مدیریت پرتفولیو بر اساس تغییر رژیم برای صندوق های بازنشستگی

This paper shows how a mean variance criterion can be applied to a multi period setting in order to obtain efficient portfolios in an asset and liability context. The optimization model allows for rebalancing activities, transaction costs, stochastic volatilities for both assets and liabilities. Furthermore, a general framework for the projection of pension fund liabilities as well as for the generation of asset returns is given. In a further step the dynamics of the liability maturity structure is modeled as customized index, whose volatility and correlation with asset returns become integral components of the applied regime switching approach. The numerical results illustrate the diversification of the assets and its risk return pattern in dependency of the liability dynamics.

The management of a pension fund is especially characterized by its guaranteed long term obligations that are usually protected either by law or by the underlying insurance policy. The funding of the fund’s pension plans or rather its liabilities is effected by the contributions of the insurees, their sponsoring firm and moreover by the return on the invested capital. Due to the long term investment horizon the return on the invested capital becomes a decisive element in funding a pension plan. In a defined benefit framework the return on the invested capital should therefore pace out the technical interest rate whereas in a defined contribution framework the return should pace out at least the guaranteed minimal return. Unlike these (usually) guaranteed elements of any retirement plan, the return on the pension fund’s asset allocation is not guaranteed. The observable stochastic volatilities on financial markets therefore necessitate a suitable Asset and Liability Management (ALM) for pension funds to safeguard the pension claims of the beneficiaries. In this context, the main task of any pension fund manager lies in the sustainable funding of the pension liabilities as well as in securing the payments of benefits to the beneficiaries. Hence, a firm implementation of sophisticated quantitative methods and concepts is indispensable in order to tackle the uncertainties that occur with any committed investment. Prominent models challenging this complex task can be found in the field of stochastic programming; like for example in Cariño et al., 1998, Mulvey and Ziemba, 1998, Consigli and Dempster, 1998, Pflug and Swietanowski, 2000, Mulvey and Shetty, 2004, Drijver, 2005 and Zenios and Ziemba, 2006 or Hilli et al. (in press). This paper is structured as follows. In Section 2, a sophisticated model to project the liabilities of a pension fund will be briefly sketched. In Section 3, a regime switching model to estimate the expected returns of the pension fund’s assets categories will be derived. Section 4 captures the key optimization problem in a way strategic asset allocation process allows to take the liability dynamic into account. It will be shown in Section 5 that the careful attention of the correlation structure between assets and liabilities, by means of the regime switching approach, will have a significant impact on the efficient asset allocation and therefore on the risk profile of the whole pension plan.

This paper documents the transfer of the one-period markowitz-approach (see Markowitz (1952)) into a multi-period setting that also accounts for the liabilities and their stochastic interactions to the asset allocation. The presented model particularly considers for rebalancing activities, transaction costs as well as regime-dependent stochastic variance–covariance matrices. The multistage stochastic program presented also accounts for future netto-cash-flows specified by the user. The objective function is a mean variance criterium that leads to decisions that are consistent with those of a quadratic utility maximization (see, also Siede (2000)). It is recalled that the quadratic form in the objective function consists of a one-rank update of the conditional variance–covariance matrix. This one-rank update is represented by the diadic product of the conditional expected returns. In general, the mean–variance criterium may be replaced by any other utility function. However, such extensions are postponed to further research. It was also shown, that the integration of liabilities in the optimization process has a decisive impact on the shortfall probabilities as well as on the composition of the efficient portfolios. In addition, the numerical approach also provides the whole distribution information of the final wealth, respectively the final surplus and is thus a crucial decision-finding tool for every institutional investor. The results point out very clearly that a consistent modeling and integration of the liabilities is therefore indispensable in an integrated portfolio management process. Recent investigations of the underlying portfolio selection approach with respect to long-term planning horizon and with respect to the sensitivity of the diversification subject to the estimation of asset returns may be fund in Niedermann, 2006 and Heuer, 2006.