Abstract. A.D. Roy’s safety first (SF) approach to financial portfolio selection is improved. Safety first means the minimization of the probability of negative returns. The improvement concerns a better estimation of the negative return probabilities by means of mean excess return risk functions. The search for the optimal SF-portfolio is similar to Roy’s geometric method but the efficient frontier is different. In case of a finite number of scenarios, SF-portfolio selection problem is reduced to a linear mixed Boolean programming problem. Figs: 2. Tabl.: 3. Refs: 29 titles.

Keywords: financial portfolio, optimization, return, downside risk, Roy safety, probability estimate, efficient frontier.