A mathematical model for dynamic stochastic asset liability management of Uganda's retirement benefit schemes

Abstract

models are well established decision tools for pension funds. They are commonly modelled as multi-stage, where a target terminal funding ratio is required, whereas at intermediate time periods, constraints on funding ratio are imposed. There is under funding when the funding ratio becomes too low; a target value of the funding ratio is pre-specified by the decision maker. Risk of under funding is usually modelled by established risk measures.

We study a long term projection of Uganda’s pension funds to assess their sustainability, and develop a mathematical model for dynamic stochastic asset liability management of Uganda’s retirement benefit schemes. We discuss the retirement benefits sector in Uganda, and then focus on the Parliamentary Pension Scheme (PPS) and the Bank of Uganda Defined Benefits Scheme (BoUDBS). We explain Defined Contribution and Defined Benefit pension funds.

We used data provided by the PPS, the BoUDBS and established mortality tables from (United Nations, Department of Economic and Social Affairs, Population Division, 2019). The data provided by the schemes includes annual investment reports and bio-data information for the scheme members. We use non-linear regression to project the PPS scheme members, and a Markov model is used to capture the schemes’ composition by aggregate age states. We incorporate the guaranteed period of pension payment by using two survival probabilities. We obtain the financial evolution for the projection period and ascertain the schemes’ sustainability. A family of stochastic programming models is developed for Uganda’s retirement benefit schemes, and applied to the financial planning problems for the PPS and BoUDBS. The decision model based on multi-stage stochastic programming is mainly used to manage assets and liabilities, by combining the Markov population model with the salary growth model and benefit payments. We use scenario generators which capture the uncertainties of asset returns, salary contribution, pension and lump sum liability payments. The scenario generation models for assets and liabilities were developed and calibrated using historical data. Using different asset investment limits, we obtain the optimal investment strategies and associated cost and risk, together with the funding situation of the schemes at each stage.

The results obtained from the deterministic projections show that both the PPS and BoUDBS are not sustainable on a long term. The PPS is not fair to its two categories of members, contributions from Members of Parliament (MPs) are used to subsidise payment of benefits for staff. The ALM model shows that the schemes reap more from government securities followed by fixed or term deposits and equities. Much lower returns are obtained from corporate bonds, loans and investment property. From the results, we recommend that the PPS should have different benefits indexation parameters for MPs and staff. The schemes should invest heavily in government securities, fixed deposits and equities, while only mandatory portion of the portfolio should be allocated to corporate bonds, loans and investment property.