Income and risk coexist, yet investors are often so focused on chasing high returns that they overlook the potential risks that can lead to high losses. Therefore, risk forecasting and risk control is the cornerstone of investment. To address the challenge, we construct a multi-factor risk model on the basis of the classical multi-factor modeling framework. For the common factors, inspired by Barra Model's factor classification. we adjust the outliers and missing values of factor exposure data, normalize and finally orthogonalize them, before computing factor returns and making further analysis. Factor return covariance matrix and idiosyncratic return variance matrix are essential tools to express stock returns in the multi-factor risk model. Firstly, we calculate the factor return covariance matrix with EWMA. To tackle the time-series autocorrelation of factor returns, we apply Newey-West adjustment. Then we estimate the idiosyncratic return variance matrix in a similar way and make Newey-West adjustment again to solve the time-series autocorrelation problem. Since the return of a single share is sensitive to missing values and outliers, we introduce structural adjustment to improve the matrix.Eventually, we obtain the return covariance matrix among stocks and compute the risk of investment portfolio based on it. Furthermore, we search for optimal portfolio with respect to minimizing risk or maximizing risk-adjusted return with our model. They provide good Sharpe ratio and information ratio for considering both absolute risk and active risk. Hence, the multi-factor risk model is efficient.

翻译：收益与风险如影随形，然而投资者往往过度专注于追逐高收益，却忽视了可能导致重大损失的潜在风险。因此，风险预测与风险控制是投资的基石。为应对这一挑战，我们在经典多因子建模框架的基础上构建了多因子风险模型。对于共同因子，受Barra模型因子分类的启发，我们对因子暴露数据的异常值和缺失值进行调整，进行标准化处理并最终正交化，随后计算因子收益并开展进一步分析。因子收益协方差矩阵和特质收益方差矩阵是多因子风险模型中表达股票收益的关键工具。首先，我们采用指数加权移动平均法计算因子收益协方差矩阵。为解决因子收益的时间序列自相关问题，我们应用Newey-West调整。随后，我们以类似方式估计特质收益方差矩阵，并再次进行Newey-West调整以消除时间序列自相关性问题。由于单只股票收益对缺失值和异常值较为敏感，我们引入结构化调整来改进该矩阵。最终，我们得到股票间的收益协方差矩阵，并据此计算投资组合的风险。此外，我们利用该模型寻找最小化风险或最大化风险调整后收益的最优投资组合。该模型在兼顾绝对风险与主动风险时展现出良好的夏普比率和信息比率。因此，该多因子风险模型是有效的。