对钟情于小盘股的投资者们来说，这几年一直非常艰难，这些股票未能像标普500指数以及纳斯达克100指数那样自2022年 末以来走出无比强劲的长期牛市轨迹。但是经过多年的痛苦时期之后，"风险因子"似乎呈现出全面回归，因此这些股票市 场风险最高的股票终于看到了越来越强劲的长期牛市上涨动力。 美股小盘股基准——罗素2000指数上一次创下历史新高是在2021年11月8日，此后一直未能突破这一历史最高点位，目前距 离该水平仅仅相差约3%。除非到周五市场行情发生重大变化，否则这将标志着该美股市场的小盘基准股指标自2000年左右 互联网泡沫破裂以来持续时间最长的一段"未创新高时期"。相比之下，美股大盘基准指数——标普500指数自今年以来已经 创下高达19次历史纪录——即2025年迄今19次创下历史新高点位。 与此同时，随着市场对于美联储降息预期持续升温，市场对于小盘股的投资情绪开始变得更加乐观，主要因为小盘股已连 续数周强势上行，且涨势跑赢标普500指数与纳斯达克。华尔街大行美国银行的一份研究显示，美联储主席鲍威尔在杰克逊 霍尔年会上释放的"最快9月降息"信号，为小盘股行情提供了重要看涨支撑。 美国银行表示，近期多项经济数据 ...

Quantitative Models and Construction Methods Factor Covariance Matrix and Specific Volatility - **Model Name**: Factor Covariance Matrix - **Construction Idea**: The factor covariance matrix is used to capture the dynamic co-variation relationships between factors, providing a systematic framework for understanding market risk transmission mechanisms[3][18] - **Construction Process**: 1. **EM Algorithm**: Used to fill missing values in factor returns. The E-step estimates the conditional expectation of missing values, while the M-step re-estimates parameters iteratively until convergence Formula: $E[f_{mis}|f_{obs}]=\mu_{mis}+\Sigma_{mis,obs}\Sigma_{obs,obs}^{-1}(f_{obs}-\mu_{obs})$[21] Log-likelihood function: $L(\mu,\Sigma)=-\frac{T}{2}\big(D ln(2\pi)+\ln\big(\operatorname*{det}(\Sigma)\big)\big)-\frac{1}{2}\sum_{t=1}^{T}(f_{t}-\mu)^{\prime}\Sigma^{-1}(f_{t}-\mu)$[22] 2. **Half-life Weighted Adjustment**: Assigns exponentially decaying weights to historical data, emphasizing recent data[26] 3. **Newey-West Adjustment**: Corrects for heteroskedasticity and autocorrelation in time series data Formula: $\Sigma_{NW}=\Sigma_{0}+\sum_{i=1}^{L}w_{i}(\Sigma_{i}+\Sigma_{i}^{\prime})$[28] 4. **Eigenfactor Adjustment**: Addresses systematic underestimation of low-risk factor combinations using Monte Carlo simulations[35][38] 5. **Volatility Regime Adjustment (VRA)**: Adjusts factor volatilities to account for cross-sectional biases Formula: $\lambda_{F}=\sqrt{\sum_{t}(B_{t}^{F})^{2}w_{t}}$ $\tilde{\sigma}_{k}=\lambda_{F}\sigma_{k}$[53][54] - **Evaluation**: The factor covariance matrix effectively captures market co-variation relationships and provides reliable inputs for portfolio optimization[18][85] - **Model Name**: Specific Volatility - **Construction Idea**: Specific volatility focuses on predicting idiosyncratic risks at the stock level, addressing missing values and data anomalies[60] - **Construction Process**: 1. **Half-life Weighted Adjustment and Newey-West Adjustment**: Similar to the factor covariance matrix, but with different half-life settings for covariance and autocovariance matrices[61] 2. **Structured Model**: Adjusts for missing and anomalous data based on the relationship between specific volatility and factor exposures Formula: $\ln(\sigma_{n}^{TS})=\sum_{k}x_{nk}b_{k}+\epsilon_{n}$[67] 3. **Bayesian Shrinkage**: Reduces mean-reversion bias by shrinking estimates toward group averages Formula: $\sigma_{n}^{SH}=v_{n}\bar{\sigma}(g_{n})+(1-v_{n})\hat{\sigma}_{n}$[72] 4. **Volatility Regime Adjustment (VRA)**: Similar to factor volatility adjustment, but incorporates market-cap-weighted cross-sectional biases Formula: $\lambda_{S}=\sqrt{\sum_{t}(B_{t}^{S})^{2}w_{t}}$ $\tilde{\sigma}_{n}=\lambda_{S}\sigma_{n}^{SH}$[79][80] - **Evaluation**: Specific volatility adjustments improve the accuracy of idiosyncratic risk predictions, particularly for stocks with high data quality[60][73] --- Model Backtesting Results Factor Covariance Matrix - **Bias Statistic**: - Random portfolios: 1.05-1.06 - CSI 300: 1.15-1.19 - CSI 1000: 1.10-1.16[91] - **Q Statistic**: - Random portfolios: 2.73 - CSI 300: 2.95-2.97 - CSI 1000: 2.72-2.83[91] Specific Volatility - **Bias Statistic**: - Random portfolios: 1.06-1.07 - CSI 300: 1.19 - CSI 1000: 1.10[93] - **Q Statistic**: - Random portfolios: 2.73 - CSI 300: 2.97 - CSI 1000: 2.72[93] --- Quantitative Factors and Construction Methods Composite Fundamental-Price Factor - **Factor Name**: Composite Fundamental-Price Factor - **Construction Idea**: Combines low-frequency and high-frequency price-volume factors with fundamental factors to predict stock returns[128] - **Construction Process**: 1. **Lasso Model**: Uses a penalty coefficient of 0.001 to select features and predict market-neutralized stock returns[128] 2. **Factor Evaluation**: - RankIC: 7.43% - ICIR: 0.72 - Annualized long-short excess return: 61.15%[131] - **Evaluation**: The factor demonstrates strong predictive power but exhibits periodic underperformance during unfavorable market conditions[130] --- Factor Backtesting Results Composite Fundamental-Price Factor - **RankIC**: 7.43% - **ICIR**: 0.72 - **Annualized Long-Short Excess Return**: 61.15% - **Annualized Long-Only Excess Return**: 18.74%[131] 800 Index Enhancement Strategy - **Annualized Returns**: - Portfolio 1 (only stock deviation control): 18.28% - Portfolio 2 (stock/industry/style deviation control): 16.26% - Portfolio 3 (stock deviation + tracking error control): 17.81%[135][144] - **Tracking Error**: - Portfolio 1: 9.14% - Portfolio 2: 4.73% - Portfolio 3: 4.99%[135] --- Evaluation and Insights - The factor covariance matrix and specific volatility models provide robust risk predictions, enabling effective portfolio optimization and risk decomposition[85][152] - The composite fundamental-price factor demonstrates strong predictive ability but requires careful management of style and industry constraints to maintain alpha generation[130][136]

智通财经3月27日讯（记者 夏淑媛） 险资获准投资公募REITs三年有余，积累了哪些有益的经验，又面 临哪些挑战备受市场关注。 截至3月26日，市场存量公募REITs已达64只，发行规模合计1697.36亿元。在所有非原始权益人战配投 资者中，保险机构参与规模占比最高，约为30%左右，参与过战配的保险机构共47家，按认购规模排名 靠前的分别是中国人寿、泰康资产、中国平安。网下投资者中，保险机构参与也相当活跃，占比达 65%。 尽管REITs走势强劲，险资布局踊跃，但投资公募REITs风险因子较高，保险资金整体参与度仍然有较 大的提升空间。 据平安资管相关人士介绍，公募REITs资本计量因子为0.5，不仅远高于其他类型的公募基金，也远高于 以物权或股权形式投资的投资性房地产。对于保险公司而言，风险因子相对较高，参与公募REITs意味 着更高的资本占用，会提高保险公司对于偿付能力管理的压力。其监管部门给予偿二代项下风险因子优 惠政策，缓解保险资金投资公募REITs产品对偿付能力的消耗。 2020年4月30日，国内公募REITs试点起航。2021年6月，首批9只产品面市，境内公募REITs市场发展拉 开帷幕。截至3 ...

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]