New Dimensions in Portfolio Optimization

In a traditional mean-variance approach a portfolio is represented by the allocation vector optimized in terms of expected returns and variances. Basic assumption is that the allocation vector may only be the driver of a portfolio risk-reward trade-off, while all constituent assets are fully specified by constant expected returns and variances. It is not the case, however, for fixed income asset classes, or any assets whose risk-return profile may be a functional of external time-dependent factors. We show that the allocation problem on asset classes level cannot be complete without risk-sensitivities dimensions, as the allocation vector cannot fully specify the portfolio. The proposed approach is a generalization of the allocation problem when assets expected returns and variances might be driven by arbitrary exposures in multiple risk-dimensions. Those risk exposures may depend on investment policies, risk strategies, tactical views, etc. The expansion of the optimization space by the strategy specified risk-dimensions leads to a multi-dimensional mean-variance efficient surface, the efficient hyper-frontier. The analytical solution of multi-dimensional optimization problem is found as a function of the risk-sensitivity matrix. The dependence of optimal allocation decisions on asset sensitivities to interest rates, investment policies and risk strategies is analyzed. Practical implications for the tactical and strategic asset allocations are considered.