This paper studies comparative static effects in a portfolio selection problem when the investor has mean-variance preferences. Since the security market is complex, there exists the situation where security returns are given by experts’ estimates when they cannot be reflected by historical data. This paper discusses the problem in such a situation. Based on uncertainty theory, the paper first establishes an uncertain mean-variance utility model, in which security returns and background asset returns are uncertain variables and subject to normal uncertainty distributions. Then, the effects of changes in mean and standard deviation of uncertain background asset on capital allocation are discussed. Furthermore, the influence of initial proportion in background asset on portfolio investment decisions is analyzed when investors have quadratic mean-variance utility function. Finally, the economic analysis illustration of investment strategy is presented.

当投资者具有均值方差偏好时，本文研究了投资组合选择问题中的比较静态效应。由于证券市场复杂，因此存在无法通过历史数据反映出专家估计的证券收益的情况。本文讨论了这种情况下的问题。基于不确定性理论，本文首先建立了不确定性均值-方差效用模型，其中证券收益和背景资产收益是不确定性变量，服从正态不确定性分布。然后，讨论了不确定背景资产的均值和标准差的变化对资本配置的影响。此外，当投资者具有二次均方差效用函数时，分析了背景资产中初始比例对证券投资决策的影响。最后，给出了投资策略的经济分析图。