A geometric approach to multiperiod mean variance optimization of assets and liabilities

We present a geometric approach to discrete time multiperiod mean variance portfolio opti-mization that largely simplies the mathematical analysis and the economic interpretation of such model settings. We show that multiperiod mean variance optimal policies can be decom-posed in an orthogonal set of basis strategies, each having a clear economic interpretation. This implies that the corresponding multi period mean variance frontiers are spanned by an orthogonal basis of dynamic returns. Specically, in a kperiod model the optimal strategy is a linear combination of a single kperiod global minimum second moment strategy an