中文摘要：

通常的投资建议和两基金分离定理之间存在较大差异，这就是著名的Canner难题。厚尾分布以及投资者对风险的厌恶水平对真实的投资组合行为有显著的影响，在考虑下侧风险的情况下，本文关注投资者如何选择投资组合、两基金分离定理在什么情况下能够成立、以及对投资者的投资策略的选择的影响如何。当目标等于无风险利率时，有文献表明两基金分离定理可以在均值——下偏距（M-LPM）中得到证明。然而，除了以无风险利率为目标外，哪些其它的目标也可以使分离定理成立的问题已经出现。本文尝试回答这个问题，并对投资建议和两基金分离定理的差异给出了合理的解释。

英文摘要：

The advice of investment is apparently inconsistent with the separation theorem, which is called Canner puzzle. Fat tail and risk preference of investors have a remarkable effect on the investment behavior. Taking into account the downside risk, the paper wants to know how to choose investment portfolio and how two-fund separation theorem can hold and its effect on investment strategy. As measures of portfolio risk, lower partial moments （LPM） have several advantages over variance, the traditional measure of risk. A separation theorem can be proven in the context of mean-LPM portfolio optimization, when the target is equal to the risk-free interest rate. The paper tries to find out which targets admit separation. The rational explications of the diversities between the popular investment advice and the separation theorem are given.