The maximum geometric mean criterion: revisiting the Markowitz–Samuelson debate: survey and analysis
本文通过几乎一阶随机占优规则，重新审视马克维茨与萨缪尔森关于长期投资组合的争论，发现对于有限长期（12-15年以上）的股票债券组合，最大几何均值组合优于所有最优短视组合。
Abstract By the Almost First-degree Stochastic Dominance (AFSD) rule, corresponding only to economically relevant preferences, for an infinite horizon the $$theoretical$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>theoretical</mml:mi> </mml:mrow> </mml:math> claim of both Markowitz and Samuelson is not intact. However, for the practically more relevant case of the long but finite horizon, with stocks-bonds portfolios, Markowitz $$empirically$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>empirically</mml:mi> </mml:mrow> </mml:math> is right as we find that the MGM portfolio coincides with the optimal myopic portfolio for all risk aversion parameters $$\alpha < 1.7$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo><</mml:mo> <mml:mn>1.7</mml:mn> </mml:mrow> </mml:math> . For $$\alpha \ge 1.7$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>1.7</mml:mn> </mml:mrow> </mml:math> the MGM portfolio dominates by AFSD rule all optimal myopic portfolios, as long as the investment horizon is 12–15 years or longer.