payouts guaranteed by the company, and the contribution is variable, depending on the capital accumulation over time. For DCPs, which have become more popular, the employees and pensioners bear the risk of low asset returns. There is no direct financial risk for the employer, although with poor returns the employer would suffer negative image effects. For example, if there would be a headline "pensions for the Siemens' pensioners must be reduced by 3% in the next year," there would be reputation risk for Siemens.
The liability side of the Siemens pension plan consists of employees, for whom Siemens is contributing payments based on the DCP outline, and retired employees who receive pension payments. Contributions are computed on an individual level as a fixed fraction of salaries, which varies across employees. The set of retired employees is treated according to Austrian mortality and marital tables. Widows and widowers (a much smaller group) are entitled to 60% of the pension payments. Retired employees receive pension payments after reaching age 65 for men and 60 for women in accordance with the legal pension plan. Payments to retired employees are based on the individually accumulated contribution and the fund performance during active employment.
The actuarial computation of liabilities is based on the assumption that active employees are in steady state; that is, staff is replaced by a new employee with the same qualification and sex, which gives rise to the constant number of employees. Newly employed staff starts with less salary than retired staff, which implies that total contributions grow less rapidly than individual salaries. There exist agreements with employees such that the annual pension payments are based on a discount rate of 6% and the remaining life expectancy at the time of retirement. It is also agreed that these annuities grow by 1.5% annually to compensate for inflation. Hence, the wealth of the pension fund must grow by 7.5% per year to match liability commitments; see the InnoALM wealth target described in [section]2.
Some EU member states rely on quantitative restrictions on asset allocations to ensure proper pension fund investments. Such rules are usually established to protect the pensioners but also lead to weakly diversified asset holdings. For example, in 2002...
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