Numerous articles use the Markowitz mean-variance approach for computing the capital asset pricing model (CAPM) and to determine the best set of assets an investor should hold. But using a symmetric risk measure is not necessarily straightforward in the mind of many investors. Many other approaches to determine a portfolio composition, e.g. faith or other behavioral determinants, appear more natural. Especially an asymmetric downside risk approach is more appealing to many investors. This work investigates the differences between portfolios based on a symmetric and on an asymmetric risk measure. Based on the Behavioral Portfolio Theory (BTP) model by Shefrin and Statman and the Markowitz classical portfolio approach the authors compare portfolios composed by stocks of the French SBR 120 market over a period of 6 years. Simulation of 100,000 virtual portfolios over the study period shows that there are only minor differences between portfolios obtained by downside or symmetric risk. Therefore, the results leave room for taking into consideration other choice criteria to complete the approach, such as the computing power if an investor wants to use much more demanding downside risk methodology or faith bases selection criteria to pick the assets.