Quantitative Models and Factor Construction Factor Selection and Data Processing Pipeline - The MSCI Barra CNE5 model includes 10 primary factors and 21 secondary factors, covering classic academic factors such as beta, size, and book-to-price ratio, as well as fundamental and technical factors like value, growth, momentum, and residual volatility[22][23][24] - Secondary factors are standardized and weighted to synthesize primary factors, with weights optimized for explanatory power. However, later versions of MSCI Barra shifted to equal weighting for simplicity[23] - Data processing pipeline includes six steps: defining the base universe, outlier handling, missing value imputation, standardization, primary factor synthesis, and secondary outlier/standardization adjustments[31][32][35] Pure Factor Return Estimation - Pure factor returns are estimated using constrained weighted least squares (WLS). Constraints are introduced to address multicollinearity caused by the inclusion of intercepts (country factors)[44][45][49] - WLS weights are inversely proportional to the square root of market capitalization, ensuring smaller residual variance for larger stocks[45] - The solution for pure factor returns is derived using matrix transformations and Cholesky decomposition, ensuring variance homogeneity[46][57][59] Evaluation of Risk Factors and Factor Systems - MSCI Barra's six-dimensional evaluation criteria include statistical significance, stability, intuition, completeness, simplicity, and low multicollinearity[75][76][77] - Quantitative metrics such as average absolute t-values, variance inflation factors (VIF), and pure factor performance are used to assess factor quality. Factors like beta, liquidity, and size exhibit strong statistical significance but may overlap in information[83][84][85] Practical Applications of Risk Models - Risk models are applied for performance attribution in external products (e.g., public equity funds) and internal portfolios (e.g., brokerage "gold stock" portfolios). Attribution results include style/sector exposures and return/risk contributions[148][151][181] - For public equity funds, factor and idiosyncratic returns are decomposed to classify funds into "style advantage" or "stock-picking advantage" categories[152][153][155] - For brokerage gold stock portfolios, attribution reveals the superior performance of newly added stocks due to idiosyncratic returns, while recent underperformance is linked to systematic exposure to small-cap factors[157][169][170] --- Factor Backtesting Results Daily Frequency Results - **Beta**: Annual return 8.20%, annual volatility 4.87%, IR 1.69[86][111] - **Size**: Annual return -6.82%, annual volatility 4.57%, IR -1.49[86][105] - **Liquidity**: Annual return -9.46%, annual volatility 3.10%, IR -3.05[86][123] - **Value**: Annual return 4.32%, annual volatility 2.40%, IR 1.80[86][134] Monthly Frequency Results - **Beta**: Annual return 2.64%, annual volatility 3.95%, IR 0.15[95][111] - **Size**: Annual return -7.02%, annual volatility 5.99%, IR -0.26[95][105] - **Liquidity**: Annual return -5.74%, annual volatility 2.77%, IR -0.45[95][123] - **Value**: Annual return 2.94%, annual volatility 2.87%, IR 0.22[95][134] Gold Stock Portfolio Attribution - **All Gold Stocks**: Total return 61.86%, factor return -54.02%, idiosyncratic return 83.46%[171] - **Newly Added Gold Stocks**: Total return 83.50%, factor return -59.75%, idiosyncratic return 108.20%[174] - **Repeated Gold Stocks**: Total return 6.39%, factor return -44.66%, idiosyncratic return 19.60%[162] Factor Contribution Analysis - **Beta**: Positive contribution across all years, cumulative return 35.75% for all gold stocks, 44.47% for newly added gold stocks[175][176] - **Liquidity**: Negative contribution, cumulative return -48.67% for all gold stocks, -57.24% for newly added gold stocks[175][176] - **Size**: Mixed contribution, cumulative return 72.78% for all gold stocks, 97.27% for newly added gold stocks[175][176]