A Sigma-Mu approach is proposed for mutual funds portfolio selection. The mean and variance of the overall performance of each asset are considered, according to an additive aggregation model, subject to weights’ preferences provided by the decision maker. These preferences concern two independent sets of weights, i.e., those pertaining to the investment indicators and those pertaining to the time periods associated with the estimation of the indicators. For the first time in the Sigma-Mu framework, a weighting matrix is exploited, assisting on the development of a method to appraise the sources of variance, due to the weighting scheme of either the indicators or the periods. The Mu's, Sigma's and covariances estimated according to the Sigma-Mu approach, enter as inputs to mixed-integer quadratic programming (MIQP) mean-variance portfolio optimization models, in order to implement an empirical testing procedure, for a period of 8 years. The underlying MIQP models are equipped to consider non-convex investment policy constraints, such as the number of securities to be included in the portfolio, specific binary buy-in thresholds, the desired exposure of the portfolio to each investment advisor etc. The dataset that has been chosen for the empirical testing includes European mutual funds, that offer a broad exposure to the whole span of investment strategies and styles. The results document that the suggested approach may effectively be utilized in mutual funds investment management, since the portfolios constructed by the suggested methodology are associated with superior absolute and risk-adjusted performance against benchmarks.

中文翻译：

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一种新颖的 sigma-Mu 多标准决策辅助方法，用于共同基金投资组合的选择


提出了 Sigma-Mu 方法用于共同基金投资组合的选择。根据加法聚合模型，根据决策者提供的权重偏好，考虑每项资产整体性能的均值和方差。这些偏好涉及两组独立的权重，即与投资指标相关的权重和与指标估计相关的时间段的权重。在 Sigma-Mu 框架中，首次利用了加权矩阵，由于指标或时期的加权方案，协助开发一种评估方差来源的方法。根据 Sigma-Mu 方法估计的 Mu、Sigma 和协方差作为混合整数二次规划 （MIQP） 均值-方差投资组合优化模型的输入，以实施实证检验程序，为期 8 年。基础 MIQP 模型能够考虑非凸投资政策限制，例如投资组合中要包含的证券数量、特定的二元买入门槛、投资组合对每个投资顾问的期望敞口等。选择用于实证检验的数据集包括欧洲共同基金，这些基金提供了对整个投资策略和风格的广泛敞口。结果证明，建议的方法可以有效地用于共同基金投资管理，因为根据建议的方法构建的投资组合与相对于基准的卓越绝对和风险调整后的表现相关。