Purpose: In addition to the seminal approach of Markowitz (1952) that is based on finding the optimal budget shares for minimizing risk, the authors also make use of the approach developed by Hatemi-J and El-Khatib (2015), which is built on finding the weights as budget shares for maximizing the risk-adjusted return of the underlying portfolio. For testing the stability of the portfolio benefits, the asymmetric interaction between oil, equity and bonds is tested. Design/methodology/approach: Oil is a major investment commodity. The literature shows mixed results regarding oils' ability to provide diversification benefits. This paper re-examines this issue by applying a new portfolio optimization approach. Findings: The authors find that oil still yields portfolio diversification benefits; contrary to the traditional Markowitz portfolio approach, the asymmetric causality test results show that oil does not cause bonds for either positive or negative changes; however, oil does cause stocks but only for stocks' negative changes. Hence, oil can still make the returns of a portfolio of stocks and bonds unstable through oil's effect on stocks. Originality/value: This is the first attempt to investigate the potential portfolio diversification benefits of stocks, bonds and oil by using the combination of risk and return explicitly in the optimization problem. The new insights provided by this article might be valuable to the investors, financial institutions and policy makers.