Multi-Period Mean CVAR Asset Allocation: Is it Advantageous to be Time Consistent?

We formulate the multi-period, time consistent mean-CVAR (Conditional Value at Risk) asset allocation problem in a form amenable to numerical computation. Our numerical algorithm can impose realistic constraints such as: no shorting, no-leverage, and discrete rebalancing. We focus on long term (i.e. 30 year) strategies, which would be typical of an investor in a Defined Contribution (DC) pension plan. A comparison with pre-commitment mean-CVAR strategies shows that adding the time consistent constraint compares unfavourably with the pure pre-commitment strategy. Since the pre-commitment strategy computed at time zero is identical to a time consistent strategy based on an alternative objective function, the pre-commitment mean-CVAR strategy is implementable in this case. Hence it would seem that there is little to be gained from enforcing time consistency.