20210612-华西证券-华西证券分析师目标价选股策略：Black-Litterman模型研究系列之三

Quantitative Models and Construction Methods 1. Model Name: Black-Litterman (BL) Model - Model Construction Idea: The BL model integrates subjective views (e.g., analyst target prices) with market equilibrium returns to optimize portfolio weights. It naturally handles stocks without analyst opinions by redistributing weights among stocks with available views [1][7][23]. - Model Construction Process: 1. Expected Return Calculation: The expected return vector is calculated as: $\mu_{p}=[(\tau\Sigma)^{-1}+P^{T}\Omega^{-1}P]^{-1}[(\tau\Sigma)^{-1}\pi+P^{T}\Omega^{-1}Q]$ - $\tau$: Weight of subjective views - $\Sigma$: Covariance matrix of asset returns - $\pi$: Equilibrium return vector - $P$: View matrix indicating which assets are involved in each view - $Q$: View return vector - $\Omega$: Confidence matrix for views [7][8]. 2. Covariance Matrix Adjustment: The adjusted covariance matrix is: $\Sigma_{p}^{*}=\Sigma+[(\tau\Sigma)^{-1}+P^{T}\Omega^{-1}P]^{-1}$ [7]. 3. Portfolio Weight Calculation: Without constraints: $w=(\delta\Sigma_{p}^{*})^{-1}\mu_{p}$ - $\delta$: Risk aversion coefficient [8]. With constraints, mean-variance optimization is applied [8]. 4. Subjective Views: - Views are derived from analyst target prices, forming long-short portfolios within industries. - Example: For Industry 1, buy stock 2 and sell stock 8, with an expected excess return of 5% [12][17]. 5. Confidence Matrix: - Confidence is based on the variance of analyst predictions. - Formula: $\Omega=P Z P^{T}$ - $Z$: Diagonal matrix of standardized variances of analyst predictions [18][19]. - Model Evaluation: The BL model effectively integrates subjective views and market data, providing optimized portfolio weights superior to simpler weighting methods [25][35]. --- Model Backtesting Results 1. BL Model Performance in CSI 300 Index - Cumulative Returns (2010-2021/5/31): - Full Portfolio: +186.52% - Positive View Portfolio: +215.15% - CSI 300 Index: +49.11% - Excess Returns: +137.41% (Full), +166.05% (Positive) [26][31]. - Annualized Returns: - Full Portfolio: Outperformed in most years except 2014, 2016-2017 [30][31]. - Portfolio Composition: - Full Portfolio: Average of 265 stocks - Positive View Portfolio: Average of 138 stocks [32][34]. - Weighting Comparison: BL weights outperformed market-cap and equal-weighted portfolios [35][38]. 2. BL Model Performance in CSI 500 Index - Cumulative Returns (2010-2021/5/31): - Full Portfolio: +354.89% - Positive View Portfolio: +469.14% - CSI 500 Index: +50.02% - Excess Returns: +304.87% (Full), +419.12% (Positive) [40][45]. - Annualized Returns: - Full Portfolio: Outperformed in most years except 2014 [45]. - Portfolio Composition: - Full Portfolio: Average of 475 stocks - Positive View Portfolio: Average of 138 stocks [46]. 3. Comparison with Direct Sorting Methods - Cumulative Returns (2010-2021/5/31): - BL Positive View Portfolio: +215.15% - Direct Sorting (Mixed, Market-Cap Weighted): +122.48% - Direct Sorting (Mixed, Equal Weighted): +120.51% - Direct Sorting (Industry, Market-Cap Weighted): +145.30% - Direct Sorting (Industry, Equal Weighted): +154.87% [47][48]. 4. Sensitivity to $\tau$ - Impact of $\tau$: - Higher $\tau$ values increase the weight of subjective views in portfolio construction. - In CSI 300, higher $\tau$ values led to slightly higher returns, with stable parameter sensitivity [54][61]. - In CSI 500, $\tau$ changes caused greater return volatility [58][59].