投资组合的运行轨迹和受力分析研究

Research on the running track and force analysis of portfolio

将某一时点投资组合看成是动点,其过去历史表现和未来变化趋势,可以用动点在"风险-收益"平面上的运动轨迹来予以刻画.也可以将2个投资组合之间的相互作用效应,看成是"万有引力".理论分析表明,适当选定准线和焦点,动点由于受到焦点的"万有引力"吸引和自身速度共同影响,其运动轨迹为圆锥曲线.实证分析结果表明,对66个投资组合的离心率进行分类,股票型和混合型基金多为椭圆型基金,货币型基金为抛物型基金,债券型基金多为双曲型基金.抛物线上分支不能很好地拟合所有的散点,需要分类拟合.利用夏普比率对投资组合进行业绩评价,发现夏普比率和离心率呈中度正相关.最后,根据物理学知识,利用椭圆型基金运行至椭圆轨道上顶点时的速率公式,可以测定出"万有引力常数"G0=1.72×10-14(λ3·周-2·元-1).

When the portfolio is regarded as a moving point in the “risk-return” plane, we can use the running track of the portfolio in the plane to describe its past historical performance and future trend. The interaction effect between the two portfolios can also be seen as “gravitation”. The theoretical analysis shows that when we select the proper alignment and focus point, the running track of the moving point is conic section, due to the common effect by the focus point “gravitation” attraction and its velocity. The empirical result is acceptable. According to the eccentricities classification of 66 portfolios, the classification result shows that most of stock funds and hybrid funds are elliptical funds, the monetary fund are parabolic funds, most of bond funds are hyperbolic funds. The upper branch of parabola can not fit all the scattered points very well, in need of classification fitting. We use Sharpe ratios to evaluate the performance of the portfolios. The result shows that Sharpe ratios is positively correlated with the eccentricities. Finally, according to physics, the “gravitational constant” can be determined by using the velocity rate formula when the elliptical fund runs to the top of the elliptic orbit. The gravitational constant G 0 is 1.72×10^-14 （ λ ^-3 ·week ^-2 ·yuan ^-1 ）.