It is well known that in the classical single-period mean-variance model,the effcient frontier with both risky and riskless assets is tangent to the efficient frontier with only risky assets.This means that the inclusion of a riskless asset does not increase the highest Sharpe ratio in the single-period setting.In this paper,we prove that the multi-period mean-variance efficient frontier generated by both risky and riskless assets is strictly separated from the one generated by only risky assets,more specifically,there exists a gap between the two efficient frontiers with and without a riskless asset.We also prove that the inclusion of a riskless asset strictly enhances the best Sharpe ratio of the efficient frontier in the multi-period setting,and offer an explicit expression for the enhancement of the best Sharpe ratio.Such findings show that,in contrast to the single-period mean-variance model,the multi-period mean-variance model includes a number of different structures and properties.Finally,a numerical example is provided to illustrate the results obtained in this paper.