Does constant asset allocation dominate buy-and-hold?

There is a widespread perception that it is optimal to keep portfolio weights constant over time, and that the optimal rebalancing frequency is just a question of the transaction cost. This is not generally true. We show that buy-and-hold is not stochastically dominated by any constant allocation strategy. Thus, there are some risk averters, including those requiring a minimal subsistence level, who are better-off with a buy-and-hold strategy when returns are i.i.d, even when rebalancing is free. Perhaps surprisingly, the longer the investment horizon, the larger the set of investors who prefer buy-and-hold over constant allocation.