Mathematical Programming of Admissible Portfolios

It is well known that when the distribution of portfolio returns is normal, the admissible set of portfolios for risk-averse investors with increasing and concave utility functions is the Markowtiz-Tobin mean-minimum variance admissible boundary: The admissible set is obtained by minimizing a convex quadratic function subject to linear constraints and can be obtained efficiently using Markowitz-Sharpe critical line algorithm. We show that the admissible set of portfolios for all investors (with increasing utility functions, including risk-averters, risk-seekers, risk-neutral and Friedman-Savage-type individuals) is the Markowitz-Tobin boundary plus a portion of the mean-maximum variance boundary. We propose a simple algorithm to obtain the mean-maximum variance boundary. Thus, our algorithm plus Markowitz-Sharpe algorithm obtains the admissible set of portfiolios for all investors.