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This paper investigates the multi-period portfolio problem under the framework of Tobin. Specifically, the paper analyzes the optimal two-period portfolio strategy compared with the buy-and-hold strategy, the stochastic rebalancing strategy and the simple rebalancing strategy. According to the result of the practical examples, we find that the unadjusted investment portfolio known as the buy-and-hold strategy, without regard to transaction cost, is superior to the simple rebalancing strategy in the long run. In fact, this is also the case when the transaction cost considered. In addition, the buy-and-hold strategy is inferior to the stochastic rebalancing strategy when the investment risk is considerably high.Keywords-the buy-and-hold strategy;the stochastic rebalancing strategy(or Duan Li's strategy), the simple rebalancing strategy(or Tobin's strategy), non-Tobin's strategy.

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