In an efficient world, an organisation can only make a profit by allocating risk to the various agents of the organisation, and by rewarding these agents for carrying the risk. In this article we describe how we accomplish this at pension funds, where the strategic decision problem of multiple risk/return management is known as asset liability management (ALM).
We first compare the ALM manager with an investment manager. The investment manager faces two issues: first, to agree an appropriate risk budget with the client, and second, to earn the risk budget a maximal expected gain. The investment manager thus has to pursue an efficient policy in the two-dimensional space of expected return and risk. The ALM-manager of a pension plan, however, lives in a much more complex decision space, whose dimensions might add up to eight rather than two. This is because the ALM manager has to take into account the risk budgets and interests of four agents: the sponsors, the beneficiaries, the regulating authorities and the managers of the plan.
In a pension plan, the sponsor can provide an important risk budget. If the sponsor – the employer in a defined benefit plan, or the employee in a defined contribution plan – provides additional contributions in case the plan is underfunded, the plan can, ceteris paribus, carry more risk and invest more in risky high-return asset classes.
Consider a sponsor with a base salary of e1bn and a pension plan with pension assets of e10bn. Suppose that the risk budget provided by the sponsor enables the plan to earn an expected additional return on investments of 150 basis points a year. If this additional return went in full to the sponsor, this return would amount to an expected rebate of 15% of the salary base each year! However, the contribution-at-risk (CaR) should not be open-ended (as is the case with the minimum funding requirement in the UK!). This can be clearly illustrated by assuming that the pension fund in our case would be confronted with a 10% under-return on investments. An immediate repair of the funded status by the sponsor would require an extreme contribution of 100% of salaries, which could obviously threaten the solvency of the company. Thus, the ALM manager has to make a joint risk-return contract with the sponsor about the maximal CaR on the one hand, and his share in the resulting expected gains on the other.
In a DB scheme, the ALM manager has to agree on a risk budget with the beneficiaries. Beneficiaries typically have conditionally indexed pension rights, which have to be covered by the revenues of the assets. The risk contract with the beneficiaries could contain a clause that indexing is postponed if the plan is in deficit, and recovered if the plan attains a surplus. The risk budgets provided by the beneficiaries – pension-at-risk (PaR) – enable the plan to carry more risk and invest more in risky high-return asset classes, which should also add to the benefits of the beneficiaries.
The ALM manager also has to take into account the regulatory authorities. Strictly speaking, a DB plan is not allowed to be in a situation of structural underfunding. However, in a probabilistic model of the uncertain future economic environment, this clause nevertheless allows for probabilities of future underfunding, or non-zero values of future surplus-at- risk (SaR). This SaR, whose maximal value has to be agreed with the sponsors and the beneficiaries, determines the third risk budget. This risk budget also has an important counterpart which is the target surplus of the plan.
Finally, there is the issue of management effect-at-risk. Consider a universe of pension plans that invest about 50% in risky assets. One plan, X, possesses a relatively large surplus as well as relatively large risk budgets with respect to CaR and PaR, whereas the risk budget with respect to SaR is in accordance with the universe. Given the larger surplus and risk budgets, management of X decides to invest 80% in risky assets, meanwhile maintaining the SaR in accordance with the universe. Suppose that risky assets in a particular year significantly underperform safer assets. Then the newspapers would list X as a bad performer, with obvious consequences for the reputation of the plan managers, although the decision that led to the performance was responsible and good.
Given the eight-dimensional decision space in which the ALM manager has to operate, how can the risk budgets of the four agents described above be optimally set and exploited?
In our experience this can best be accomplished by applying a corporate model of the plan which makes use of scenarios for the key drivers of uncertainty regarding the economic environment and the development of the liabilities. The usefulness of such a corporate model (or management flight simulator) is established in two (interrelated) phases of our ALM projects – decision support focused on the insight of the decision-makers, and optimisation focused on improving the efficiency of ALM policies. In this article we will further describe the usefulness of ALM models to decision makers.
Prior to an ALM project, responsible agents of a pension plan probably feel uncomfortable and insufficiently informed when they are asked to specify relevant risk budgets, and what gain they would require in return. This is understandable, for several reasons:
q Intuition. The responsible agents do not have sufficient intuition about the risks, which corresponds to specific values of the several risk measures (SaR, PaR, CaR and MaR).
q Universe. Their decision on a maximal allowable risk is certainly dependent on the risk budgets that are provided by their peers (MaR).
q Underlying assumptions. The risk budgets should be specified in view of the underlying assumptions of the uncertain quantities that drive the relevant risks. For example a 5% SaR of e0.5bn has a completely different interpretation in a probabilistic world with a prudent expected equity risk premium, rather than in a ‘new economy’ setting.
q Trade-off of risk and return. Most of the agents a priori have insufficient knowledge on the ‘return-elasticity of risk’. For example, what is the expected reduction of the contribution rate if the sponsor provides one additional unit of contribution risk? Clearly the responsible agents require insight into these elasticities before they can come to a well-founded agreement on these risk budgets.
Thus, the ALM-manager is not confronted with a clear-cut optimisation problem in which all the agents a priori specify the objectives and the risk budgets, which the manager could in principle immediately solve to optimality. Therefore, in phase one of our ALM projects we apply ALM models and ALM software as management flight simulators to support the plan agents in deciding on these issues. That is, in this phase of the projects, rather than aiming at a mathematically optimal ALM policy, our ambition is to give the responsible agents adequate quantitative insight into the above issues.
How do we realise this ambition? Of course, the quality, tractability, scope and flexibility of the ALM models are important to facilitate the learning process. Another quintessential factor of success is graphical presentation, some examples of which are shown.
Figure 2 displays the consequences of different asset allocations of an ALM policy for the average expected contribution rate one the one hand (x-axis), and the probability of underfunding on the other (y-axis). Each pie denotes an asset allocation, where the different colours display the percentages invested in different asset classes. Note that the pension plan could obtain negative average expected contribution rates, but this can only be accomplished at an exponential increase of SaR.
Figure 3 (which refers to a different pension plan) is focused on so-called integral ALM decision making. The pies on the right policy line, referred to as ‘clean’ (short for clean funding), are based on a funding policy where the sponsor donates additional contributions if the funded ratio drops below 110%, and receives overshoots above110% as contribution rebates in return. The pies on the second policy line, referred to as ‘buf’ (buffer funding), are based on a funding policy where the contribution is increased if the funded ratio drops below 115%, and decreased if the funded ratio exceeds 135%. Clearly in the second case the plan is less vulnerable to market risks. Given a risk budget of a maximal probability of 5% in the event that the funding ratio drops below 90%, this implies that the plan can invest more than 65% in equity, rather than 40% in the clean funding case. As can be verified from the figure, this implies an expected average contribution rate of about –3% of salaries, rather than +7%.
In our opinion the usefulness of these pictures is twofold:
q Intuition and insight. These presentations create the possibility to work out which economic scenarios have led to particular developments of the contributions, pensions and surplus. Clearly, the responsible agents can see and verify it all. In practice this significantly facilitates building up intuition and insight with respect to the quintessence of the decision-making process.
q Decision-making. Secondly, the information in the pictures distinctly quantifies the risk-return trade-offs and elasticities referred to above. Here we showed only the risk with respect to surplus, and the expected benefits with respect to the contribution rate. In practice decision-makers of course also take into account other important aspects, such as the risk with respect to the contribution rate (such as the probability that the contribution rate exceeds critical values) and the risks and benefits with respect to the beneficiaries.
In combination with the graphical presentations of the individual scenarios, the information with respect to these various trade-offs in practice enables the responsible agents to take well-founded decisions on the risk budgets on the one hand, and on the distribution of the revenues which are gained from the risk budgets on the other.
Finally, what have been the practical consequences of ALM decision support? In our home base, the Netherlands, with about e450bn of pension assets, almost all pension plans support their strategic decision-making by regular asset liability projects. More and more, pension plans in the rest of Europe are getting active in this field as well.
Starting about 15 years ago, ALM first supported the pension plans in deciding to reallocate their assets from about 100% fixed income to about 50% of equity and real estate. Secondly, as a result of the integral approach to ALM, this landslide in the portfolios has been accompanied by the introduction of explicit agreements containing SaR, CaR and PaR on the one hand, as well as the distribution of the market gains to these risk providers on the other.
Recently, the investment part of ALM decision support has been getting more focused on evaluating the (multi-dimensional) ALM efficiency of ‘non-classical asset classes’, such as private equity, commodities, currency hedging, derivatives, and state dependent asset allocation.
C Guus E Boender and R Martijn Vos are with Ortec Consultants in Rotterdam