The Tredje AP-Funden -The Third National Swedish Pension Fund is known to most as the AP3 fund for short. On 1 January 2001, new legislation came into effect in Sweden that radically changed the mandate of the Swedish government AP Funds. Flexible investment rules were introduced allowing the funds to increase their exposure to foreign assets and equity classes.
According to the new legislation, each of the funds is required to carry through its own ALM study with the purpose of trying to find an asset mix that maximises expected return in relation to the risks taken, where both return and risk should be interpreted in terms of outgoing pensions.
The fund believes that its own ALM-study combines a state-of-the art approach in modelling with some novel insights of how the Swedish elderly pension system is functioning and the buffer funds’ role therein.
As part of the ALM more than 1m scenarios were tested combining three demographic paths with three asset assumption sets and about 100 different portfolios over a 40 years simulation horizon.
Such an endeavour requires ongoing work in parallel modelling of medium and long-term asset return forecasts. This combines the traditional equilibrium standpoint of ALM with a possibility to accommodate medium term disequilibrium.
In addition, AP3 carried out analysis of marginal allocation effects that allowed an heuristic use of steepest descent optimisation to search for the optimal portfolios. This factored in risk described as both the fifth and first lower percentiles of system key variables to capture the effect of distribution tails.
Furthermore, hedge funds were introduced at ALM level with reverse calculations regarding what their expected return should at least be, or how much risk could be permitted for hedge funds to appear in the strategic allocation.
The two main types of parameters for the AP3 model structure and input are those related to demography and those related to asset return/risk assumptions. For the 2001 study, the fund used three alternative parameterisations in both of these dimensions. The fund does not carry on its own demographic modelling, but relies on deterministic calculations provided by the National Social Insurance Board. These projections are then randomised in the AP3 model given the stochastic input from the asset model (inflation, wage inflation, assets). On the asset assumption side, three alternative scenarios were tested, as well as a few stress tests scenarios. The asset side was modelled using a ramification of the well-known Wilkie model to capture the true complexity of a multi-asset, multi-currency portfolio.
The simulation statistics were stored in a database that allowed a detailed study of distributional properties of the key variables of the pension system. In particular, in addition to expected values, also percentile information was stored (up to first percentile).
AP3’s balance sheet is probably one of simplest imaginable. The asset side consists of two components, the buffer funds and the contribution capital – the present value of the future pension income in equilibrium demography. The liabilities are given by the pension debt – the present value of future outgoing pensions in equilibrium. A static description of the system is relatively simple. Its dynamics make modelling challenging. The system incorporates a unique feature called automated balancing mechanism, also known as ‘the brake’, which introduces a complex dependency between the asset and liability sides.
The National Social Insurance Board monitors each year the solvency of the system by looking at the ratio of assets to liabilities – the balance ratio. The solvency will obviously vary from year to year as a function of changes in demography, economy and buffer fund value. If the balance ratio falls below one, the brake is triggered and indexation of outgoing pensions is reduced lowering liabilities of the system temporarily. Eventually the system finds a new balance at a lower level and the original indexation path is restored. The expected loss of benefits-measure mentioned above tries to capture the effect of the brake as it is felt by the beneficiaries in terms of non-received pensions.
This measure was formulated by the fund in connection with last year’s ALM study.

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