The Markowitz model refers to single-period investing. A common practice is using this model for multi-period investing with portfolio rebalancing at specified times. Such investing is sub-optimal compared to dynamic multi-period investing but is much simpler, which matters in practice. Usually, the investor controls the risk implicitly by selecting the desired mean return within the range of mean returns. Next, the investor assesses the risk according to his/her mean return - risk profile. However, this setup does not apply to multi-period investing because the ranges of possible mean returns and the relation between mean return and risk vary from period to period. As a result, the mean return selected in one period can correspond to a different level of risk in the next one. To address this issue, we propose an approach where the investor's risk is assessed relative to the possible mean return range and can be kept relatively consistent throughout the entire investment horizon.
Juszczuk et al. (Mon,) studied this question.