We analyze the properties of the optimal portfolio policy for a multiperiod mean-variance investor facing multiple risky assets in the presence of general transaction costs such as proportional, market impact, and quadratic transaction costs. For proportional transaction costs, we find that a buy-and-hold policy is optimal: if the starting portfolio is outside a parallelogram-shaped no-trade region, then trade to the boundary of the no-trade region at the first period, and hold this portfolio thereafter. For market impact costs, we show that the optimal portfolio policy at each period is to trade to the boundary of a state-dependent rebalancing region. Moreover, we find that the rebalancing region shrinks along the investment horizon, and as a result the investor trades throughout the entire investment horizon. Finally, we show numerically that the utility loss associated with ignoring transaction costs or investing myopically may be large.