Issue: 2026/Vol.36/No.1, Pages 1-23
MEAN RETURN - STANDARD DEVIATION INVESTING ON THE FLUCTUATING EFFICIENT FRONTIER
Przemysław Juszczuk
, Ignacy Kaliszewski , Janusz Miroforidis , Dmitry Podkopaev
Cite as: P. Juszczuk, I. Kaliszewski, J. Miroforidis, D. Podkopaev. Mean return - standard deviation investing on the fluctuating efficient frontier. Operations Research and Decisions 2026: 36(1), 1-23. DOI 10.37190/ord/210425
Abstract
The Markowitz mean return -- standard deviation portfolio selection 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 possible mean returns. Next, depending on the location of the selected value in the range, 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 to use a flexible approach, where the investor's risk is assessed relative to the possible mean return range and thus can be kept relatively consistent throughout the entire investment horizon. We experimentally examine the adequacy and predictive power of the proposed relative risk assessment in multi-period investments with rebalancing versus single-period over-the-whole-horizon investing.
Keywords: Markowitz model, portfolio investing, mean return -risk profile, rebalancin
Received: 21 October 2024 Accepted: 8 September 2025
Published online: 8 September 2025