A Justification of Constant Mix Investment Strategies

The aim of this paper is to justify the use of constant mix investment strategies as an approximation for periodically rebalanced investment strategies. In Dhaene et al. (2005), general optimization problems are solved in a lognormal framework by deriving convex order bounds based on comonotonicity. The multi-period optimal portfolio selection problems discussed in Dhaene et al. (2005) are solved working in the class of constant mix strategies. As this class requires the investment portfolio to be rebalanced on a continuous basis, it can not be applied in practice. However, constant mix strategies have clear computational advantages compared to the more realistic class of periodically rebalanced strategies. Therefore it is important to investigate the appropriateness of these constant mix strategies, which is the main goal of this paper. Our numerical results confirm that, within our lognormal framework, continuous rebalancing can be seen as a limiting case of periodic rebalancing. Moreover, we see that results obtained by periodically rebalancing the available assets are very close to those obtained through continuously rebalancing them, which justifies the use of constant mix strategies. JEL code: G11, Subject Category: IM10