Time consistent vs. time inconsistent dynamic asset allocation: Some utility cost calculations for mean variance preferences

We solve for the time consistent dynamic asset allocation of an investor with a mean variance objective function in a multiple assets affine setting. We use as a benchmark the pre-commitment strategy widely used in the literature and assess the potential welfare gains from pre-commitment by comparing the time consistent strategy to the pre-commitment, time inconsistent, strategy. The gains from pre-commitment are simply considerable since, in some cases, at the 5 years horizon the yearly certainty equivalent of the pre-commitment strategy is 48% compared with 9% for the time consistent strategy. However, these welfare gains result from huge and unrealistic positions in the risky assets; in some cases, the pre-commitment strategy is more than 60 times the time consistent strategy. We thus looked for alternative time inconsistent strategies that improve relative to the time consistent strategy while still involving reasonable risky asset positions. To identify these strategies, we explore an original aspect of the time consistent mean variance strategy: the presence of intertemporal hedging in such a strategy reflects welfare degradation. Therefore, a natural candidate is the time consistent strategy without the intertemporal hedging component. The second component of the time consistent strategy is the traditional myopic component discounted. We show that this component could be seen as a standard myopic strategy which is marked to market and the discount factor acts as a tailing factor. This marked to market myopic (MMM) strategy is shown to yield reasonable risky assets positions and substantial welfare gains at long horizons relative to the time consistent strategy. We also show that it dominates the standard myopic strategy as well as the equally weighted strategy.