Multiperiod Mean Conditional Value at Risk Asset Allocation: Is It Advantageous to Be Time Consistent?

We formulate the multiperiod, 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 pension plan. A comparison with precommitment mean-CVAR strategies shows that adding the time consistent constraint compares unfavorably with the pure precommitment strategy. Since the precommitment strategy computed at time zero is identical to a time consistent strategy based on an alternative objective function, the time zero precommitment mean-CVAR strategy is implementable in this case. Hence it would seem that there is little to be gained from enforcing time consistency.