Mean-variance portfolio selection and efficient frontier for defined contribution pension schemes

Abstract

We solve a mean-variance portfolio selection problem in the accumulation phase of a deflned contribution pension scheme. The e‐cient frontier, which is found for the 2 asset case as well as the n + 1 asset case, gives the member the possibility to decide his own risk/reward proflle. The mean-variance approach is then compared to other investment strategies adopted in DC pension schemes, namely the target-based approach and the lifestyle strategy. The comparison is done both in a theoretical framework and based on simulations. As a result, it turns out that the target-based approach can be formulated as a mean-variance optimization problem. It is shown that the corresponding mean and variance of the flnal fund belong to the e‐cient frontier and also the opposite, that each point on the e‐cient frontier corresponds to a target-based optimization problem. Furthermore, numerical results indicate that the largely adopted lifestyle strategy seems to be very far from being e‐cient in the mean-variance setting.

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